–     heading adopted from Francesco Berto’s Gödel book.

”We make to ourselves .. pictures of the reality”. ( (2.06)  →  2.1 , 2.12 , 2.201 , 4.06  →  (4.1 , 4.25 , 5.01) )

---

Wittgenstein’s picture theory of language shortly either PToL or picture theory. If not using only (4.01) , i.e. applying ”numbers assigned to the individual propositions” (1*).

When quotes from the preface of Tractatus , there is nothing but Preface (in brackets). Otherwise re-ferences simply with Wittgenstein’s notation (1* , 1.1 , 1.11 , 2 .. 7). Quotes I take using both Ogden and Pears/McGuinness translations. Sometimes also in German, to compare. Underlines and boldings are mine. As also spaces, if not already in Logisch-philosophische Abhandlung. Italics are Wittgenstein’s.

This paper is Ludwig Wittgenstein only throughout Tractatus Logico-Philosophicus. So be it enough to say, that he started his career as a philosopher and logician in England in 1911. At the University of Cam-bridge.  –  Alongside Bertnard Russell.  –  With turbulence around the philosophy of mathematics and logic!

And, of course :  Ludwig Wittgenstein

–   –   –   –   –

SO  FAR  A  DRAFT … INDEED !

An  interpretation  of  Wittgenstein’s  picture  theory  of  language.

Contents ..

Foreword

1 .     Wittgenstein’s ”fundamental thought” (4.0312)

2 .     ”The aim of the book” (Preface / (4.112 , 4.114) )

3 .     A consequence of Russell’s paradox

4 .     Language / ”Universal – language”

5 .     The correspondence theory of truth

6 .     The logic of the correspondence theory

7 .     Picture theory is an implication of independence

8 .     Determination of the concept ”reality”

9 .     ”The existence of an internal relation” (4.125)

10 .     The consistency of picture theory / (4.0641)

11 .     ”The logical forms are anumerical” (4.0312 , 4.128 , 6.4321)

12 .     ”Das Mystische” / ”The mystical” (6.44 , 6.45 , 6.522)

Appendix 1 :  ”The sense of a proposition” (4.2 , 4.46).

Appendix 2 :  On the concept of ”the substance of the world” (2.021).

Appendix 3 :  The enumeration of paragraps used.

Epilogue

References

Foreword

Above all, this paper deals with two things.

First : To construct throughout the correspondence theory of truth propositions that can be consistent and provably ”true or false”.

Second : Is it possible, in logic to express the totality of these well-formed, consistent and provably ”true or false” , propositions?

Few words for the struckture of this presentation. I begin with facts, which seems to me evident, undeniable. These things are not even interpretation, but straightforward, literal and comparative reading of Tractatus. These evident facts are good basis for interpretation. First two parts of the paper present the evident things, facts. If the first part can be seen as a result of Wittgenstein’s aim, it is nice starting point / what goes around comes around. To rest these undeniable facts, it is then anything but to go on. Step by step, maybe a bit more interpretation, with my literal and comparative reading of Tractatus, until the last part ”Das Mystische” / ”The mystical” (6.44 , 6.45 , 6.522) , where I make still an outline.

1 .     Wittgenstein’s ”fundamental thought” (4.0312)

”The possibility of propositions is based upon the principle of the representation of objects by signs. My fundamental thought is that the ”logical constants” do not represent. That the logic of facts cannot be represented”. (4.0312)

”Die Möglichkeit des Satzes beruht auf dem Prinzip der Vertretung von Gegenständen durch Zeichen. Mein Grundgedanke ist, dass die ”logischen Konstanten” nicht vertreten. Dass die  L o g i c  der Tatsachen nicht vertreten lässt”. (4.0312)

That  –  ”.. the logic of facts cannot be represented”  –  is the final step and symmary of Wittgenstein’s effort to fullfil ”the aim of the book” (Preface).

Paragraph (4.0312)  is a good starting point to (get) grasp of what is all about of picture theory. It’s little numerical weight notwithstanding. Not to talk about proposition (4.0312) ! not so little weight for the ”gödelian” insight. If nothing else in the beginning of my journey with Tractatus to comprehend, then ! hold on .. proposition ! (4.0312) .. may anticipate ! Kurt Gödel’s incompleteness theorems ?

As soon as you understand the meaning of ”facts” / (3.12 , 314 , 4.06)  you comprehend the ”things” , who’s ”.. the logic .. cannot be represented” (4.0312).

”The sign through which we express the thought I call the propositional sign. And the proposition is the propositional sign in its projektive relation to the world”. (3.12 , 3.14 , 406 , underline with bolding continues (3.14) )

”The propositional sign consists in the fact that its elements, the words, are compined in it in a definite way. The propositonal sign  i s  a fact ”. (3.12 , 3.14 , 4.06)

Thus  –  ”.. the  proposition .. in  its  projektive  relation  to  the  world .. i s  a  fact” (3.12 + 3.14).

”Propositions can be true or false  o n l y  by being pictures of the reality”. (3.12 , 3.14 , 4.06)

Combining paragraphs (3.12 , 3.14 , 4.06) , by reading that ”projektive relation to the world” is synonym to ”picture of reality” , we get the two-part meaning of the ”facts” , second part being a consequence of the first part :

1.     ”Propositions .. by being pictures of the reality” are ”facts”.

2.     I f f  ”.. the proposition .. can be true or false .. the proposition .. is a fact”.

( ”Iff” means the same as ”if and only if”. )

The second part of the meaning of the ”facts” is what Wittgenstein in the first place have in mind, when he writes in preface of ”the aim of the book”. Due to the ! Russell’s paradox the possibility of any consistent and provably ”true or false” proposition is at stake. Thus the main question of Tractatus / PToL is  that ”.. the proposition .. can be true or false ..” (3.12 + 4.06)  –  consistently and provably.

Now, by 1. and 2. , it possible to substitute expression ”fact” in proposition (4.0312)  to comprehend the ”things” , who’s ”.. the logic .. cannot be represented” (4.0312). You can substitute ”fact” either (using) ”pictures of reality” or (using) ”propositions can be true or false” to get to the point :

1.     ”The logic of ”pictures of reality” cannot be represented”. (3.12 , 3.14 , 4.0312 , 4.06)

2.     ”The logic of ”propositions can be true or false” cannot be represented”. (3.12 , 3.14 , 4.0312 , 4.06)

However, at this point of Tractatus (1 , 1.1 .. 1.13 .. 2 .. 4.0312 .. 7)  using ”pictures of reality” fits, because ”propositions” as ”pictures of reality” are here already ”propositions” , that ”can be true or false” , when ”a proposition” to be (consistent and provably) ”true or false” rest on the correspondence theory of truth.

PToL is ! y e t  an expression of the correspondence theory of truth (2.21 , 2.221 , 2.222 , 2.223 , 4.031).

Only by applying some theory of truth in a language ”within” (4.114)  Wittgenstein can realise what ”the book will” / ”the object of philosophy” (Preface , (4.112 , 4.114) ) , i. e. to show all the propositions, that can be consistent and provably ”true or false” (1.13 , 2.06 , 2.063 , 2.18 , 3.12 , 3.14 , 4.001 , 4.06 , 4.1 , 4.211 , 4.25 , 5 , 5.01 , 5.47).

Abovesaid, it is quite evident that ! ”.. t h e  l o g i c .. cannot be represented” (4.0312)  i s  the logic of the well-formed propositions by correspondence theory of truth.

ABOVESAID , it is quite evident : ” The facts in logical space are the world” (1.13)  a r e ”in logical space” of correspondence theory of truth.

The fact, that ”the facts” are ”in logical space” of correspondence theory of truth (1.13 , 2.221 , 2.222 , 3.12 + 3.14 , 4.031 , 4.06) , is the reason why Wittgenstein’s aim ends up ! ”Das Mystische” / ”The mystical” (6.44 , 6.45 , 6.522) : The logic of correspondence theory* of truth, ”the facts” being based on it* , ”cannot be represented” (4.0312) , and ! nevertheless  it* is correct, j u s t  because of ! (4.0312). Wittgenstein’s ”fundamental thought” (4.0312)  shows, implies to wit that there are ”truths” , which are ”.. inexpressible .. cannot .. put into words” (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.552)  in any single logic(al formalism). Thereby, indeed ! ”.. the world .. is .. exists” (6.44) , the assumption of (ontological) realism holds true. The totality of ”the facts” / ”the world” is inexhaustible (1.1 , 1.13 , 2 , 2.06 , 2.063 , 2.221 , 2.222 , 3.12 + 3.14 , 4.001 , 4.031 , 4.06 , 4.128).

Therefore Wittgenstein’s effort fails (4.0312) , and the last proposition (7)  of Tractatus is what it is.

But before ending up, it is time take so far only the next step. The second part of the evident facts.

2 .     ”The aim of the book” (Preface / (4.112 , 4.114) )

”.. The book deals with the problems of philosophy, and shows, I believe, that the reason why these problems are posed is that the logic of our language is misunderstood. The whole sense of the book might be summed up in the following words : what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.

Thus the aim of the book is to draw a limit to thought, or rather  –  not to thought, but to the expression of thoughts : for in order to be able to draw a limit to thouhgt, we should have to find both sides of the limit thinkable ( i. e. we should have to be able to think what cannot be thought). It will theorefore only be in language that the limit can be drawn, and what lies on the other side of the limit will simply be nonsense. ..”. (Preface)

So, Wittgenstein’s aim  –  ”.. is to draw a limit .. to the expression of thoughts .. in language ..” / ”from within”. (Preface / (4.112 , 4.114) )

”The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity. A philosophical work consists essentially of eludications. The result of philosophy is not a number of ” philosophical propositions” , but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it where, opaque and blurred”. (4.112 , 4.114 , underline with bolding continues (4.114) )

”It should limit the thinkable and thereby the unthinkable. It should limit the unthinkable from within through the thinkable”. (4.112 , 4.114)

”The object of philosophy is .. delimit .. the thoughts ..” (4.112).

”.. Philosophy should .. limit .. from within .. the thinkable” (4.112 + 4.114).

What is this (Preface / (4.112 , 4.114) )  all about ?

Keyword is ”thought” (3 , 3.12 , 4 , 4.06).  –  What is ”a thought” ?  –  What are ”the thoughts” ?  –  ”The thinkable” ?

”The logical picture of the facts is the thought”. (3 , 3.12 , 4 , 4.06 , underline continues (3.12) )

”The sign through which we express the thought I call the propositional sign. And the proposition is the propositional sign in its projektive relation to the world”. (3 , 3.12 , 4 , 4.06)

Thus  –  ”.. the thought .. is the propositional sign in its projektive ralation to the world” (3 + 3.12).

”A thought is a proposition with a sense”. (3 , 3.12 , 4 , 4.06)

It is reasonable to assume that ”a propositon with a sense” indicates ”in its projektive relation to the world”.

”Propositions can be true or false only by being pictures of the reality”. (3 , 3.12 , 4 , 4.06)

Evident answer to the question of ”the thoughts” , at the same pace and hand in hand with the two-part meaning of ”facts” / ( (3 , 3.12 , 4)  →  4.06) , second part being a consequence of the first part, is that ”the thoughts” are :

1.     ”Propositions” as ”pictures of the reality”.     2.     ”Propositions” that ”can be true or false”.

”The thinkable” (4.114)  is therefore every ”propositional sign” , which as ”a picture of reality” implicates it ”can be true or false” (3.12 , 4.01 , 4.06). Thus ”.. limit .. the thinkable” (4.112 , 4.114)  means to limit ”the propositions” that as ”pictures of reality can be true or false” (4.06).

What about the meaning of ”draw a limit” ?  –  For example draw a limit of ”apples” ?  One obvious meaning is to show or express nothing but all ”apples” , i. e. to show only the totality of apples among the (all) fruits.

Mutatis mutandis, ”apples” to well-formed propositions, ”the aim of the book” (Preface)  is nothing but to show or express all ”propositions” , which as ”pictures of reality” can be ”true or false”.

(Maybe better example to the meaning of ”draw a limit” would be ”good apples” vs. ”rotten apples”. )

And of course, logician Wittgenstein will express  –

”The totality of propositions is a language”. (Preface / ( (3 , 3.12 , 4)  ←  4.001  ←  (4.06 , 4.112 , 4.114) ) )

To put Wittgenstein’ s aim in one sentence is to say, that he asks :

”Is it possible to express in logic all the well-formed propositions which can be consistently and provably ”true or false” ?

But why ”the object of philosophy” (4.112 , 4.114)  is determined as it is ?

3 .     A consequence of Russell’s paradox

Gottlob Frege’s effort to define the basic consepts of mathematics and logic, reduce mathematics to logic, failed. Bertnard Russell showed, that there was a mistake, an aberration in Frege’s arguments. This, Russell’s paradox in 1901, ten years before Ludwig Wittgenstein’s arrival to Cambridge.

There is lot of (good) knowlwdge in internet of the meaning of Russell’s paradox. Here it’s role is as one of the Wittgenstein’s ”leitmotifs” to Tractatus and therefore it must be with, take part, but no more. To resolve Russell’s paradox (3.333)  is on the backround of Wittgenstein’s aim.

Wittgenstein seems to interpret Russell’s paradox quite simply. He gets straightaway the point : There is anymore, not yet ! a single proposition that can be said to be consistent and provable ”true or false”. That’s why (1.1 , 2.06 , 2.063 , 2.1 , 4.06).

”True or false” may easily be the ”drei Worten” in Tractatus – motto.

Thus by ”drawing a limit to the expression of thoughts in language within” (Preface / (3 , 3.12 , 4 , 4.001 , 4.06 , 4.112 , 4.114 , 4.211 , 4.25 , 5 , 5.01) )  Russell’s paradox can be overcome. If  ”the totality of propositions is a language” (4.001 , 4.06) , in which every proposition is provable and consistent ”true or false” , can be formed, then  –  ”.. Russell’s paradox vanishes” (3.333)  –  and if can not be formed, as it will be (4.0312 , 4.128 , 6.4321) , even ! and only then both the consictency of logic and that logic is ”truth” – preserving stand, troughout the logic of correspondence theory of truth. Also, ! only when

”The logical forms are anumerical”. (2.18 , 3.12 + 3.14 , 4.0312 , 4.06 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.522)

the implicit assumption of (ontological) realism of correspondence theory holds true, i. e. ”the truths” / ”true” propositions, which are ”.. inexpressible .. cannot .. put into words” (4.1212 , 6.522)  represent the outside of any language existing world.

”The mystical” (6.44 , 6.45 , 6.522) , especially to a logician, is simply that the well-formed language of correspondence theory implies ! that in that (well-formed) language ! exists ”true”  propositions, which however ”.. cannot be said” (4.1212). Hence the proof of the outside of any language, any human mind, existing world is inside the well-formed language of correspondence theory ”.. as a limited whole ..” (6.44 , 6.45 , 6.522). And to try open this ”limited whole” entails to step on ! outside of ! the (whole) well-formed language of correspondence theory ; so there is no other choice, to a logician, than ”.. one must be silent” (7).  –  Or if not ! realise to say that a well-formed language of correspondence theory is ! incomplete, will be never complete(d) ; but ever inexhaustible.

Actually, by taking into account the value of the concept of ”truth” in logic , Wittgensteins effort is to rebuild the whole logic from the very beginning, or (at least) show its right place. The concept of ”truth” is accompanied by so called tree law of thought, i. e. the law of excluded middle, the law of noncontradiction and the law of identity (2.0233 , 2.02331 , 2.17 , 2.18 , 2.21 , 3.203 , 4.06 , 4.211 , 5.53 , 5.5303).

So, what is needed to accomplish the abovesaid task? What tools or prequisites are needed to show ”the totality of propositions .. being pictures of reality” (4.001 , 4.06) ?  When starting point is that there exists not yet ! a single proposition that can be said to be consistent and provable ”true or false”.

4 .     Language / *”Universal – language”

*From now on  –  ”u – language.”

”If all objects are given, then at the same time all possible state of affairs are also given”. (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031)

”Man possesses ability to construct languages capable of expressing every sense ..”. (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031)

When Wittgenstein says ”.. It will .. only be in language that the limit can be drawn ..” (Preface)  it is to say something self-evident, or even tvial. ”The expression of thoughts” are always said, pronounced in some language. Wittgenstein’s task ”to draw a limit to the expression of thoughts” (Preface)  have to be done in the same space, together with ”the expression of thoughts”. Especially when ”the thoughts” (3 , 3.12 , 4 , 4.06)  to be expressed must first to be done in some language  –

”We make ourselves pictures of facts”. (20124 , 2.021 , 2.0211 , 2.0212 , 2.1 , 3 , 3.12 , 3.14 , 3.203 , 3.3 , 4 , 4.002 , 4.06)

”The logical picture of the facts is the thought”. (20124 , 2.021 , 2.0211 , 2.0212 , 2.1 , 3 , 3.12 , 3.14 , 3.203 , 3.3 , 4 , 4.002 , 4.06)

Although Wittgenstein do not tell straight out that to ”.. make ourselves pictures of facts” / ”thoughts” (2.1 , 3)  we need first a language as a ! substance of ”the making” , it is no doubt. ”The logical picture” is then, second due to the logic of the (chosen) theory of truth, i. e. correspondence theory, which is another and the main substance of ”the making”.

The language involved must be ”u – language”. If not, then there can be no steps on the ”ladders” (6.54)  of Wittgensteins task. If language involved is not assumed to be ”u – language” , i. e. a language where everything can be in principle said, is possible to express, then it is from the very beginning impossible to fullfil the task :

Construct all the propositions, which can be consistently and provably ”true or false” , and then express these well-formed propositions.

Before Wittgenstein can say his last paragraph (7) , he must express ! the ”whereof .. one must be silent” (7). Beforehand there can be no limit ; nothing ”whereof” to be silent, no limit what can be said in a language. Not even in the context of Wittgenstein’s task when the language as ”u – language” is talking about itself, i. e. talking about the well-formed relation of the language itself to reality as the logic of the (chosen) theory of truth imply. It is to say ! everything of that relation, in PToL ; also ”.. the logical form .. whereof .. one must be silent” (2.18 , 4.12 , 4.121 , 7).

While ”the making” (2.21) of the well-formed propositions is possible to say, to ! enumerate them is not. The totality of well-formed propositions is inexpressible (4.0312 , 4.1212 , 4.128 , 6.4321 , 6.522) ; precisely as the essence of correspondence theory as a theory of (ontological) realism necessitates. If the totality of well-formed propositions of correspondence theory, i. e. ”.. pictures of the reality” (4.06) , could be said in ”u – language” by means of logic, then the fact of (ontological) realism that the reality exists independent of (human) mind stands not. Reality instantiates, manifests itself in ”u – language” throughout the totality of ”.. pictures of the reality” (1.1 , 1.13 , 2.06 , 2.063 , 2.1 , 2.141 , 3.12 , 3.14 , 4.06). Thus, in order to the essence of correspondence theory to hold true it have to be so, to be ! proved so, that the totality of well-formed propositions ”.. cannot be said” (4.1212).

All the same, Wittgenstein’s doctrine of ”.. the substance of the world” (2.021)  is in my book ! simply .. ”u – language” (1.1 , 1.13 , 3.12 + 3.14 , 4.06  ←  (20124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031) ). ”U – language” is the sphere where to ”.. make ourselves pictures of facts” (2.1 , 3.12 + 3.14 , 4.06) , by applying (3.5)  in it correspondence theory, which is the basis, the ! true substance of picture theory.

”The facts in logical space are the world”. (1.1 , 1.13  →  (2.21 , 2.221 , 2.222)  →  (3.12 + 3.14 , 4.031 , 4.06) )

Hence, one could add in between ”.. facts in logical space .. / of the correspondence theory / .. are the world” (1.1 , 1.13  →  (2.21 , 2.221 , 2.222)  →  (3.12 + 3.14 , 4.031 , 4.06) ).

Wittgenstein’s ”substance” – doctrine is precisely this ”applying” , a combination of ”u – language” and correspondence theory of truth. If not take into account that Wittgenstein’s ”substance” – doctrine is already a combination of ”u – language” and correspondence theory, then for example paragraph 2.014 may be difficult to understand.

”Objects contain the possibility of all states of affairs”. (1.1 , 1.13 , 2.014 , 2.06 , 2.063 , 2.11 , 2.203 , 3.02 , 3.332 , 3.333 , 4.01).

At least the logic of correspondence theory explains paragraph 2.014 well (as we shall see). The logic of correspondence theory explains why ”objects contain ..” (1.1 , 1.13 , 2.014 , 2.06 , 2.063 , 2.11 , 2.203 , 3.02 , 3.332 , 3.333 , 4.01).

Even if Wittgenstein’s ”substance” – doctrine is a combination of ”u – language” and correspondence theory in order to show well-formed propositions, first there must be a language as ”u – language” ; to apply correspondence theory (in it).

”Objects form the substance of the world. Therefore they cannot be compound”. (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031)

In my book, when paragraphs (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031)  are put, read together, the result is just a ! pure ”u – language”. What is a pure ”u – language” ?  Simply, it is a ”language” , which is not yet combined with any theory of truth. Hence, logically  –

”Substance is what exists independently of what is the case”. ( (1 , 1.1 , 1.11 , 1.12 , 2)  ←  2.024  →  (2.06 , 2.063) )

That, ”independently of facts” ( (1 , 1.1 , 1.11 , 1.12 , 2)  ←  2.024  →  (2.06 , 2.063) ) , is to say that ”the substance” of Wittgenstein’s aim is a ”u – language” where not yet (expressed) any ”true or false” propositions. To say that, to determinate a pure ”u – language” , Wittgenstein ! applies correspondence theory, ! in ”u – language”. To answer, in respect to ”what” pure? By the same token Wittgenstein, the first paragraps of Tractatus, conceives the concepts of ”world” and ”reality”. Determination of these concepts is necessary to analysis of correspondence theory. Otherwise there can be no making of ”true or false” propositions as ”pictures of the reality” (2.1 , 4.06).

And, as we shall see, due to the logic of correspondence theory (4.061) ”u – language” is also first a pure language, where not yet ! a single proposition can be said to be consistent and provable ”true or false”. Just as to overcome Russell’s paradox presupposes. The endpoint of Russell’s paradox must be the starting point of the analysis of correspondence theory. Inherently, throughout the logic of that truth-theory. So ”.. the substance of the world .. what exists independently of what is the case” ( (1 , 1.1 , 1.11 , 1.12 , 2)  ←  2.021 , 2.024  →  (2.06 , 2.063) )  is already a combination of ”u – language” and correspondence theory, in fact ! really so that correspondence theory ! also determinates ”the world”. By applying correspondence theory twice to ”u – language”. Without (as we shall see) this self-reference to be a circular argument, exactly due to the the logic of the correspondence theory.

”If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true”. (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031 , underline continues (2.012) )

It / (2.0211)  would be circular argument because of ”sense” is a prequisite a proposition can be ”true or false”. Hence, the ”sense” of a proposition is independent of its (possible) ”truth or falsehood” (1.1 , 1.12 , 1.13 , 2.024 , 3.12 + 3.14 , 4.06 , 4.061) ; in the beginning a proposition is not necessarily ”a picture of the world” (2.0212).

”It would then be impossible  t o  f o r m  a picture of the world (true or false)”. (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031)

”The name means the object. The object is  i t s  meaning. (”A” is the same sign as ”A”)”. (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031)

”Only the propositon has sense ; only in the context of a proposition has a name meaning”. (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031)

Abovesaid is not trivial in the context of picture theory, as it is self-evident only in the context of (pure) ”u – language” , yet without correspondence theory.

”In the proposition a state of affairs is, as it were, put together for the sake of experiment. One can say, instead of, This proposition has such and such a sense, This proposition represents such and such a state of affairs”. (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031)

While Wittgenstein talks a lot, in many paragraphs* , ”objects” and ”things” , I take most of them* with only by numerical sign. If at all. This neglect is because of here, in this paper Wittgenstein’s doctrine of ”the substance of the world.” (1.13 , 2.021 , 3.203 , 3.3 , 4.23 , 5 , 5.01)  concideres only, be it said once more, in the context of (pure) ”u – language” and especially with the concepts of ”truth” and ”provability”.

”The name occurs in the proposition only in the context of the elementary proposition”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01 , underline with bolding continues (5.01) )

”Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

”The elementary propositions are the truth-arguments of propositions”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

This ”consideration” is fully according to the meaning of ”the world” (1 , 1.1 , 1.11 , 1.12 , 2 , 1.13 , 2.06 , 2.063 , 2.1 , 2.14 , 2.141 , 2.21 , 2.221 , 2.222 , 2.223 , 3.12 + 3.14 , 4.01 , 4.031 , 4.0311 , 4.06 , 4.1 , 4.25 , 5 , 5.01). The determination of the world, reality is in the context of the logic of the chosen truththeory. Correspondence theory necessitates to conceive the world, reality. Completely, in the ”u – language”. In order to make it possible to analyse the well-formed relation of ”u – language” to reality.

And (as we shall see) correspondence theory is the chosen truththeory since its logic has the same starting point as (the consequence of) Russell’s paradox, i. e. there exists not yet ! a single proposition that can be said to be consistent and provable ”true or false”.

5 .     The correspondence theory of truth

If there is still evident, undeniable facts in Tractatus, along with (the meaning of) ”facts” , ”thoughts” and ”draw a limit” , then one is the correspondence theory of truth.

”The picture agrees with reality or not ; it is right or wrong, true or false”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05)

”What the picture represents is its sense”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05 , 4.031)

”In the agreement or disagreement of its sense with reality, its truth or falsity consists”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05 , 4.031)

”In order to discover whether the picture is true or false we must compare it with reality”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05 , 4.031)

Anyway, one must take into account that PToL is not direcly an act of the correspondence theory. It must be ”.. applied ..” (3.5) , in the ”u – language”.

”The picture is a model of reality”. (2.12 , 3 , 3.12 , 3.5 , 4.01)

”A propositional sign, applied and thought out, is a thought”. (2.12 , 3 , 3.12 ,  3.5 , 4.01)

”The proposition is a picture of reality. The proposition is a model of the reality as we think it is” (2.12 , 3 , 3.12 , 3.5 , 4.01)

How ”.. the proposition is a model of the reality ..” ?  Only, not until when applying the correspondence theory of truth in its original form to, or in the ”u – language”. In its original form? Instead of saying ”a picture” it is to say ”a (declarative) sentence” or ”a proposition” to get the correspondence theory of truth in its original form.

Thus, we have correspondence theory in its original form simply by substituting term ”picture” with term ”proposition” or ”(declarative) sentence” in paragraphs (2.21 , 2.221 , 2.223 , 2.224 , 2.225). Only the coordination of ”u – language” and the correspondence theory in its original form accomplish the picture theory.

(Correspondence theory has also another ”original form” , without representing ”sense”. )

With respect to PToL Tractatus is actually an analysis of applying the correspondence theory of truth in ”u – language” to get, derive and eventually decide all well-formed propositions, i. e. all propositions that can be provably and consistent ”true or false” ; to overcome Russell’s paradox.

How these well-formed propositions, ”facts in logical space” of correspondence theory of truth, will be ”pictures of reality” (1.1 , 1.13  →  (2.21 , 2.221 , 2.222)  →  (3.12 + 3.14 , 4.031 , 4.06) ) ?

6 .     The logic of the correspondence theory

The main, principal question of correspondence theory is relation between language / ”u – language” and reality. It is a question of logic since it concerns the consistency of the correspondence theory. It asks if there are any (necessary) conditions in the relation between language / ”u – language” and reality which the consistency of the correspondence theory presupposes in order that a proposition or what a proposition represents  c a n  agree or disagree with reality .. without falling into ! a circular argument or contradiction ?

”If one does not observe that proposition have a  s e n s e  independent of the facts, one can easily believe that true and false are two relations between signs and things signified with equal rights. One could then, for example, say that ”p” signifies in the true way what ”¬p” signifies in the false way, etc.”. (4.061)

Paragraph (4.061)  means that ”.. the proposition has sense .. represents such and such a state of affairs .. independent of the facts ..” (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.002 , 4.031 , 4.061). And it means that, since ”the facts” (3.12 + 3.14 , 4.06)  are inevitable ”in logical space” (1.13) of some theory of truth, the correspondence theory (2.21 , 2.221 , 2.222 , 4.031) ! i t s e l f  is the origin of independence. The logic of the correspondence theory, in its original form, i. e. not yet as picture theory, says that independence is a necessary condition in the relation between language / ”u – language” and reality to the consistency of that truth-theory. Independence is an axiom of correspondence theory. If it stands not, then in the case of truth correspondence theory falls into a circular argument and in the case of falsehood correspondence theory falls into a contradiction.

Paragraph (4.061)  says that every possible sentence, when correspondence theory is assumed to hold true, which ”.. has sense .. represents such and such a state of affairs” (3.3 + 4.031) independent of reality, that is, independent of whether to ! provable agree or disagree with reality. Otherwise there would be no consistent way to ”.. compare .. such and such a state of affairs .. with reality” (2.223 + 4.031)  and so, not until ! by comparing,  be able to prove, verify ”.. the agreement or disagreement of  .. such and such a state of affairs .. with reality ..” (2.21 , 2.221 , 2.222  + 4.031).

That the correspondence theory in its original form is the source of independence becomes clear when there is in the beginning only not yet defined ! original, true concept of ”reality” , instead of allready having definition of world and reality, as Wittgenstein in Tractatus (1 , 1.1 , 1.11 , 1.12 , 1.13 , 2 , 2.06 , 2.063). The fact that correspondence theory in its original form is the source of independence becomes as well easier to realize if we first replace a ”.. proposition represents such and such a state of affairs” (4.031) simply with ”x” , and then let ”reality” be replaced by ”y”.

Now  –  suppose the opposite, i. e. independence stands not.

But, what independence means? Definition of concept ”independence” is needed. In order to answer the meaning of the opposite. ”Independence” and the opposite ”dependence” are concepts that deals with relations, in between some entities, objects or things. An entity, object or a thing ”x” is independent if(f and only if) it (can) exists by oneself, i. e. its existence necessitates nothing else, be it the existence of whatever other ”x ’ ” , ”y” or ”z”. Thus, the philosophy of independence is that if (some) ”x” is independent of (some) ”y” , then the baseline is that ”x” and ”y” cannot be expressed together, in  same space. However, if ”x” and ”y” are, have to be expressed together, connected to each other, interrelate as it is the case in correspondence theory ”the sense of a proposition” and ”reality” have to be, then by independence ”the sense of a proposition” cannot be derived, infered from that connexion to ”reality”. By PToL, as an implication of independence, this means that exactly that ”.. something .. identical .. in common with reality .. the logical form .. of reality” (1.13 , 2.06 , 2.063 , 2.16 , 2.161 , 2.17 , 2.18 , 3.12 , 3.14 , 4.03 , 4.06)  cannot be derived, infered throughout any single logic. To wit ”the logical form” (2.2)  of a proposition of ”u – language” represents ”reality” ! i n ”u – language” and express ”the sense of a proposition” in a way that it can (provable) agree or disagree reality. Thus in the end of the analysis of the logic of correspondence theory the initial independence converts to undecidability of  the totality of well-formed propositions of correspondence theory (4.0312 , 4.128 , 6.4321).

So, what it means if (some) ”x” is not independent of (some) ”y” ?

It means that always when (some) ”x” , then also (some) ”y” is to be with, and ”x” derived from ”y”.

Now let’s get back to the situation, thinking experiment that a ”.. proposition represents such and such a state of affairs” (4.031)  not independent of ”reality”.  –  What happens?

The obvious result is that always when a ”.. proposition represents such and such a state of affairs” (4.031)  the expression of reality is also ! present. It is to say, that ! the ”reality” which in question ”.. a sense ..  such and such a state of affairs .. agrees with .. or not ..” (2.21 , 2.221 , 2.222 , 4.031)  will be present.

And if this, to put a ”.. proposition represents such and such a state of affairs” (4.031)  in an appearance together with ”reality” , then it is not possible correspondence theory of truth to escape, avoid circular argument or contradiction, and to be consistent. To wit in the instance of proposition to be ”true” , proposition express (also) the ”reality” to agree with and in the instance of proposition to be ”false” , proposition express (also) the ! ”reality” to agree with not.

A .     In the instance of proposition to be ”true” the result is  –  a circular argument.

There is no difference between a proposition or what it represents and reality. A proposition or what it represents and reality are the one and the same, equivalent. There is, can be no question of agreement or disagreement, nothing to compare with.  –  Correspondence theory is not possible.

B .     In the instance of proposition to be ” false” the result is  –  vicious circle  –  contradiction.

What it entails, if a proposition express also, except ”such and such a state of affairs” (4.031) , the ”reality” that said ”such and such a state of affairs” is to agree with not ?  It entails, necessitates that a proposition in question express  a l s o ! a n other ”such and such a state of affairs” (4.031) , which represents ”the reality” that in the first place said ”such and such a state of affairs” is to agree with not. There must be ”something” existing to agree with not! Reality cannot be empty, to be formed (only) by ”.. non-existence of states of affairs ..” (1, 1.1 , 2 , 2.06 , 2.063). If reality is empty there is ! ”nothing” that initially said ”such and such a state of affairs” is to agree with ! not, which is to say that the falsehood of a proposition is impossible, not only to prove, but in principle not possible. If there is ”nothing” / ”no thing” to agree with not, then the initially said ”such and such a state of affairs” ! have to agree ! ! ”everything” , whatsoever. And thereby (the meaning of) the falsehood of a proposition ! converts inevitable, logical truth (4.061 , 4.062).

What this necessary ”something” existing  –  to agree with not  –   is, means?

It means that the another ”such and such a state of affairs” (4.031)  have to be in the agreement with reality. Otherwise ”it” cannot represent reality, as it is formed by ”.. the existence of states of affairs” (1 , 1.1 , 2 , 2.06 , 2.063 , 3.4 , 3.411 , 3.42 , 4.0641 , 4.21 , 4.25).

But! If a proposition express also, except in the first place said ”such and such a state of affairs” (4.031) , another ”such and such a state of affairs” , representing reality, with which initially said ”such and such a state of affairs” do not agree, conclusion will be contradiction. A fallacy by infering from what is ”truth” that what is ”false”. Not to say a violation of the law of identity , i. e. a ”janus faced” mixed proposition, with its (both) ”true” and ”false” side.

Even if correspondence theory is contingent, i. e. conditional or dependent of the possibilities of both truth values ”truth” and ”falsehood” of propositions, these ”possibilities” cannot be expressed together. But to exclude each other, by the laws of the law of excluded middle, the law of noncontradiction and the law of identity. This ”to exclude each other” is in a nutshell the core of Wittgenstein’ s ”fundamental thought” (4.0312 , 4.128 , 6.4321) , and it may seem self-evident. It’s not, but it is a question of ! ”truths” , i. e. ! totalities or nexus of possible ”true” propositons, which (totalities) exclude ”each others”. There are exhaustible many compatible, contingent totalities of possible ”true” propositons excluding ”each others” , and ”to exclude each others” is to say that those ”outside-being” propositions are ”false”.

Thus in the end the logic of correspondence theory (4.061) , as Wittgenstein’ s ”fundamental thought” (4.0312 , 4.128 , 6.4321) , says that the totality* of ”pictures of reality” (4.06)  cannot be derived by any single logic or algorithm. Instead, it* is exhaustible or at least inexpressible.

Independence in the relation between language / ”u – language” and reality is a necessary condition to the consistency of correspondence theory. However as such, alone in it’ s original form, independence is not enough. Provability is still an open question, and also the consistency of correspondence theory may not be airtight, or to be at most for no use ( , but drawing ”true or false” – lots).

If a proposition or what a proposition represents (4.031)  and reality cannot be expressed together, in  same space, in conjunction with each other, then to compare ”.. such and such a state of affairs .. with reality” (2.21 , 2.221 , 2.222 , 2.223 , 4.031)  is not possible. To prove ”.. the agreement or disagreement of .. such and such a state of affairs .. with reality ..” (2.222 , 4.031)  fails. To prove a proposition ”true or false” fails, applying correspondence theory of truth.

Correspondence theory is empty-handed. There are no, not yet any, well-formed propositions. Thus there cannot be yet any effort ”to draw a limit to the expression of thoughts in language within” (Preface / (3 , 3.12 , 4 , 4.001 , 4.06 , 4.112 , 4.114 , 4.211 , 4.25 , 5 , 5.01) )  in order to overcome Russell’s paradox (3.333). So, the starting point to show validity of correspondence theory is the same than the consequence of Russell’s paradox. And ”the same” by the logic of truth-theory itself, as it shall be in order to (3.333).

PToL is the way to get out from this dead-end of correspondence theory. If only independence stands, conjunction, relation between ”u – language” and reality don’t stand. Both correspondence theory and ”the aim of the book” (Preface / (4.112 , 4.114) ) fails, without making a proper ”u – language” ( (1 , 1.1 , 1.11 , 1.12 , 1.13 , 2 , 2.06 , 2.063)  ←  2.1) , compatible with the logic of correspondence theory.

7 .     Picture theory is an implication of independence

The essence of picture theory is to bridge the gap, bring together ”u – language” and reality, so that what a proposition represents (4.031)  and reality can be compared, and then by comparing it is possible to prove ”.. the agreement or disagreement of .. such and such a state of affairs .. with reality ..” (2.222 , 4.031).

”The picture is a fact”. (1.13 , 2.141 , 3.12 , 3.14 , 4.06)

To remind, that the well-formed propositions are ”the facts” ! to be made ”.. in logical space ..” of  the correspondence theory as ”.. pictures of reality” (1.13 , 2.1 , 2.141 , 2.21 , 2.221 , 2.222 , 2.223 , 3.12 , 3.14 , 4.031 , 4.06). A proposition is ”a fact” exactly in that sense that it ”can be true or false” , provably and concistently (4.21 , 4.211 , 5 , 5.01) ; and not only by chance, drawing lots or by (random) oracle, if only independence stands.

”It is clear that however different from the real one imagined world may be, it must have something  –  a form  –  in common with the real world”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

”In order to be a picture a fact must have something in common with what it pictures”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

”In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

”What the picture must have in common with reality in order to be able to represent it after its manner – rightly or falsely  –  is its form of representation”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

”What every picture, of whatever form, must have in common with reality in order to be able to represent it at all  –  rightly or falsely  –  is the logical form, that is, the form of reality”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

”The picture has the logical form of representation in common with what it pictures”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

Thus ”.. the logical form of representation ..” (2.2)  represents  –  or even ! is  –  reality, in PTol.

In other words, if a proposition has ”the form of reality” (2.022 , 2.16 , 2.161 , 2.17 , 2.18) ,  then its ”truth or falsehood” is possible, i. e. can be proved. Thus, in my book,  it is decent to say, conclude that this ”have in common with reality” (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2)  is identical, means the same than ”the ”truth or falsehood” of a proposition is provably possible”. Thus, in by book, it is decent, by taking  into account the ! place (2.203 , 3.13 , 3.318)  of ”the form of reality” (2.18) , to conclude that a well-formed proposition* of correspondence theory as ”a picture of reality” (4.01) ! contains  b o t h ”truth-possibilities” / both ”true” and ”false” ; as a matter of fact it* contains all its* ”truth-possibilities”.

”The picture represents what it represents, independently of its truth or falsehood, through the form of represention”. (2.21 , 2.22 , 2.221 , 2.222 , 4.031 , 4.1 , 4.2) , alleviivaus jatkuu (2.221) )

”What the picture represents is its sense”. (2.21 , 2.22 , 2.221 , 2.222 , 4.031 , 4.1 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

No doubt, ”.. independently of .. truth or falsehood ..” (2.22)  since the question concerns ! just, not until the possibility of ”.. the agreement or disagreement of .. such and such a state of affairs .. with reality ..” (2.222 , 4.031). It is just, not until the question of ! provability. i. e. the well-formed ”.. proposition is the expression of its truth-conditions” (4.1 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01).

Clearly, no doubt, the principal question of PToL or even in Tractatus is that of the possibility of ”truth and falsehood” of a proposition. More genarally it concerns not only the possibility of well-formed, provable and consistent, proposition as ”.. a picture of reality” (4.01) , but on the whole that ! at all any truth value is possible (4.46 , 4.464). And to answer these questions of (all possible) truth values a theory of truth is needed, in Tractatus clearly correspondence theory. To analyse picture theory without that truth-theory is, at least in my book, next to nothing. Correspondence theory explains well many things of Wittgenstein’s book. For example the determination of world* and reality* in the beginning of book, not only because of these concepts* are essential part of correspondence theory but because of the logic of correspondence theory, the necessary independence. Picture theory as an implication of independence presupposes to conceive the concepts ”world” and ”reality” , in order to be able to say ”pictures of ! (exactly) ”what””. And notably correspondence theory explains (at least in my book) the most abstruse parts of Tractatus, such as Wittgenstein’s ”substance” – doctrine as a whole. Also in the context of ”.. the truth-possibilities of elementary propositions ..” (1.13 , 2.021 , 2.06 , 2.063 , 3.203 , 3.3 , 4.1 , 4.2 , 4.23 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01). Without taking into account the logic of correspondence theory it may be difficult, if not even impossible, to grasp paragraps like  –

”Objects contain the possibility of all states of affairs”. (2.014 , 2.0141 , 2.201 , 2.202 , 2.203 , 3.02 , 3.318 , 3.332 , 3.333 , 4.431)

”The possibility of its occurring in states of affairs is the form of an object”. (2.014 , 2.0141 , 2.201 , 2.202 , 2.203 , 3.02 , 3.318 , 3.332 , 3.333 , 4.431)

”This fixed form consists of the objects”. (2.022 , 2.023 , 2.16 , 2.161 , 2.17 , 2.18 , 3.12 , 3.14 , 4.01 , 4.06)

Finally, the analysis of the logic of correspondence theory, is the way to Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321) , which mutatis mutandis anticipate Gödel’s incompleteness theorems.

”The proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand”. (4.022 , 4.03)

”Der Satz zeigt seinen Sinn. Der Satz zeigt, wie es sich verhält, wenn er wahr ist. Und er sagt, dass es sich so verhält”. (4.022 , 4.03)

”A proposition must communicate a new sense with old words. The proposition communicates to us a state of affairs, therefore it  must be  e s s e n t i a l l y  connected with the state of affairs. And the connexion is, in fact, that it is its logical picture. The proposition only assert something, in so far as it is a picture”. (4.022 , 4.03)

”Ein Satz muss mit alten Ausdrucken einen neuen Sinn mitteilen. Der Satz teilt uns eine Sachlage mit, also muss er  w e s e n t l i c h  mit der Sachlage zusammenhängen. Und der Zusammenhang ist eben, dass er ihr logisches Bild ist. Der Satz  s a g t  nur insoweit etwas aus, als er ein Bild ist”. (4.022 , 4.03)

Only as ”.. a model of reality” a proposition is  a b l e  to say, assert its ”truth or falsehood” (2.06 , 2.12 , 4.01 , 4.022 , 4.03 , 4.06 , 4.25) , to assert that what a (pure) proposition allready represents, i.e. ”.. such and such a state of affairs .. agrees with reality or not ..” (2.21 , 4.031 , 4.064).  As ”.. a model of reality” (2.12 , 4.01)  a proposition bridges the gap, brings together ”u – language” and reality. In other words, on the whole, ”u – language” , by beeing ”.. connected with the state of affairs ..” (4.03)  show, express the possibilities of ”.. the existence and non-existence of  the state of affairs” , and contains these ”truth-possibilities of the elementary propositions .. the truth-arguments of propositions” (1 , 1.1 , 2 , 2.014 , 2.06 , 2.063 , 2.11 , 2.201 , 2.202 , 2.203 , 2.221 , 2.222 , 2.223 , 4.031 , 4.1 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01). A proposition as ”a picture of reality” (4.01)  represent its (own) ”truth and falsehood” ; that is to say ! all its provable ”truth-possibilities” (4.46 , 4.464). In PToL all the provable ”truth-possibilities” of propositions stand for, represent, ”in logical space” (1.13)  of correspondence theory, ”reality” / ”facts” ; and it is exactly ”all the provable ”truth-possibilities” of propositions” / ”logical forms” , which ”.. the logic .. cannot be represented” (2.15 , 2.16 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.0312 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.44 , 6.522). It is precisely the logical means, an algorithm of how ”.. the elements of the picture are combined with another in a definite way .. in order .. a picture .. to be .. true or false .. that cannot put into words ..” (2.021 , 2.1 , 2.15 , 2.161 , 2.17 , 2.18 , 2.21 , 3 , 3.12 , 3.14 , 3.203 , 3.3 , 4.06 , 4.128 , 4.23 , 5.01 , 5.55 , 5.5571 , 6.522)  –  Concerning especially the contingent ”.. truth .. of propositions ..” (4.46 , 4.464).

8 .     Determination of the concept ”reality”

As said, the analysis of correspondence theory as well asks, precisely PToL ! presupposes to conceive reality, the concepts ”world” and ”reality” ; in order to be able to say ”pictures of ! (exactly) ”what”” / ”logical forms of ! (exactly) ”what””. –  But how this necessary determination can be done?

Applying again correspondence theory to ”u – language”. And not strange enough, it avoids to be circular argument. This self-referential use of correspondence theory in its own case has an advantage. It escapes a dilemma. If some other thing, theory would determinate reality then we would meet the question of ! what is the relation between correspondence theory and that ”other thing, theory”. But by means of correspondence theory (to conceive reality) we are in same nexus, catecory.

”The world is the totality of facts, not of things”. (1.1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)

What is ”a fact”? Altogether, ”a fact” is plainly a ”true or false” proposition. Thus, ”the totality of facts” is the totality of (all) ”true or false” propositions. ”The world” consist of all ”true or false” propositions, or as Wittgenstein calls ”true positive and true negative” propositions, i. e. it is ”true” that this is the case or it is ”true” that this is not the case. (1.12 , 2.06 , 2.063 , 4.1 , 4.25 , 5.5151).

”The existence and non-existence of states of affairs is reality. (We call the existence of states of affairs a positive fact, and their non-existence a negative fact.)”. ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031)

”The total reality is the world”. (1.1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)

”Propositions represent the existence and non-existence of states of affairs”. (1.1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  (4.1 , 4.21 , 4.25 , 5 , 5.01) )

”The simplest kinds of proposition, an elementary propopositon, asserts the existence of states of affairs”. (4.1 , 4.21 , 4.25 , 5 , 5.01)

”If an elementary proposition is true, the state of affairs exists ; if an elementary proposition is false, the state of affairs does not exist”. (4.1 , 4.21 , 4.25 , 5 , 5.01)

”Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)”. (4.1 , 4.21 , 4.25 , 5 , 5.01)

All the (possible) truth values of propositions are functions, or variables, in relation to the ”truth and falsehood” of their ”elementary propositions .. the truth-arguments of propositions” (4.1 , 4.21 , 4.25 , 5 , 5.01).

”The elementary propositions are the truth-arguments of propositions”. (4.1 , 4.21 , 4.25 , 5 , 5.01)

Hence, Wittgenstein conceives ”reality” as follows : ”Propositions represent .. reality” (4.1 + 2.06)  by representing all the possibilities of truth and falsehood of ”the truth-arguments of propositions” (4.1 , 4.2 , 4.21 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01). And the existing world, here and now on the whole, in its moments (of time and space) consist of those ”positive and negative” propositions which are ”true” ; coincide, happen to be ”true” , i. e. realise their ”truth-possibilities”.

”Propositions represent .. reality” (4.1 + 2.06) is the same as to say that ”propositions” ! stand for ”reality” by representing the truth and falsehood of ”the truth-arguments of propositions”.

Anyway we meet another question, ! the question : Why the determination of reality by means of correspondence theory itself is not a circular argument ?

This, ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031) , take place ! to wit in the ”u – language” independent of reality ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.0124 , 2.021 , 2.0211 , 2.0212 , 2.024 , 3.203 , 3.3 , 4.002 , 4.031 , 4.061). Hence, there is not a single proposition, which one can point and say, assert proposition to be (provably) ”true or false”. To compare is not (yet) possible. Hence, the determination of reality by means of correspondence theory itself is not a circular argument. It ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031)  is a tautology. To say in the ”u – language” independent of reality that .. ”the reality” is a totality of true ”positive” and true ”negative” propositions (1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.21 , 2.221 , 2.222 , 4.031 , 5.5151) says nothing more, nothing less than, for example .. ”it’s raining or not”.

One can say that Wittgenstein’s determination of ”reality” follows direct from the definition of correspondence theory. If one postulates, takes correspondence theory as premise (2.21 , 2.221 , 2.222 , 2.223) ! with ”u – language” , where ”everything” can be said / ”.. all objects are given ..” (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031) , then the consequence is by definition that of Wittgenstein’s determination of ”reality”. Without no follow-up to show and say yet any single well-formed proposition (2.0231).

The point of Wittgenstein’s determination of ”reality” , and then further (the point of) the analysis of ”pictures of reality” ,  is that they are done ”.. in language .. within ..” (Preface / 4.112 , 4.114). Wittgenstein simulates both reality and the relation between ”u – language”  and reality, in ”u – language” itself : By the rules of the logic of correspondence theory.  –  Tractatus / PToL is a ! great piece of self-reference.

9 .     ”The existence of an internal relation” (4.125)

”The existence of an internal relation between possible states of affairs expresses itself in language by an internal relation between the propositions presenting them”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 ,  2.12 , 2.201 , 2.202 , 2.203 , 3.02 , 4.01 , 4.03 , 4.1 , 4.125 , 4.1251 , 4.21 , 4.25 , 5 , 5.01)

”Das Bestehen einer internen Relation zwischen möglichen Sachlagen drückt sich sprachlich durch eine interne Relation zwischen den sie darstellenden Sätzen aus”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3.02 , 4.01 , 4.03 , 4.1 , 4.125 , 4.1251 , 4.21 , 4.25 , 5 , 5.01)

Self-reference is, will be due to the logic of correspondence theory. Independence must stand as an axiom. It effects all the way of the analysis of correspondence theory. Also in the context when  –

”We make ourselves pictures of .. the reality”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 3.12 , 3.14 , 4.06)

And then, finally in Wittgenstein’s effort ”.. to draw a limit .. to the expression of thoughts ..” (Preface / (4.112 , 4.114) : Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  is due to the independence. The initial external independence between ”u -language” and reality converts by ! (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.201 , 2.202 , ! 2.203 , ! 3.02 , 4.1 , 4.125 , 4.25 , 4.3 , 4.41 , 5.01)  to undecidability of  the totality of well-formed propositions of correspondence theory.

It is independence between language / ”u – language” and reality which says that first, in the beginning of the analysis of correspondence theory, there exists only a pure ”u – language” (1 , 1.1 , 1.11 , 1.12 , 2 , 2.021 ,  2.024 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031 , 4.061) , i. e. n o t  yet any proposition or (declarative) sentence is, can be provably ”true or false” ; to compare a proposition or what it represents with reality is not possible. There is yet no propositions that ”.. represent the existence and non-existence of states of affairs”. ( (1.1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  4.1 , 4.21 , 4.25 , 5 , 5.01). A pure ”u – language” is the first level of Wittgenstein’s ”substance” – doctrine, to ”.. make ourselves pictures of facts” (2.06 , 2.1 , 2.141 , 3.12 + 3.14 , 4.06 , 4.1 , 4.25 , 5 , 5.01). With and ! by the correspondence theory of ”truth”. That there is not yet any well-formed, consistent and provable ”true or false” proposition is the reason for paragraphs (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4733 , 5.5563).

”.. Logic treats of every possibility, and all possibilities are its facts. ..”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

If there exists not yet any provably ”true or false” propositions, then all possible propositions, or (declarative) sentences, of ”u – language” are instances of ”.. facts in logical space ..” of correspondence theory ( (1.13)  →  2.141 , 2.21 , 2.221 , 2.222 , 2.223 , 3.12 + 3.14 , 4.01 , 4.031 , 4.06 ). In principle, in first place every ”.. proposition represents such and such a state of affairs”. (2.021 , 3.203 , 3.3 , 4.031) , which can agree or disagree with reality. That’s the essence of correspondence theory. Anyway it leaves, by necessary independence, the provability of ! any truth values open ; which implies (as we shall see) that also the consistency of correspondence theory is still, further an open question. It will be a question of ! the provability of ! ! the consistency of correspondence theory.

”Every proposition must already have a sense ; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

There ”.. must already ..” (4.064)  exist propositions, or (declarative) sentences, possible to constitute in ”u – language” that ”.. have a sense ..” (4.064). Otherwise there would be ”nothing” to ask and it will be ! ”.. impossible to form a picture of the world (true or false)”. (2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031). Wittgenstein’s ”substance” – doctrine has two layers. First is that of maybe trivial, that if not ”already” possible to say ”something” , i. e. to represent ”.. such and such a state of affairs” (4.031 , 4.064) , then ”nothing” which ”.. agrees with reality or not ..” (2.21). The second layer is anyway nothing but empty ; that a ”.. proposition has .. already .. such and such a sense ..” (4.031 + 4.064) ! concerns just the provability of a proposition, altogether ! to show any possible truth values of a proposition (2.021 , 2.0211 , 2.0212 , 3.202 , 3.203 , 3.23 , 3.3 , 4.031 , 4.2 , 4.21 , 4.22 , 4.221 , 4.23 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 4.46 , 4.464 , 5 , 5.01). Every well-formed proposition of correspondence theory ”.. contains .. a l r e a – d y ..” (2.01231 , 2.014 , 2.021 , 2.203 , 3.02 , 3.13 , 3.203 , 3.3 , 3.318 , 3.333 , 4.06 , 4.064 , 4.122 , 4.1221 , 4.123) ! a l l  its possible truth values, i. e. a l l ”.. the truth-possibilities of .. the truth-arguments of propositions” (4.2 , 4.21 , 4.23 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 4.46 , 4.464 , 5 , 5.01) , and that is the reason why ! ( (3.332 , 3.333)  →  4.0312).  –  What is in common with both layers of ”.. the substance of the world ..”* (1.13 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 2.024 , 3.12 , 3.14 , 3.203 , 3.3 , 4.002 , 4.031 , 4.061)  is that it* ( (4.128 , 4.23 , 5.01)  →  5.55 , 5.5571)  precedes and also in a certain ! exhaustible way finally exceeds any possible truth values of a proposition, other than ”.. two extreme cases .. tautological .. self-contradictory” (4.46 , 4.464).

”Logic must take care of itself. A possible sign must be able to signify. Every thing which is possible in logic is also permitted. ..”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

”.. What makes logic a priori is the impossibility of illogical thought”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

”We cannot give a sign the wrong sense”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

”Frege says : Every legimately constructed proposition must have a sense ; and I say : Every possible proposition is legimately constructed and if it has no sense this can only be because we have given no meaning to some of its constituent parts. ..”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

”In fact all the propositions on our everyday language, just as they stand, are in perfect logical order.  –  This utterly simple thing, which we have formulate here, is not an image of the truth, but the truth in its entirety”. (2.0121 , 4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

But, how ”the existence of an internal relation” (4.125) , that what makes a proposition ”picture of reality” , is due to the independence ?  And to answer to that question implies also an answer to the second question, i. e. why it is ”.. a logical impossibility .. give a sign the wrong sense” (5.4732 + 6.375) ? To the well-formed proposition, which ”.. represents .. its sense .. t h r o u g h  .. the logical form of representation in common with .. the form of reality” (2.18 + 2.2 + 2.22 + 2.221) ,  it will be ! ”.. a logical impossibility .. give .. the wrong sense” (1.1 , 2.06 , 2.063 , 2.201 , 2.202 , 2.203 , 2.22 , 3 , 3.02 , 3.12 , 3.13 , 4.1 , 4.2 , 4.25  ←  (5.4731 , 5.4732 + 6.375) ).

The answer to the first question becomes by itself, as ”.. a logical necessity ..” (6.375). The necessary independence (2.024 , 4.061)  to the consistency of correspondence theory is in  i t s  f i r s t  phase an  e x t e r n a l  relation between ”u – language” and reality.  –  Thus to that

”What every picture, of whatever form, must have in common with reality in order to be able to represent it at all  –  rightly or falsely  –  is the logical form, that is, the form of reality”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

there is no other place ! than ”.. in language .. within ..” (Preface / 4.112 , 4.114). To wit, there exist, by independence, nothing but a yet pure ”u – language” (1 , 1.1 , 1.11 , 1.12 , 2 , 2.0124 , 2.021 , 2.0211 , 2.0212 , 2.024 , 2.06 , 2.063 , 3.203 , 3.3 , 4.002 , 4.031).

Hence, consistently, both the determination of reality and then to bridge the gap, bring together ”u – language” and reality, throughout the determination of it,  have to be done in ”u – language” itself. And exactly the latter, to ”.. make ourselves pictures of .. the reality”. (2.06 , 2.1 , 2.141 , 3.12 , 3.14 , 4.06) , is a kind of great piece of self-reference :

1.    In ”u – language” it is possible to speak about the connexion, relation between ”u – language” and reality.

2.    Even so and precisely that ”u – language” itself contains the well – formed relation.

This (1. and 2.) is ”in logical space” of correspondence theory + ”u – language” made simulation, model of well-formed relation between ”u – language” and reality (1.13 , 2.0124 , 2.06 , 2.063 , 2.021 , 2.1 , 2.11 , 2.12 , 3.203 , 3.3  →  (2.21 , 2.221 , 2.222)  →  (3.12 + 3.14 , 4.001 , 4.002 , 4.031 , 4.06 , 4.1 , 4.23 , 4.25 , 5 , 5.01) ).

And that what self-reference means, presupposes, i. e. ”.. Reality must .. be completely described ..” (2.06 , 4.023 , 4.06 , 4.1)  is possible to do, express. B u t ! the result of this complete analysis of reality, i. e. ”.. the form of  a l l  propositions .. the truth-possibilities of .. the truth-arguments of propositions .. c a n n o t  be said .. in advance .. all at once” (2.014 , 2.0141 , 2.021 , 2.17 , 2.18 , 2.2 , 3.203 , 3.3 , 4.0312 , 4.12 , 4.121 , 4.1212 , 4.128 , 4.23 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 4.46 , 4.464 , 5 , 5.01 , 5.47 , 6.4321 , 6.44 , 6.522 , 7).  –  Hence / ! (3.13 , 4.2  →  (3.332 , 3.333) ) , Wittgenstein’s aim (Preface / (4.112 , 4.114) )  fails.

In my book, not even so much as an interpretation, but straightforward, literal and comparative reading of Tractatus, ”.. the form of all propositions ..” (2.17 , 2.18 , 2.2 , 5.47)  is that these ”.. something .. in common .. identical .. with reality .. the form of reality” (2.022 + 2.16 + 2.161 + 2.17 + 2.18)  having propositions are able to be ”true or false” , provably ”true or false”. The meaning, function of ”.. the logical form of representation in common with .. the form of reality” (2.18 + 2.22)  concerns ! altogether exactly the provability of the truth values, both ”truth and falsehood”. It is ! just the provability of ! both ”truth and falsehood” , which every well-formed proposition of correspondence theory as ”.. a picture of reality .. completely .. contains .. as .. a logical necessity ..” (2.201 , 2.203 , 3.02 , 4.01 , 4.023 , 4.1 , 4.25 , 6.375).  –  Due to the necessary independence to the consistency of correspondence theory.

My literal and comparative reading of Tractatus / PToL, with some comments in between, goes as follows ; some of the main paragraps also in original German, to compare :

”We make ourselves pictures of facts”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

”The picture presents the facts in logical space, the existence and non-existence of atomic facts”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

( ”Atomic facts” is synonym to  –  means the same than  –  ”states of affairs”. )

Thus ”the facts” are similar / ∼ to ”the existence and non-existence of atomic facts” ; actually they are equivalent (4.1).

”The picture is a model of reality”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

”A model” must be showed, played somewhere. ”Somewhere” is in Tractatus ”u – language” itself, where the structure of well-formed propositions of correspondence theory (2.21 , 2.221 , 2.222 , 4.031 , 4.2) , made by applying correspondence theory to ”u – language” (2.1 , 3.5) , stand for, represent reality (2.15 , 2.17 , 2.18 , 2.2 , 2.22 , 3.12 , 3.14 , 4.06).

”The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

So, ”.. a possibility of the existence and non-existence of atomic facts” (2.201)  stands for, represents reality in ”.. a model of reality” (2.12)  made in ”u – language” by applying the logic of correspondence theory (1.13 , 2.06 , 2.063 , 2.1 , 2.11  →  (2.21 , 2.221 , 2.222 , 3.12 , 3.14 , 4.031 , 4.06) ). That is why the definition of well-formed propositions of correspondence theory is like said in paragraphs (4.2 , 4.4 , 4.431).

”The picture represents a possible state of affairs in logical space”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

”The picture contains the possibility of the state of affairs which it represents”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

Thus, a well-formed proposition of correspondence theory as ”.. a picture of reality .. contains the possibility of .. the existence and non-existence of atomic facts” (2.201 , 2.203 , 4.01).

”Das Bild stellt die Sachlage im logischen Raume, das Bestehen und Nichtbestehen von Sachverhalten vor”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.1 , 4.25 , 5 , 5.01)

In my book it is in original German even more evident that ”die Sachlage” und ”das Bestehen und Nichtbestehen von Sachverhalten” means the same, are equivalent.

”Bas Bild bildet die Wirklichkeit ab, indem es eine Möglichkeit des Bestehens und Nichtbestehens von Sachverhalten darstellt”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.1 , 4.25 , 5 , 5.01)

”Bas Bild stellt eine mögliche Sachlage im logischen Raume dar”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.1 , 4.25 , 5 , 5.01)

”Das Bild enthält die Möglichkeit der Sachlage, die es darstellt”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.1 , 4.25 , 5 , 5.01)

Deshalb : ”Das Bild enthält die Möglichkeit .. des Bestehens und Nichtbestehens von Sachverhalten ..”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.1 , 4.25 , 5 , 5.01)

”The thought contains the possibility of the state of affairs which it thinks. What is thinkable is also possible”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 , 3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

”Der Gedanke enthält die Möglichkeit der Sachlage, die er denkt. Was denkbar ist, ist auch möglich”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

Indeed ! ”.. What is thinkable is also possible”. (3.02)  Otherwise, it have to be forbidden to use, by nature self-referential, some language / ”u – language” to construct (2.06 , 2.1 , 4.06) ! not yet existing ”true or false” , or any truth values having, propositions*. (Forbidden perhaps by some ”Deux ex Machina”.) In other words ”.. the fact that we cannot think illogically” (3.02 , 3.03 , 3.031 , 5.473, 5.4731 , 5.4731)  derives that Wittgenstein initiates, after the jolt of Russell’s paradox, from scratch. Only with the tools of presupposed ”universal – language” (2.0124 , 4.002)  and some necessary theory of truth, i. e. the correspondence theory (2.21 , 2.221 , 2.222 , 2.223 , 4.031)  to use, apply in ”u – language”. Correspondence theory because of its logic is in accordance with the end result* of Russell’s paradox. The logic of correspondence theory determinates the ”thinkable” in that ”applied” (3.5) , well-formed ”u – languge”.

The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

”If the elementary proposition is true, the atomic fact exist ; if it is false the atomic fact does not exist”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

”The elementary propositions are the truth-arguments of propositions”. (1.13 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.141 , 2.201 , 2.202 , 2.203 , 3.02 ,  3.12 , 3.14 , 4.06 , 4.1 , 4.21 , 4.25 , 5 , 5.01)

( Recall, ”atomic facts” is synonym to  –  means the same than  –  ”states of affairs”. )

Now, by the literal and comparative reading of paragraphs (2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.21 , 4.25 , 5.01)  we get, at least in my book, the following definition of the well-formed proposition of the correspondence theory as ”a picture of reality” (2.06 , 2.12 , 4.01) :

The well-formed proposition of the correspondence theory ”contains the possibility” of both truth values, ”truth” and ”falsehood” , of its ”elementary propositions” , i. e. ”truth-arguments”.

To consummate, fix the above-said definition one may still consider paragraphs (4.3 , 4.41) , along with others.

”The truth-possibilities of the elementary propositions mean the the possibilities of the existence and non-existence of the atomic facts”. (4.3 , underline continues (4.41) )

”The truth-possibilities of the elementary propositions are the conditions of the truth and falsehood of the propositions”. (4.41)

Thus the well-formed proposition of the correspondence theory as ”.. a picture of reality .. contains .. the conditions of the truth and falsehood ..” of its ! o w n (2.06 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3.02 , 4.01 , 4.21 , 4.25 , 4.3 , 4.41 , 5.01).  –  In short :

The well-formed proposition ”contains the possibility” of its ”truth and falsehood”.

Is this, a clear offence against the law of noncontradiction, the dead-end of correspondence theory? No, it is not! Instead it is a first sign of Wittgenstein’s ”fundamental thought” (4.0312). It is ! the question of the provability of the consistency of correspondence theory. How independence, as an axiom of the consistency of correspondence theory, stands still in the well-formed ”u – language” ?  Independence makes ”u – language” to contain the relation, i. e. ”.. something in common ..” (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06) , between ”u – language” itself and reality / ”.. the form of reality” (2.18). As said, in its first phase independence has already taken the place of external relation between ”u – language” and reality.

The definition of the well-formed proposition of the correspondence theory can be given also, more straightaway, as below  –

”To the proposition belongs everything which belongs to the projection ; but not what is projected. Therefore the possibility of what is projected but not this itself. In the proposition, therefore, its sense is not yet contained, but the possibility of expressing it. (”The content of the proposition” means the content of the significant proposition.) In the proposition the form of its sense is contained, but not its content”. ( (2.06 , 2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 2.201 , 2.21 , 2.22 , 2.221 , 2.222)   ←  3.13 , 3.318 , 3.332 , 3.333 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5.01)

Since ”.. the form of reality .. the logical form of representation in common with what it pictures” (2.17 , 2.18 , 2.2)  m e a n s  the possibility, ”.. to be able to ..” (2.17 , 2.18)  be ”true or false” , it is ! no doubt, by paragraph (3.13) , to conclude the definition of the well-formed proposition of the correspondence theory : If in ”.. a picture of reality .. is contained ..” (3.13 , 4.01)  truth values ”true or false” , it is evident that both truth values ”true and false” are included in.

It is also evident, because of the consistency, that ”.. In the proposition .. its sense is not yet contained ..” (3.13). If it would be included in, then not only the possibility of ”.. the agreement or disagreement of its sense with reality ..” (2.21 , 2.221 , 2.222 , 4.031) , b u t  also ”.. the agreement or disagreement .. with reality ..” (2.222) ! itself would be included in ”.. a model .. picture of reality” (2.06 , 2.11 , 2.12 , 2.201 , 4.01). The function, significance of PToL is not to express in ”u – language” the truth values of well-formed propositions of the correspondence theory, contrary to the essence of said truth-theory,  but to show in ”u – language” only the possibility of truth values of those propositions (which ”possibility” makes the propositions well-formed). Otherwise correspondence theory would be nothing but a ! contradictory branch of solipsism / ! ( (3.318 , 3.332 , 3.333)  ←  ! 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5.01).

”The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of atomic facts”. ( (2.06 , 2.11 , 2.201 , 2.202 , 2.203 , 3.318) →  4.2  →  (4.21 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5.01) ).

Hence, also here one could add in between ! ”.. with the .. / proposition itself contained / .. possibilities of the ..” ( (2.06 , 2.11 , 2.201 , 2.202 , 2.203 , 3.318) →  4.2  →  (4.21 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5.01) ).

Thereby, any longer ”.. the propositonal sign cannot be contained in itself .. because the functional sign already contains the prototype of its own argument and it cannot contain itself ..” ( (2.06 , 2.11 , 2.201 , 2.202 , 2.203 , 3.318) →  3.332 + 3.333 →  (4.2 , 4.21 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5.01) ).

In my book the fact that ”.. the functional sign already contains the prototype of its own argument ..” (3.333)  is the key to comprehend PToL  s i n c e  it  m e a n s  t h a t ”.. the functional sign already contains the .. possibilities of the existence and non-existence of atomic facts .. truth-possibilities of the .. truth-arguments of .. its  o w n ..” (2.06 , 2.1 , 2.201 , 2.203 , 3.333 , 4.2 , 4.3 , 4.41 , 5.01) , and  leads to Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  in order to avoid non-consistency. The key since even if it would be possible to ”.. the propositional sign .. be contained in itself ..” (3.332) , it would not be possible to say, ”.. put into words .. the expression of its truth-conditions” (3.318 , 3.332 , 3.333 , 4.022 , 4.03 ,  4.1212 , 4.2 , 4.21 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01 , 6.522)  because of this aim ”.. to draw a limit .. to the expression of thoughts .. in language ..” / ”from within”. (Preface / (4.112 , 4.114) ) ! g o e s  beyond itself , i. e. ”.. determines a logical place other .. outside ..” (3.4 , 3.41 , 3.411 , 4.064 , 4.0641)  the thought ”.. totality of propositions .. as a limited whole ..” (4.001 , 6.44 , 6.45 , 6.522). That ”to contain” means in the end ”to go beyond” may be an anomaly, but it is anyway an anomaly within and according the rules of the logic of correspondence theory.

”I conceive the proposition  –  like Frege and Russell  –  as a function of the expressions contained in it”. (3.318 , 3.332 , 3.333 , 4.4 , 4.431 , 5 , 5.01)

”No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the ”whole theory of types”)”. (3.318 , 3.332 , 3.333 , 4.4 , 4.431 , 5 , 5.01 , underline continues (3.333) )

”A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself. If, for example, we suppose that the function F(x) could be its own argument, then there would be a proposition ”F(F(fx) )” , and this outer function F and the inner function F must have different meanings ; for the inner has the form φ(f x) , the outer the form ψ(φ(f x)). Common to both funktion is only the letter ”F” , which by itself signifies nothing. ..”. (3.318 , 3.332 , 3.333 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

As a laymen’s example may be good enough such ”experiment” , that would it be possible a definite circle contain itself so that both circles, the outer and the inner, be the same, have the same (value of) surface area or the same size, dimension of  perimeter? I think not ( , and so also the law of identity would be broken, if  not (3.332 , 3.333) ).

”A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions”. (3.318 , 3.332 , 3.333 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”The expression of the agreement and disagreement with the truth-possibilities of the elementary propositions expresses the truth-conditions of the proposition. The proposition is the expression of its truth-conditions”. (3.318 , 3.332 , 3.333 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

If ”the propositional sign” could ”contain itself” , t h e n  not only ”.. the conditions of the truth and falsehood of the propositions .. the truth-possibilities of the elementary propositions .. the truth-arguments of propositions” (4.4 , 4.431 , 5.01)  would be contained in a well-formed proposition of correspondence theory, b u t  also ! ”the expression of agreement and disagreement with the truth-possibilities of the elementary propositions” (4.2 , 4.4 , 4.431 , 5.01)  would be present. Hence PToL would be an expression of reality itself ! in ”u – language” (instead of beeing ”.. a model .. picture of reality” (2.12 , 4.01) ) , which would be a clear contradiction ; a contradictory branch of solipsism (as we shall see).

That Wittgenstein says ”.. that solipsism strictly carried out coincides with pure realism ..” (5.64) , means in by book, the other way round, that the correspondence theory of truth as a truth theory of (ontological) realism coincides with solipsism in the beginning of its analysis. Independence means, as it stands between ”u – language” and reality in the beginning on the analysis of correspondence theory, that there is in the first place nothing else than a pure ”u – language” (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031) ; without any connexion to reality, and so either no provable  truth values of propositions yet possible to express. Hence, by virtue of first step of the logic of correspondence theory everyone can say ”.. my language mean .. my world” (5.6 + 5.63) ; as I mind it. It is to say that still incomplete, unfinished logic of correspondence theory can be used to ’justify’ everyone’s ”alternative ”truths”” as (possible) ”facts” , but with no proof ! no matter what  –  being the point of ”justifying”.

I am here now, to re-write this paper.

10 .     The consistency of picture theory / (4.0641)

To understand the magnitude, weight of paragraph (4.0641) , notwithstanding its (not very significant) numerical weight, also some previous paragraphs are introduced, and re-introduced. Before and after the main proposition (4.0641).

”Only facts can express a sense, a class of names cannot”. (1.13 , 2.06 , 2.063 ,  2.1 , 2.141 , 3 ,  3.12 + 3.14 , 3.141 ,  3.142 , 3.3 , 4 , 4.01 , 4.031 , 4.06)

The fact about ”facts” in Tractatus is that ”they” are , throughout applying correspondence theory of truth in ”u – language” , primarily ”pictures of reality” , i. e. m o d e l s ”.. of the reality as we think it is .. the existence and non-existencence of state of affairs” (2.06 , 2.1 , 2.12 , 4.01 , 4.1). There are not yet by the logic correspondence theory (2.024 , 4.061)  any real facts ; at least not those of their truth value being provable. ”A picture of reality” is every proposition, as a contingent* one, that ”.. represents .. its sense .. such and such a state of affairs” in a way that is possible to prove proposition ”true or false” , in the words of said theory of truth to prove ”..  the agreement or disagreement of its sense with reality ..” (2.221 , 2.222 , 4.01 , 4.031 , 4.06). Recall, that both truth values ”truth” and ”falsehood” are possible to the contingent proposition. Simply because of there are not yet any ”true or false” proposition, which means that in order to be able to be either ”true” or ”false” ! both truth values must be possible (2.11 , 2.201 , 2.202 , 2.203 , 3.02 , 4.1 , 4.2 , 4.25 , 4.3 , 4.41 , 5 , 5.01) , present in a well-formed proposition of correspondence theory.

*In my book also the ”.. two extreme cases .. tautological .. self-contradictory” (4.46 , 4.464) , contrary to the view of Wittgenstein (4.461 , 4.461 , 4.463) , are ”pictures of reality”.  W h y ?  –  A well-formed proposition of correspondence theory contains  a l l  of its ”truth-possibilities” , as linked above (2.11 .. 5.01)  show.

My view of ”pictures of reality” / of ”.. a proposition with a sense” (3 , 4)  will be said in Appendix 1.

Term ”a sense” , as an expression of Wittgenstein’s ”substance” – doctrine (2.021 , 2.0211 , 2.0212 , 3.202 , 3.203 , 3.23 ,  3.3 , 4.2 , 4.21 , 4.23 , 4.25 , 5.01) , indicates three different things. First in order that it is altogether possible to say, model ”.. the existence and non-existence of state of affairs” (2.06 , 2.12 , 4.01 , 4.1) , there must be already possible in pure, any ”pictures of reality” not yet made (2.06 , 2.1 , 4.01) , ”u – language” to make (declarative) sentences that ”.. represent such and such a state of affairs” (4.031). Otherwise nothing to ”assert” or ”deny” , in the second level of ”a sense” ; in the context of a proposition already being ”.. a picture of reality” (4.01). Finally, the third case of ”a sense” indicates the fact that to show, construct ”.. a proposition with a sense” (3 , 4)  presupposes what Wittgenstein says in the paragraph ! (4.2) ; with the ! point  t h a t ”.. a proposition .. contains .. already .. the possibilities of the existence and non-existence of atomic facts” ( 2.203 , 3.333 , 4.1 , 4.2 , 4.21 , 4.25 , 4.3 , 4.41 , 5.01).

”Every proposition must already have a sense ; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641 , 5.5151)

”One could say, the denial is already related the logical place determinated by the proposition that is denied. The denying proposition determines a logical place other than does the proposition denied. The denying proposition determines a logical place, with the help of the logical place of the proposition denied, by saying that it lies  o u t side the latter place. That one can deny again the denied proposition, shows that what is denied is already a proposition and not merely the preliminary to a proposition”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641 , 5.5151)

”.. The denying proposition determines a logical place other .. o u t side .. the denied proposition ..” (3.4 , 3.41 , 3.411 , 4.064 , 4.0641 , 5.5151)

”The denying proposition”?  –  What about ”the denied proposition”?  –  Best by way of an example.  –  The meaning of ”a logical place other”?

Let the proposition ”Finland is not a country with great sand deserts” to be an example of ”the denying proposition”. That what it denies, is evident, i. e. ”the truth” of the positive form of itself : ”Finland is a country with great sand deserts”. Which ”positive form” for one’s part asserts its ”truth”. Thus what is ”denied” here is ”the truth” of the positive proposition ”Finland is a country with great sand deserts”. (It is no sense, if the object of denial is the proposition, or what it represents, itself.) The other way round, proposition ”Finland is not a country with great sand deserts” says, asserts that it is ”true” that ”Finland is not a country with great sand deserts” ; which is to say that it denies, as a ”denying proposition” (4.0641) , ”the truth” of proposition ”Finland is a country with great sand deserts” , in a role of a ”denied proposition” (4.0641).

How it is possible by the logic of correspondence a positive proposition, like ”Finland is a country with great sand deserts” , to be false ?

Thus, now it is to ask what it presupposes to say that it is ”true” that ”Finland is not a country with great sand deserts”? It is a question of the significance of ”.. a logical place other ..” (4.0641). Obviously that the proposition ”Finland is a country with great sand deserts” is false presupposes that topography of Finland is formed in a different mannner ; for example that (it is true that) Finland is a country of great woods and thousands of lakes. Thus, to say that the proposition ”Finland is a country with great sand deserts” is false presupposes in principle all the other possibilities of the topography of Finland (3.3 , 3.31 , 3.311 , 3.4 , 3.41 , 3.411 , 3.42 , 4.064 , 4.0641 , 5.5151) , and that at least one possibility of these (other) possibilities of the topography of Finland is right, true. Making the ”falsehood” of the proposition ”Finland is a country with great sand deserts” possible, i. e. making ”.. the .. d i s agreement of  i t s  sense with reality ..” (2.21 , 2.221 , 2.222 , 4.031)  ! possible, by that there is in reality ”something” existing, ”a sense”* of the proposition ”Finland is a country with great sand deserts*” , t o ! d i s agree with (2.21 , 2.221 , 2.222 , 4.031 , 4.064).

Clearly what is said above by one example, also examples of what Wittgenstein calls ”positive fact” / ”positive proposition” and ”negative fact” / ”negative proposition” (1.13 , 2.06 , 2.063 , 2.1 , 2.12 , 3 , 3.12 , 3.14 , 4 , 4.01 , 4.06 , 5.5151) , can be extrapolated to any well-formed proposition of correspondence theory.

(If a ”positive proposition” is true, it’s a ”positive fact”. If a ”negative proposition” is true, it’s a ”negative fact”. )

This paragraph (4.0641)  is the only one which implies the way of circumventing that what in the beginning seems to a clear, by no means to circumvent, offence against the law of noncontradiction. It also suggests the way Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  comes true, and it is also one feature of ”the mystical” (6.44 , 6.45 , 6.522) , that is to say ”.. a limited whole .. determines a logical place .. o u t side ..” (4.0641 , 6.45) ! i t self.

”The proposition determines a place in logical space : the existence of this logical place is quaranteed by the existence of the constituent parts alone, by the existence of the significant proposition”. (1.13 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 2.1 , 2.15 , 2.151 , 2.1511 , 2.1514 , 3.12 , 3.14 , 3.203 , 3.3 , 3.4 , 3.41 , 3.411 , 3.42 , 4.0311 , 4.06 , 4.064 , 4.0641 , 5.5151 , underline continues (3.411) )

(That, what I am going to say below, concerning the meaning, the substance of paragraph 4.0641 , contradicts not paragraph 2.0211 , since in the latter paragraph  there would be the question of ”the sense” of  that ”another proposition” , the question on ”what” is ”the truth” of that ”another proposition” then based, premised on ?  –  And thereby Wittgenstein concludes 2.0212. )

Recall : ”a place in logical space” is ”a fact” , by applying the correspondence theory in ”u – language” (1.1 , 1.13 , 3.4  →  (2.21 , 2.221 , 2.222)  →  (2.0124 , 2.021 , 3.12 + 3.14 , 3.203 , 3.3 , 4.002 , 4.031 , 4.06) ). Once again, it is the logic of correspondence theory that effects what Wittgenstein says in paragraph (4.0641) , showing the way that independence (1.1 , 1.12* , 1.13** , 2.06 , 2.063  →  (2.024* , 4.061**) )  is combined with the fact ”.. pictures of reality .. must have something in common with .. reality ..” (1.13 , 2.06 , 2.063 , 2.1 , 2.12 , 2.16 , 2.17 , 2.18 , 3 , 3.12 , 3.14 , 4.06) ; in the sense of the provability of truth values of propositions. If and only if a proposition ”.. have something in common with .. reality .. to .. compare it with reality” (2.16 , 2.17 , 2.18 , 2.223)  is possible, in order to prove whether a proposition is ”true or false” (2.21 , 2.221 , 2.222 , 4.031). That independence applies further to ”the pictures of reality” (4.06)  means that the function of independence transforms to undecidability of the totality of ”pictures of reality” , i. e. to that what Wittgenstein’s ”fundamental thought” / ”.. My fundamental thought is .. That the logic of facts cannot be represented” ( (1.13 , 3.12 + 3.14 , 4.001 , 4.01 , 4.06)  ←  4.0312)  says. There will be always ”.. a logical place other ..” (4.0641) , a well-formed proposition, beyond any effort of logic ”.. in advance .. all at once ..” (5.47)  to express the totality of propositions that can be proved ”true or false”. Wittgenstein’s result is (in my book) an uncomputability result. And it is not to say that there exists well-formed propositions which cannot be ever said, but that there are ! yet ”truths” to be expressed (by new means of logic ; computers and algorithms).

”The propositional sign and the logical co-ordinates : that is the logical place”. (1.13 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 2.1 , 2.15 , 2.151 , 2.1511 , 2.1514 , 3.12 , 3.14 , 3.203 , 3.3 , 3.4 , 3.41 , 3.411 , 3.42 , 4.0311 , 4.06 , 4.064 , 4.0641 , 5.5151)

”The geometrical and the logical place agree in that each is the possibility of an existence”. (1.13 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 2.1 , 2.15 , 2.151 , 2.1511 , 2.1514 , 3.12 , 3.14 , 3.203 , 3.3 , 3.4 , 3.41 , 3.411 , 3.42 , 4.0311 , 4.06 , 4.064 , 4.0641 , 5.5151)

What is the object of ”.. the possibility of an existence” (3.411) , that ”.. a picture of reality .. determines ..” (1.13 , 2.06 , 2.063 , 3.12 , 3.14 , 3.4 , 3.411 , 4.01) ?

The object is ! not ”the possibility” of the existence of reality itself (2.0231). Why not? Since the existence of reality is a postulate, already premised by the correspondence theory. As a theory of (ontological) realism.

The object of ”.. the possibility of an existence” (3.411)  is the possibility of well-formed propositions of the correspondence theory, in fact in this point of PToL ”.. the possibility of .. the pictures of reality” (3.411 , 4.06) ! themselves. So far, until paragraph (4.0641) , Wittgenstein has shown, by constructing ”.. a model of reality” (2.06 , 2.1 , 2.12)  i n ”u – language” , i. e. the connexion between ”u – language” and reality, applying the logic of correspondence theory, that well-formed propositions of the said truth theory have to be ”.. pictures of reality” (2.06 , 2.1 , 2.12 , 2.16 , 2.17 , 2.18 , 2.21 , 2.221 , 2.222 , 4.031 , 4.06). Now (4.0641)  the question is ! how ”.. the pictures of reality” (4.06)  function, do the trick when concerning the possibility of propositions to have contingent truth values ”true or false” between the cases ”tautological” and ”self-contradictory” (4.46 , 4.464). Both truth values, ”true” and ”false” , have to be possible.  –  PToL have to do the trick that there it is a ! consistent possibility that (in short)  –

The well-formed proposition ”contains the possibility” of its both ”truth” and ”falsehood”.

The object of ”.. the possibility of an existence” (3.411)  will be the possibility of ”.. a logical place other ..” (4.0641) , as a necessary one ”possibility” to the consistency of PToL / correspondence theory. If there is no ”logical place other” , i. e. no ”.. other .. proposition with a sense” (4 , 4.031 , 4.0641 ) , then there is ”nothing” that ”a sense” (4.064)  of ”the denied proposition” (4.0641)  can disagree. This necessary ”.. possibility of an existence .. a logical place other ..” (3.411 , 4.0641)  i m p l i e s  that ! (that) ”.. other .. proposition with a sense” is true, i. e. ”.. its sense .. agrees with reality ..” (2.21 , 2.221 , 2.222 , 4.031).

Hence, because of ”.. a place in logical space .. is the possibility of an existence .. a logical place other ..” (3.4 , 3.411 , 4.0641)  it, consequently that applies to every ”place in logical space” , is  s o  t h a t  –

”Although a proposition may only determine one place in logical space, the whole logical space must already be given by it”. (1.13 , 2.021 ,  2.0211 , 2.0212 , 2.06 , 2.063 , 2.1 , 2.15 , 2.151 , 2.1511 , 2.1514 , 3.12 , 3.14 , 3.203 , 3.3 , 3.4 , 3.41 , 3.411 , 3.42 , 4.0311 , 4.06 , 4.064 , 4.0641 , 5.5151)

Every ”logical place” have its own set of possible ”logical place other” (3.4 , 3.41 , 3.411 , 4.064 , 4.0641 , 5.5151). These to each other ”(an)other propositions” are interrelated throughout the possibility on their both ”truth” and ”falsehood” , and so ”the whole logical space” (3.42)  is present.

Hence, ”.. the whole logical space must already be given..” (3.42)  because of ”.. one place in logical space .. presupposes the forms of  a l l  propositions ..” (3.4 , 3.311 , 3.42)  that are expressions of ”.. the possibility of an existence ”.. logical place other ..” (3.3 , 3.31 , 3.311 , 3.4 , 3.41 , 3.411 , 3.42 , 4.064 , 4.0641 , 5.5151) , and which propositions then in effect include or exlude each other by their truth.

As in the example of the model of topography of Finland all different, not yet standing, possibilities of topographical  forms include or exlude each other by their (truth value) ”truth” ; in many different ways, like in special kind of jigsaw puzzle.

Thereby, when in the first level of Wittgenstein’s aim* (Preface / (4.112 , 4.114) ) ”u – language” must be postulated and then in its* second level of applying in ”u – language” correspondence theory where by the logic of truth-theory there is ! no choice but ”.. In the proposition the form of its sense is contained ..” (3.13 , 4.2) , it  i s  inevitable that ”.. the forms of all propositions ..” of any ”.. logical place other .. must already be given ..” (2.0124 , 3.3 , 3.31 , 3.311 , 3.4 , 3.41 , 3.411 , 3.42 , 4.002 , 4.064 , 4.0641 , 4.2 , 4.23 , 5.01 , 5.5151).

”The totality of .. pictures of reality” (1.13 , 2.06 , 2.063 , 2.1 , 3 , 3.12 , 3.14 , 4 , 4.001 , 4.06)  is a nexus, will be a nexus of all sets of ! compatible propositions, that is to say all the possible different, contingent combinations of ”.. the truth-possibilities of .. the truth-arguments of propositions” (2.06 , 4.1 , 4.25 , 4.26 , 4.27 , 4.28 , 4.3 , 4.41 , 4.46 , 4.464 , 5.01)  which comport with. Anyway this totality of all sets of compatible propositions is ”.. without number” (4.0312 , 4.128 , 6.4321). That ”.. the whole logical space must already be given ..” (3.42) , by a nexus* of all sets of compatible propositions, but ! which* ”.. cannot be said .. in advance .. all at once ..” (1.13 , 2.021 , 2.06 , 2.063 , 2.17 , 2.18 , 2.2 , 3.203 , 3.3 , 4.12 , 4.121 , 4.1212 , 4.128 , 4.2 , 4.23 , 4.25 , 4.3 , 4.41 , 5.01 , 5.47  →  (5.55 , 5.5571 , 6.522 , 7) )  i s  the essence of Wittgenstein’s ”fundamental thought” (4.0312).

”Every proposition must already have a sense ; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc”. (1.13 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 2.1 , 2.15 , 2.151 , 2.1511 , 2.1514 , 3.12 , 3.14 , 3.203 , 3.3 , 3.4 , 3.41 , 3.411 , 3.42 , 4.0311 , 4.06 , 4.064 , 4.0641 , 5.5151)

”Must the sign of the negative proposition be constructed by means of the sign of the positive? Why should one not be able to express the negative proposition by means of a negative fact? (Like : if ”a” does not stand in a certain relation to ”b” , it could express that aRb is not the case.) But here also the negative proposition is indirectly constructed with the positive. The positive proposition must presuppose the existence of the negative proposition and conversely”. (1.13 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 2.1 , 2.15 , 2.151 , 2.1511 , 2.1514 , 3.12 , 3.14 , 3.203 , 3.3 , 3.4 , 3.41 , 3.411 , 3.42 , 4.0311 , 4.06 , 4.064 , 4.0641 , 5.5151)

The key point is in the last sentence : ”.. The positive proposition must presuppose the existence of the negative proposition and conversely” (4.0641 , 5.5151). The point is that well-formed propositions, the possibility of (their) truth values, presuppose each other. At least when it is the case in between ”.. two extreme cases .. tautological .. self-contradictory” (4.46 , 4.464) ; when it concerns the existence of propositions with contingent, possible truth values of both ”true” and ”false”. These in between ”.. two extreme cases .. ” (4.46)  contingent propositions have ”.. the truth-possibilities of the elementary propositions .. the truth-arguments of propositions” (4.46 , 5.01)  b o t h ”true” a n d ”false”. They have the possibility to be either ”true” or ”false”. Either ”.. such and such a state of affairs .. agrees with reality or not ..” (2.21 , 2.221 , 2.222 , 4.031 , 4.464). The problem of the consistency of PToL / well-formed proposition of correspondence theory concerns the possibility of ”.. disagreement of  i t s  sense with reality .. falsity ..” (2.21 , 2.221 , 2.222 , 4.031 , 4.464).

To come back to paragraph (4.0641) , it is evident, ”.. the proposition denied ..” (4.0641)  means that the ”truth” of a proposition is denied ( , as above shown by an example). It is not ! as well the proposition itself or its ”sense” (4.031)  that is denied, but the truth value, and precisely the ”truth”. Thus ”.. the denied proposition ..” (4.0641)  is ”false”. Now the principal, already (in chapter 6) made, question is ! how it is logically possible of a well-formed proposition of correspondence theory to be ”false” ?  –  As a truth-theory of (ontological) realism!

What makes the possibility of ”.. n o n-existence of states of affairs .. a negative fact ..” (2.06 , 5.5151) ? (For example, it is true that Finland is not a country with great sand deserts  –  but thousands of lakes.)

Anyway one may (and it’s no wonder) wonder first of all ! what is the argument, premise to definition of well-formed proposition of correspondence theory? To argue ! that a well-formed proposition of correspondence theory contains  a l l  the possibilities of its truth values,  both ”truth” and ”falsehood” (2.06 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 4.25 , 4.3 , 5 , 5.01  →  (4.46 , 4.464) ) , and ! not to fall into a contradiction.

How it is logically possible that (to say it short) a well-formed proposition ”contains the possibility” of its both ”truth” and ”falsehood” ?

These wonders, astonishments of the possibility of well-formed proposition of correspondence theory to be ”false” and the possibility of correspondence theory to be consistent are interrelated. The answer to both questions is actually quite simple. Instead of saying a well-formed proposition ”contains the possibility” of its both ”truth” and ”falsehood” , it is to say  –

A well-formed proposition of correspondence theory ”contains the possibility” of  b o t h  its  o w n ”truth” a n d ! ”the truth” of  a n  o t h e r ”proposition”.

This definition of a well-formed proposition of correspondence theory makes it truth-preserving. Thus, finally Wittgenstein’s aim (Preface / (4.112 , 4.114) )  is an effort to decide all the propositions that are, can be provable true.

”A n  o t h e r ”proposition”” is precisely ”.. a logical place other .. o u t side the ..” (4.0641)  first said ”false” proposition, ”.. the proposition denied ..” (4.0641) , and throughout the logic of correspondence theory the ”other ”proposition”” must be by ”.. a logical necessity ..” (6.375) ”true”.  –  Why ?

If (ontological) realism is presupposed as it along correspondence theory is, at least in my book, then in the case that a proposition is false there must be ”something” in reality what ”.. such and such a state of affairs .. agrees with .. not” (2.21 , 2.221 , 2.222 , 4.031).

Reality cannot be empty, formed by ”.. non-existence of states of affairs ..” (1, 1.1 , 2 , 2.06 , 2.063). If reality is empty there exists ! ”nothing” that a proposition or what it represents is suppose to agree with ! not (2.21 , 2.221 , 2.222 , 4.031). In other words the falsehood of a proposition is impossible, not only to prove, but in principle not possible. Which ”non-possibility” turns out to be a contradiction. If there is ”nothing” / ! ”not a thing” to agree with not, then a proposition or what it represents ! have to agree ! ! ”everything” , whatsoever. And thereby (the meaning of) ”the falsehood of a proposition” converts inevitable ! to ”truth of a proposition” (4.061 , 4.062) , and thereby  –

”.. contradiction fills the whole logical space and leaves no point to reality ..” (4.463).

Ergo, to avoid a contradiction, there must be ”something” that represents  i n ”.. a model of reality .. the existence of states of affairs” (2 , 2.06 , 2.1 , 2.11 ,  2.12)  that ”.. a sense .. of the proposition denied .. agrees with .. not ..” (2.21 , 2.221 , 2.222 , 4.031 , 4.064 , 4.0641). This necessary ”something” is precisely ”.. a logical place other .. o u t side .. the denied proposition ..” (3.4 , 3.41 , 3.411 , 4.064 , 4.0641 , 5.5151). And since this ”an other ”proposition”” stands  f o r ”.. the existence of states of affairs” (2 , 2.06 , 2.1 , 2.11 , 2.12)  it must be by definition true ; in order to (be able to) ! show ”.. the existence of states of affairs” (2 , 2.06 , 2.1 , 2.11 , 2.12)  that ”.. a sense .. of the proposition denied .. agrees with .. not ..” (2.21 , 2.221 , 2.222 , 4.031 , 4.064 , 4.0641).

One can say that ”.. the logical place of the proposition denied .. ” (4.0641)  concerns the logical, i. e. the consistent possibility ”.. of the proposition denied ..” to be false.

It is ”.. a logical necessity ..” (6.375)  the other ”proposition” to be true since by representing ”.. the existence of states of affairs” (2 , 2.06)  i t  replaces ! the not possible ”.. n o n-existence of states of affairs ..” (2.06). If there is not ”something” existing in reality, which ”a sense” of a proposition ”.. agrees with .. not” (2.21 , 2.221 , 2.222 , 4.031 , 4.064) , then it is ”.. a logical impossibility” (6.375)  of a proposition to be false.

Let’s consider the question in the context of contingent, possible truth values ”true or false” ; that is to say in the context between ”.. two extreme cases .. tautological .. self-contradictory” (4.46 , 4.464). It is a question of the possibility that ”.. the significant proposition .. represents such and such a state of affairs” in a way that  ”.. such and such a state of affairs .. agrees with reality .. not ..” (2.21 , 2.221 , 2.222 , 4 , 4.031 , 4.464).

Recall, correspondence theory is a truth-theory of (ontological) realism, i.e. ”.. what is the case, and .. is not the case” (1.12 , 2.06 , 2.063)  exists independent of any (human) mind and its means, artefacts. Which, the independent existence of reality of any (human) mind and its means, presupposes not (at all) paradoxically the determination of reality, by means of (human) mind, i. e. to conceive world, reality in ”language” / ”u – language” , in order to ”.. make ourselves pictures of .. the reality” (2.06 , 2.1 , 4.01 , 4.06).

Thus, by the necessary determination of reality, the question of the possibility that ”.. the significant proposition .. represents such and such a state of affairs” in a way that  ”.. such and such a state of affairs .. agrees with reality .. not ..” (2.21 , 2.221 , 2.222 , 4 , 4.031)  can be transformed into the question of the possibility of ! a proposition to be ”false” ?

”One could say, the denial is already related the logical place determinated by the proposition that is denied. The denying proposition  d e t e r m i n e s  a logical place  o t h e r  than does the proposition denied. The denying proposition determines a logical place, with the help of the logical place of the proposition denied, by  s a y i n g  that  i t  lies  o u t side the latter place. That one can deny again the denied proposition, shows that what is denied is already a proposition and not merely the preliminary to a proposition”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641)

”.. The denying proposition  d e t e r m i n e s  a logical place  o t h e r .. with the help of the logical place of the proposition denied, by  s a y i n g  that  i t  lies  o u t side the latter place ..” (4.0641).

So  –  ”.. a place in logical space .. is the possibility of an existence .. a logical place other ..” (3.4 + 3.411 + 4.0641) , when ”a sense” of a ”proposition” is denied, that is to say ”.. the agreement .. of its sense with reality ..” (2.221 , 2.222 , 4.031)  is denied by the denying ”proposition” itself. For example proposition ”Finland is not a kingdom” denies itself the truth of ”its” positive form / ”Finland is a kingdom”.

What is the trick in this (notwithstanding its numerical weight pivotal) paragraph 4.0641 to overcome, erase the abovesaid    contradiction    ?

H o w  –  ”.. a logical place  o t h e r ..” (3.4 , 3.41 , 3.411 , 4.0641) , i. e. an o t h e r  ”.. proposition with a sense” (3.4 , 3.41 , 3.411 , 4 , 4.064 , 4.0641)  i s  the key correspondence theory to be correct ?

An another proposition  –  ”.. a logical place other ..” (4.0641)  –  is necessary. Otherwise it would be not possible to say, assert a proposition to be ”true  o r  false” , i. e. t o ! d e n y  the truth of a proposition.

The key, plain and (beautiful) simple, is that the ”truth” of an another proposition  r e p r e s e n t s, is an exression or a manifestation of the  p o s s i b i l i t y  of a(nother) proposition to be ”false”.

Recall part 6. (of my paper).

So  –  ”.. a place in logical space .. is the possibility of an existence .. a logical place other ..” (3.4 + 3.411 + 4.0641) , when the possibility of ”falsehood” of a proposition is in question.

This paragraph is the only one which suggests, implies the way of circumventing that what in the beginning seems to a clear, no way to circumvent, offence against the law of noncontradiction. It / (4.0641)  also implies how Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  realises.

”The picture presents the facts in logical space, the existence and non-existence of atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , ! 2.11 , 2.12 , 2.201 , 2.202 , ! 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”The facts in logical space” (1.13 , 2.11)  of the correspondence theory (2.21 , 2.221 , 2.222 , 3.12 + 3.12 , 4.06).

”Das Bild stellt die Sachlage im logischen Raume, das Bestehen und Nichtbestehen von Sachverhalten vor”. (2.11)

In my book ”die Sachlage” / ”the facts” and ”das Bestehen und Nichtbestehen von Sachverhalten” / ”the existence and non-existence of atomic facts” are synonyms, with a meaning that is the same. Thus ”die Sachlage” / ”the facts” is going to be substituted by ”das Bestehen und Nichtbestehen von Sachverhalten” / ”the existence and non-existence of atomic facts” in paragraph 2.203 ( , and so on .. ! 4.25 .. ).

”The picture is a model of reality”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”Model of reality” (2.12)  throughout the correspondence theory  –  applying it in ”u – language”.

”The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Recall the detemination of ”reality”* (2.06) , and substitute ”it”* here (2.201)  by ”the existence and non-existence of atomic facts”.

”The picture represents a possible state of affairs in logical space”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”The picture  c o n t a i n s  the  p o s s i b i l i t y  of the state of affairs which it represents”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , ! 2.11 , 2.12 , 2.201 , 2.202 , ! 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Let us remember here the synonyms in paragraph 2.11 , and perhaps look at the original text.

”Das Bild  e n t h ä l t  die  M ö g l i c h k e i t  der Sachlage, die es darstellt”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , ! 2.11 , 2.12 , 2.201 , 2.202 , ! 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Hence, in my book, by substituting ”the facts” with ”the existence and non-existence of atomic facts” we get, can conclude :

”The picture  c o n t a i n s  t h e  p o s s i b i l i t y  of  the  existence  and  non-existence  of atomic facts”. (2.11 + 2.203)

And here (2.11 + 2.203 + 3.02 + ! 4.25)  it is not only as if for fun to compare original text in German with translations, but to show what is the case. By original text we get, can conlude :

”Das Bild  e n t h ä l t  die  M ö g l i c h k e i t  das  Bestehen  und  Nichtbestehen  von  Sachverhalten, die es darstellt”. (2.11 + 2.203)

(The form ”.. das Bestehen und ..” (2.11 + 2.203)  may be not right according to german grammar, anyway here is  the thought essential. )

”The thought contains the  p o s s i b i l i t y  of the state of affairs which it thinks. What is thinkable is also possible”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”In order to know an object, I must know not its external but all internal qualities”. (2.01231 , 2.0124 , 2.014 , 2.0141 , 2.022 , 2.023 , 4.1221 , 4.123)

”If all objects are given, then at the same time all possible state of affairs are also given”. (2.01231 , 2.0124 , 2.014 , 2.0141 , 2.022 , 2.023 , 4.1221 , 4.123)

”Objects contain the possibility of all states of affairs”. (2.01231 , 2.0124 , 2.014 , 2.0141 , 2.022 , 2.023 , 4.1221 , 4.123 , underline continues (2.0141) )

”The possibility of its occurring in states of affairs is the form of an object”. (2.01231 , 2.0124 , 2.014 , 2.0141 , 2.022 , 2.023 , 4.1221 , 4.123)

”It is clear that however different from the real one imagined world may be, it must have something  –  a form  –  in common with the real world”. (2.01231 , 2.0124 , 2.014 , 2.0141 , 2.022 , 2.023 , 4.1221 , 4.123)

”This fixed form consits of the objects”. (2.01231 , 2.0124 , 2.014 , 2.0141 , 2.022 , 2.023 , 4.1221 , 4.123)

Wittgenstein’s thought, that the provability of the truth values of propositions are based, premised on ”objects” (2.014 , 2.02 , 2.0201 , 2.021  →  (1.13 , 2.06 , 2.063 , 2.201 , 4.25 , 5 , 5.01) ) , i. e. the meanings of names in their propositional context (3.203 , 3.3 , 4.23) , is indeed natural and evident. The existence of any language presupposes, is based on the meanings of its names in their propositional context. And here in Tractatus one has to take into account the logic of correspondence theory, to fully understand Wittgenstein’s ”substance” – doctrine (2.021).

”The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of  atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

( ”Atomic facts” is synonym to  –  means the same than  –  ”states of affairs”. )

Independence is an external relation between ”u – language” and reality. Thus that

”What the picture must have in common with reality in order to be able represent it after its manner – rightly or falsely  –  is its form of representation”. (2.022 , 2.16 , 2.161 , 2.17 , 2.18 , 2.2 , 3.12 , 3.14 , 4.01 , 4.06)

can take its place only ! ”i n  language .. within ..” (Preface / 4.112 , 4.114).

And not (at all) strange enough, it avoid to be circular argument, Wittgenstein determinates reality by means of correspondence theory, that is throughout the same theory, which asks to conceive reality.

To do the determination of reality by means of correspondence theory itself, and here we are again doing with self-reference, is (an advantage) to avoid the dilemma of ! what is the relation between correspondence theory* and that ”theory” , which would do  o u t side of it* the conception of reality. By means of correspondence theory we are in same nexus, catecory.

Why is ”the determination of reality by means of correspondence theory itself” not circular argument ?

”The existence and non-existence of states of affairs is reality. (We call the existence of states of affairs a positive fact, and their non-existence a negative fact.)”. ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031)

This, ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031) , take place ! to wit in the ”u – language” independent of reality. Hence, there is not a single proposition, which one can point and say, assert proposition to be (provably) ”true or false”.  –  To compare is not (yet) possible,

Thus, ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031)  is a tautology. It is a tautology to say that .. ”the reality” is a totality of true ”positive” and true ”negative” propositions (1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.21 , 2.221 , 2.222 , 4.031 , 5.5151)  because it is to say nothing more, nothing less than, for example .. ”it’s raining or not”.

The determination of reality by means of correspondence theory itself must be a tautology in that sense that the determination said is only prequisite, first step to prove correspondence theory adequate.  –  Otherwise, if not tautology, the determination said would be a circular argument.

If one premises correspondence theory of truth, then the self-referential determination said is intuitive, ! given that it is a tautology.

Anyway, having said that fact of tautology, one must add that the result to prove correspondence theory valid cannot be ! anymore a tautology ; if so, one have ! ended up to a circular argument, unto itself.  –  We would be in the situation of Sisyfos.

How the fact, that proposition (4.061)  is for the sake of correspondence theory to be consistent, emerges by saying ”independent of reality” , instead of ”independent of facts” ?

This is easier to realize if we replace a ”.. proposition represents such and such a state of affairs” (4.031) simply with ”x” , and then let ”reality” be replaced by ”y”.

So, what it means if (some) ”x” is not independent of (some) ”y” ?

It means that always when ”x” , then also ”y” (is at least possible to be with).

Now let’s get back to the situation, thinking experiment that a ”.. proposition represents such and such a state of affairs” (4.031)  not independent of ”reality”.  –  What happens?

The obvious result is that always when a ”.. proposition represents such and such a state of affairs” (4.031)  there is also ! the expression of reality ; it is to say ! the ”reality” which that ”.. such and such a state of affairs .. a g r e e s  with .. or not ..” (2.21 , 2.221 , 2.222 , 4.031).

And this, to put a ”.. proposition represents such and such a state of affairs” (4.031)  in an appearance together with ”reality” , is not possible if we presuppose correspondence theory of truth to escape circular argument and to be consistent : To wit in the instance of proposition to be ”true” , proposition express (also) the ”reality” to agree with and in the instance of proposition to be ”false” , proposition express (also) the ! ”reality” to agree with not.

A .     In the instance of proposition to be ”true” the result is  –  a circular argument.

B .     In the instance of proposition to be ” false” the result is  –  vicious circle  –  contradiction.

”The world is all that is the case”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”The world is the totality of facts, not of things”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”The world is determined by the facts, and by their being all the facts”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”For the totality of facts determines both what is the case, and also all that is not the case”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

To recollect ”the aim of the book” (Preface) and the correspondence theory of truth (2.21 , 2.221 , 2.222 , 2.223 , 4.031)  to fulfil ”the aim” , it is logical that Wittgenstein at first determines ”the world” , ”the reality” (2.06 , 2.063). A determination of ”reality” not only because ”reality” is a concept of the theory of truth, but it is precisely cause of the logic of the correspondence theory (4.061) ; otherwise we are not able to ”.. make ourselves pictures of facts” ( (1.1)  →  2.06 , 2.063  →  (2.1) ).

And  s i n c e  there are no ”facts” , i. e. ”propositions” , that can be ”true or false” (3.12 + 3.14 , 4.06) , other than throughout applying the correspondence theory to, or in ”u – language” , it is precisely the ! ”logical space” of the theory of truth being in question where ”the facts” are to be done  –

”The facts in logical space are the world”. (1.13  →  (2.21 , 2.221 , 2.222)  →  (3.12 + 3.14 , 4.031 , 4.06) ).

”The facts in logical space are the world” (1.13) , constituted by the correspondence theory of truth ; by its ”logical space” in ”u – language” , and therefore the ”logical space” needed is to be determined by the correspondence theory itself.  –  Tractatus, a book of cool use of self-reference.

”What is the case  –  a fact  –  is the existence of states of affairs”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”A state of affairs (a state of things) is a combination of objects (things)”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”It is essential to things that they should be possible constituents of state of affairs”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

(To my mind it is better to translate ”Der Sachverhalt” as ”a state of affairs” , but let it be some times otherwise, with these ! fine-tuned terms. )

”.. If things can occur in atomic facts, this possibility must already lie in them. (A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.) .. If I can think of an object in the context of an atomic fact, I cannot think it apart from the possibility of this context”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”If all objects are given, then at the same time all possible state of affairs are also given”. (2.0124)

”All objects are given” ?  –  ”U – language”.

Wittgenstein’s doctrine of ”of the substance of the world” function with the (chosen) theory of truth. The logic of correspondence (4.061)  makes it to ”.. a  l o g i c a l  necessity ..” (6.375)  that  –

”Objects contain the possibility of all states of affairs”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

”The possibility of its occurring in states of affairs is the form of an object”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.01 , 2.011 , 2.012 , 2.0121 , 2.0122 , 2.0123 , 2.0124 , 2.014 , 2.0141 , 2.021 , 2.0211 , 2.0212 , 3.203 , 3.3 , 4.031)

This ”form of an object” (2.014 + 2.0141)  is the quality  –  essence of well-formed propositions  –  who’s ”.. the logic .. cannot be represented” (4.0312 , 4.128).

It is time to outline this (perhaps little bit messy) part of the paper.

Simply : If not ”u – language” , t h e n  it  is  n o t  possible … ”.. make to ourselves .. the totality of .. pictures of reality” (2.1 + 4.001 + 4.06).

Simply : If not ”u – language” , t h e n  there is  n o  place or sphere to apply correspondence theory of truth to achieve, find out the necessery and suffiecient terms for those propositions, that can be ”true or false”. It is clear that ”find out the necessery and suffiecient terms for those propositions, that can be ”true or false”” (applying some theory of truth) is prequisite to examine the possibility to express all propositions, that can be ”true or false”. It is these ”necessery and suffiecient terms” which show that Wittgenstein’s aim is not possible / (2.18 , 4.0312 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321).  –  How, it is to be answered later.

”U – language” constitutes the basis, the space to Wittgenstein’s effort, and ”u – language” is just that he calls ”the substance of world” (2.021). If not that basis, then no ”substance” to apply some theory of truth. To make ”thoughts” and ”facts” (1.13 , 2.1 , 3 , 3.12 , 3.14 , 3.5 , 4 , 4.06).

”Objects form the substance of the world. Therefore they cannot be compound”. (1.1 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031)

(Propositions 2.06 and 2.063 I book later, in the context of how Wittgenstein determines ”the reality”. )

”If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true”. (1.1 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031)

It / (2.0211)  would be circular argument because of ”sense” is a prequisite a proposition can be ”true or false”.

”It would then be impossible to form a picture of the world (true or false)”. (1.1 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031)

”The name means the object. The object is its meaning. (”A” is the same sign as ”A”)”. (1.1 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031)

”Only the propositon has sense ; only in the context of a proposition has a name meaning”. (1.1 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031)

Wittgenstein wants to be precise. Else ”.. only in the context of a proposition has a name meaning” sounds quite evident, trivial.  –  But not trivial in the context of (3.202 , 3.23 , 4.2 , 4.23 , 5 , 5.01) !

”In the proposition a state of affairs is, as it were, put together for the sake of experiment. One can say, instead of, This proposition has such and such a sense, This proposition represents such and such a state of affairs”. (1.1 , 2.021 , 2.0211 , 2.0212 , 2.06 , 2.063 , 3.203 , 3.3 , 4.031)

Thus, to put together (2.021 + 2.0211 + 2.0212 + 3.203 + 3.3 + 4.031)  it is ”u – language” (2.0124 , 4.002) , which ”form the substance of the world” ( (1.13)  ←  2.021 →  ( 3.12 + 3.14 , 4.06) ) ; the one side or layer of Wittgenstein’s doctrine of the ”substance”.

To get a grip of Wittgenstein’s doctrine of the ”substance” , as a whole, one must take along the other side, layer of that doctrine.

5 .     The correspondence theory of truth

If there is still evident, undeniable facts in Tractatus, along with (the meaning of) ”facts” , ”thoughts” and ”draw a limit” , then one is the theory of truth.

”The picture agrees with reality or not ; it is right or wrong, true or false”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05)

”What the picture represents is its sense”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05 , 4.031)

”In the agreement or disagreement of its sense with reality, its truth or falsity consists”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05 , 4.031)

”In order to discover whether the picture is true or false we must compare it with reality”. (2.21 , 2.221 , 2.222 , 2.223 , 2.224 , 2.225 , 3.04 , 3.05 , 4.031)

Anyway one must take into account that PToL / ”the proposition is a picture of reality ..” (4.01)  is not direcly an act, statement of the correspondence theory.

”The proposition is a picture of reality. The proposition is a model of the reality as we think it is” (4.01)

How ”.. the proposition is a model of the reality ..” ?

As said before ”u – language” , or if you wish (some) ”language” , function with the chosen theory of truth as ”the substance of the world” , and here ! for obvious reasons the theory is the correspondence theory.  –  For ”obvious reasons” a bit later / the logic of correspondence theory.

Thus, ”.. the proposition is a model of the reality as we think it is” (2.06 , 2.1 , 3.5 , 4.01) , when applying the correspondence theory of truth to, or in ”u – language”.

So, the role of a ”language” as ”.. the substance of the world ..” (2.021 , 3.203 , 3.3 , 4.031)  is to be the necessary basis, platform when : ”We make to ourselves pictures of facts” (2.1 , 3.5 , 4.01 , 4.2211) , i. e. in the first place / Russell’s paradox ”propositions” , that ”can be true or false” (4.06 , 4.211 , 5 , 5.01).

”Even if the world is infinitely complex, so that every fact consists of infinitely many states of affairs and every state of affair is composed of infinitely many objects, there would still have to be objects and state of affairs”. (4.2211)

In the context of proposition 1.13 there could be with good reason (in) between, after ”.. facts in logical space ..”  an addition, enhancement, ”of correspondence theory” , and accordingly with propositions 2.1 and 3.5 an addition following, ”throughout the (applying of) correspondence theory of truth (in ”u – language”)”.

”The applied, thought, propositional sign, is the thought”. (3.5)

Thus, we have first correspondence theory in its original form, which is easy to get by substituting term ”picture” with term ”proposition” or ”sentence” in paragraps (2.21 , 2.221 , 2.223 , 2.224 , 2.225).

Only the coordination of ”u – language” and the correspondence theory in its original form accomplish the picture theory.

(Correspondence theory has also another ”original form” , without representing ”sense”. )

With respect to PToL Tractatus is actually an analysis of applying the correspondence theory of truth in ”u – language” to get, derive and eventually decide all well-formed propositions, i. e. all propositions that can be provably and consistent ”true or false” ; to overcome Russell’s paradox.

6 .     The logic of the correspondence theory

What are the ”obvious reasons” that the theory of truth to overcome Russell’s paradox, is the correspondence theory?  –  First a little introduction.

If we agree the premise that as a corollary of Russell’s paradox there are anymore, not yet a single proposition that can be ”true or false”  –  at least provably and consistent  –  then the starting point (or first step) of an analysis of applying the correspondence theory of truth in ”u – language” is the same. Hence, what brings Russell’s paradox and the correspondence theory of truth together is that starting point of correspondence theory and corollary of Russell’s paradox are equal.

First pas of applying the correspondence theory of truth in ”u – language” is to wit, precisely that there are not a single proposition that can be ”true or false” , at least provably and consistent.  –  And this ”first pas” is not an evidence that correspondence theory is invalid, but has its (logical) premise  –

”If  one does not observe that proposition have a  s e n s e  indenpendent of the facts, one can easily believe that true and false are two relations between signs and things signified with equal rights. One could then, for example, say that ”p” signifies in the true way what ”¬ p” signifies in the false way, etc.”. (4.061)

What is the significance, ! magnitude of this  –  ”if .. not .. proposition have a  s e n s e  independent of the facts .. then .. ”p” signifies in the true way what ”¬ p” signifies in the false way, etc.” (4.061) ?

The answer is that, if paragraph (4.061)  stands not, then the correspondence theory of truth is not consistent, b u t  contradictory.

T h i s  fact  turns out, emerges distinctly when saying ”independent of reality” instead of ”independent of facts”.

This otherwise saying does not change the meaning of proposition (4.061) , because Wittgenstein determines ”reality” as ”facts” , and these ”facts” are (then) precisely ”true” or ”false” propositions throughout correspondence theory , i. e.  ”.. proposition represents such and such a state of affairs” , which ”.. agrees with reality or not ..” (2.21 , 2.221 , 2.222 , 4.031).  –  The answer, why Wittgenstein determines, even must determine ”reality” , little bit later.

”The existence and non-existence of states of affairs is reality. (We call the existence of states of affairs a positive fact, and their non-existence a negative fact.)”. (2.06 , 2.063)

”The total reality is the world”. (1, 1.1 , 1.11 , 1.12 , 1.13 , 2 , 2.06 , 2.063)

”A positive fact” is a ”proposition” , that ”.. represents such and such a state of affairs” , which ”.. agrees with reality ..” (2.21 , 2.221 , 2.222 , 4.031)  and concequently ”a negative fact” is a ”proposition” , that ”.. represents such and such a state of affairs” , which ”.. agrees with reality .. not ..” (2.21 , 2.221 , 2.222 , 4.031) , i. e. it is not the case that ”.. proposition represents such and such a state of affairs” , which ”.. agrees with reality ..” (2.21 , 2.221 , 2.222 , 4.031). For example it is not the case that ”Finland is a kingdom” (as Sweden is), and so it is ”true” / ”a negative fact” (2.06)  that ”Finland is not a kingdom” , the case being ”true” / ”a positive fact” (2.06)  that ”Finland is a republic”.

Thus, ”the reality” consists of all true ”positive” and ”negative” propositions (1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.21 , 2.221 , 2.222 , 4.031 , 5.5151) , and the totality of these propositions ”.. is the world”* (2.063) , which are indeed basis to model ”it”*.  –  ”Reality” has to be conceived in order to be possible to say that (2.12).

And ! truly, Wittgenstein can determine, conceive ”the reality” with the correspondence theory of truth nonetheless the fact that it’s precisely correspondence theory, which ask the determination of ”the reality”.

How the fact, that proposition (4.061)  is for the sake of correspondence theory to be consistent, emerges by saying ”independent of reality” , instead of ”independent of facts” ?  One must take into account that the concept ”reality” is first in the correspondence theory, and ”facts” are then (only) the necessary definition of ”reality” ! so that we are able to ”.. make ourselves .. pictures of reality” (1 , 1.1 , 2 , 2.06 , 2.063 , 2.1 , 3.12 + 3.14 , 4.06).  –  ”Pictures of ”w h a t”” ?  –  Since independence, that question is inevitable.

Suppose that a ”.. proposition has such and such a sense .. represents such and such a state of affairs” (4.031)  so that ”.. a sense .. a state of affairs” is not independent of the reality. Now, take a look to the consistency of correspondence theory and you can see, that correspondence theory to be consistent is not possible, it stands anymore.

This is easier to realize if we replace a ”.. proposition represents such and such a state of affairs” (4.031) simply with ”x” , and then let ”reality” be replaced by ”y”.

So, what it means if (some) ”x” is not independent of (some) ”y” ?

It means that always when ”x” , then also ”y” (is at least possible to be with).

Now let’s get back to the situation, thinking experiment that a ”.. proposition represents such and such a state of affairs” (4.031)  not independent of ”reality”.  –  What happens?

The obvious result is that always when a ”.. proposition represents such and such a state of affairs” (4.031)  there is also ! the expression of reality ; it is to say ! the ”reality” which that ”.. such and such a state of affairs .. a g r e e s  with .. or not ..” (2.21 , 2.221 , 2.222 , 4.031).

And this, to put a ”.. proposition represents such and such a state of affairs” (4.031)  in an appearance together with ”reality” , is not possible if we presuppose correspondence theory of truth to escape circular argument and to be consistent : To wit in the instance of proposition to be ”true” , proposition express (also) the ”reality” to agree with and in the instance of proposition to be ”false” , proposition express (also) the ! ”reality” to agree with not.

A .     In the instance of proposition to be ”true” the result is  –  a circular argument.

B .     In the instance of proposition to be ” false” the result is  –  vicious circle  –  contradiction.

It’s not enough, with  A .  and  B . .  –  Also the law of identity seems to be broken.  –  Actually the law of identity is broken already in  A . .

How to see in  A . ! the difference of sides of this ! ”Janus faced” – proposition. All the same, mixed up ! Here we can avail proposition 4.1241  –

”One cannot distinquish forms from one another by saying that one has this property, the other that : for this assumes that there is a sense in asserting either property of either form”. (4.1241)

But in  B . , there the law of identity is broken in a way of vicious circle.

Suppose that in the instance of proposition to be ”false” , proposition express the ! ”reality” to agree with not.  –  What  this .. a ”proposition express the ! ”reality” to agree with not” .. means ?

It  m e a n s  that  –  a ”.. proposition represents ..” .. BOTH .. ”.. such and such a state of affairs” , which an o t h e r ! ”.. a g r e e s  with reality ..” , AND  an o t h e r .. then ! ”.. n o t ..” (2.21 , 2.221 , 2.222 , 4.031) : The ”false” proposition express also ! t h a t ”state of affairs” , which the ”state of affairs” expressed by ”false” proposition in order to be ”false” agrees not, i. e. the ”false” proposition express ! an o t h e r ”proposition” , which represents the reality that the ”state of affairs” expressed by ”false” proposition in order to be ”false” agrees not.  –  So, ”both – and” means that the ”false” proposition express another ”proposition” , which is ! necessary (by definition) ”true”.

Thus, we meet, confront again (our mean ”friend” , )  an ”Double faced” – proposition. But now not so ”.. that there is a sense in asserting either property of either form”. (4.1241)  –  Why  n o t ?  –  BECAUSE OF  here  we  s u f f e r  A  CONTRADICTION.

A propositition cannot express  b o t h  the ”state of affairs” , of  w h i c h ! ”(an) o t h e r”  will be ”in the agreement .. with reality ..” (2.222)  and ! ”( a n ) o t h e r”  will be ”in the .. disagreement .. with reality ..” (2.222)  if it is supposed the law of noncontradiction to stand : A proposition contradicts  i t self.

And it don’t help to assume that a proposition express (an) o t h e r*  proposition, which ”.. represents .. a state of affairs” (4.031)  to be ”in the agreement .. with reality ..” (2.222) , and which other* ”.. a state of affairs” ! thus represents the ”reality” , with which ”.. a state of affairs” (4.031)  expressed by the first proposition ”.. agrees .. not” (2.21).

There would be instead of one with itself contradicting  proposition two contradicting propositions.

However  –  ”.. a logical place  o t h e r ..” (3.4 , 3.41 , 3.411 , 4.0641 , originally in German ”other” with spaces) , i. e. ! an o t h e r  ”.. proposition with a sense” (3.4 , 3.41 , 3.411 , 4 , 4.064 , 4.0641)  i s  the key the correspondence theory of truth to be correct.

But is an another proposition necessary?  –  Suppose, it is not.  –  The result would be to end up in out of the frying pan, into the fire!

If not  –  ”.. a logical space  o t h e r ..” (3.4 , 3.41 , 3.411 , 4.0641) , i. e. ! an o t h e r  ”.. proposition with a sense” (3.4 , 3.41 , 3.411 , 4 , 4.064 , 4.0641)  –  then there would be … ! ”n o t h i n g”  to be agreed with reality . . ! n o t.

It would be either to be impossible a proposition to be ”false” o r  a proposition to be (possible) ”false” , intended / ”..  meant to be false ..” (4.062) , means the unlimited opposite  –  and is always ”true” !

Hence, if there would be not another ”.. proposition with a sense .. in the agreement .. with reality ..” (2.21 , 2.221 , 2.222 , 3.4 , 3.41 , 3.411 , 4 , 4.031 , 4.064 , 4.0641) , then it would be either impossible a ”.. proposition represents .. a state of affairs .. in the disagreement .. with reality ..” (2.21 , 2.221 , 2.222 , 4.031) , i. e. ”in the .. disagreement .. with ..” ! that an o t h e r  ”.. proposition with a sense .. in the agreement .. with reality ..” (2.21 , 2.221 , 2.222 , 3.4 , 3.41 , 3.411 , 4 , 4.031 , 4.064 , 4.0641)  o r  a proposition intended to be ”false” m e a n s  the unlimited opposite  –  and is always ! ”true” .

It would be not possible to say, assert a proposition to be ”true or false” ; affirm or deny a proposition as ”.. a picture of reality” (4.01 , 4.064)  to be ”true or false”.

This may show up as an un- or even surreal ”language game” , but one must keep in mind that, indeed all this ”surreal” happens, takes it’s place ”.. in logical space ..” (1.13 , 3.12 + 3.14 , 4.06)  throughout applying the correspondence theory of truth in ”u – language”. To make in ”u – language” a model of the (valid) relation between ”language” / ”u – language” and ”reality” , postulated by correspondence theory.

So, finally  –  why the theory of truth to overcome Russell’s paradox, is the correspondence theory ?

It is a fact, even an axiom that the correspondence theory of truth presupposes independence. The concept of ”independence” is crucial. Wittgenstein says ”its” validity already in the first pages of his book, in context of the determination of reality  –

”Die Substanz ist das, was unabhängig von dem was der fall ist, besteht”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.021 , 2.0211 , 2.0212 , 2.024 , 2.06 , 2.063 , 3.203 , 3.3 , 4.061 , 4.064)

”Substance is what exists independently of what is the case”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.021 , 2.0211 , 2.0212 , 2.024 , 2.06 , 2.063 , 3.203 , 3.3 , 4.061 , 4.064)

As a concequence, corollary of independence, that ”u – language”* , none of ”its”* propositions ”.. with a sense” (4) , and reality cannot put in an appearance together, is then ! the first pas for picture theory. There is  n o  relation, connection or connexion between ”u – language” and reality ; there is  n o  conjuntion  –  ”u – language” and reality.

To say  –     ” ”u – language”  and  reality ”     –  must be cancelled, if only independence stands.

The concequence of independence is that it is not possible to compare ”what a .. proposition represents .. its sense .. with reality”. (2.21 , 2.221 , 2.222 , 2.223 , 4.031).

To compare (some) ”x” to (some) ”y” necessitate, that ”x” and ”y” can perform together, in same space and that possibility is negated by independence.

If it is negated that a ”.. proposition represents such and such a state of affairs” together, in same space with reality, then compare ”.. such and such a state of affairs .. with reality” (2.21 , 2.221 , 2.222 , 2.223 , 4.031)  is not possible.

Thus, it cannot be demonstrated, proved that a ”.. .. proposition represents such and such a state of affairs .. in the agreement or disagreement .. with reality ..” (2.222 , 4.031).

A proposition can still be ”true or false” , but only ! by chance , and why not ! then .. by chance both ”true” and ”false”. One might argue that if (and when) independence is a necessary condition of the consistence of the correspondence theory and since it stands, it is enough to the law of noncontradiction to hold.  –  Anyway, as it turns out the consistence of ! PToL has to be proven.

So, if we can agree that as a corollary of Russell’s paradox there are anymore, not yet a single proposition that can be ”true or false” , at least provably and consistent, then starting point of analysis of correspondence theory and (corollary of) Russell’s paradox are equal.

And be it for better or worse with the supposed corallary of Russell’s paradox to hold, the starting point of analysis of correspondence theory hold true : Since independence (2.024 , 4.061)  there is not yet a single proposition that can be ”true or false” , at least provably and consistently.

To say the other way round what Wittgenstein says in paragraph 5.64 , ”.. that solipsism strictly carried out coincides with pure realism ..” , the correspondence theory of truth as a truth theory of (ontological) realism coincides with solipsism in the beginning of its analysis : IF, and as it ! must to be ..    ” ”u – language”  and  reality ”      .. THEN  there is nothing else (left) in the beginning on the analysis of correspondence theory than (our) ”u – language” (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031).

So, all what Wittgenstein says in his picture theory is ! modelling, i. e. simulation in ”u – language” of what it is as for the valid relation between ”u – language” and ”reality” , postulated by correspondence theory of truth and the rules of (classical) logic.

7 .     Picture theory as an implication of independence

To recollect, one must consider that PToL / ”the proposition is a picture of reality ..” (4.01)  is not direcly an act, statement of the correspondence theory, but only the coordination of ”u – language” and the correspondence theory in its original form accomplish the picture theory.

Picture theory is already an expression of what the logic of the correspondence theory presupposes of proposition to be provable and consistent ”true or false”.

In PToL Ludwig Wittgenstein show what are the necessary and sufficiet conditions of these well-formed, provable and consistent ”true or false” , propositions.

After Russell’s paradox the question ”how a proposition can be provable and consistent ”true or false”?” has to be done.

The baseline of picture theory is therefore correspondence theory in its original form. Before the question of the  l o g i c  of correspondence theory  –  which  d e r i v e  to  PToL.

It is possible to comprehend Tractatus from the very beginning truth-  and proof-theoretically. From the point of view of correspondence theory and its logic. Reality has to be determinated so that it is conceivable, ! to what ”u – language” is connected ; with what ”u – language” .. ”.. must have something in common .. in order to be able to represent it .. rightly or falsely ..” (2.16 , 2.161 , 2.17 , 2.18 , 2.21).

First there are nothing else than (pure) ”u – language” and ”its” propositions ”.. with a sense” (2.221 , 4 , 4.031) , on which we assert ”.. the agreement or disagreement .. with reality ..” (2.222) , and second, forthwith ! the question ”how to assert ”provable and consistent”” ?  And if independence must stand, stands for the sake of consistency, there is still the question concerning the requisite of provability : HOW  a ”.. proposition represents .. its sense” (2.221 , 4.031)  so, in a way that ”.. the agreement or disagreement of its sense with reality ; its truth or falsity ..” (2.222)  can be proven ?

Thus, the meaning of the term ”sense” , the meaning of ”every proposition must already have a sense ..” (4.064) , has two sides, layers.

The first is purely dealing with the existence of the theory of truth, or not to say ! overall on behalf of (existence of) the meaningful language.

The second, and the ! point, deals with how to assert ”.. the agreement or disagreement of .. sense .. with reality ..” (2.22 , 2.221 , 2.222 , 4.031 , 4.2)  so that the ”truth or falsity” of a proposition in question can be provable (2.223) ; and of course ! further, to be consistent.

These two sides, layers of ”sense” are the subtle sides and layers of ”the substance of the world” (2.021).

The first layer is that of even trivial. No doubt, if no ”.. proposition represents such and such a state of affairs” (4.031) , there is nothing to be to ask and assert (4.064) , to be ”true or false” ( , or even there is nothing to be said at all in any language).

Although this first layer is not the point* of the doctrine of ”the substance of the world” (2.014* , 2.021 , 2.0211 , 2.0212 , 3.202 , 3.203 , 3.23* , 3.3* , 3.31 , 3.311 , 3.318 , 4.2* , 4.21 , 4.22 , 4.221 , 4.2211 , 4.23* , 4.25* , 4.3* , 4.4* , 4.41* , 4.431* , 5 , 5.01) , it is the baseline, underneath, of picture theory. The base- line to come back / (4.0312 , 4.128) , with never-ending ”asking, asserting and ! proving” ( , or otherwise .. P = NP ..).

Especially the first layer of the doctrine of ”the substance of the world” (2.021)  must be said because of  the fact, concerning the consistency of correspondence theory, that the  –

”Substance is what exists independently of what is the case”. (1 , 1.1 , 1.11 , 1.12 , 2 , 2.021 , 2.0211 , 2.0212 , 2.024 , 2.06 , 2.063 , 3.203 , 3.3 , 4.061 , 4.064)

”Independence” means that at first every ”.. proposition represents such and such a state of affairs” (2 , 2.021 , 2.024 , 2.06 , 3.203 , 3.3 , 4.031 , 4.064)  independently* of ”.. the agreement or disagreement .. with reality ..” (2.222). If not so* , then it would be impossible to say a proposition is ”true or false” , since we would have to know ”truth or falsity” of a proposition before it can have a ”sense” , which is in turn a prequisite a proposition to be ”true or false” , and ergo, we have a checkmate (2.0212) / circular argument or even with ”falsehood” vicious circle.

Also the later, proof-theoretical meaning of ”sense” is expressed independently of ”truth or falsity” of a proposition since this (later) second layer of ”the substance of the world” (2.021)  is still, ! just an expression of ”truth-conditions” (2.22 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 ,  4.431 , 5 , 5.01) ; of ! all well-formed propositions (4.022 , 4.46 , 5.4711).

Hence, what said in paragraph 4.064 hold true also of the later proof-theoretical meaning of ”sense”. Every well-formed proposition is ”.. already .. the expression of its truth-conditions” (2.06 , 2.1 , 2.11 , 2.18 , 2.201 , 2.203 , 2.22 ,  3.13 , 3.318 , 3.332 , 3.333 , 4.022 , 4.064 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 4.46 , 5 . 5.01 , 5.4711).

”Every proposition must already have a sense ; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc”. (4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563)

Hence : ”We cannot give a sign the wrong sense” (4.064 , 5.473 , 5.4731 , 5.4732 , 5.4733 , 5.5563).

(It is obvious that a well-formed proposition cannot have a ”wrong sense”. )

Not to mention the core, essence of the meaning of picture theory, as an implication of independence, would be not possible. When Wittgenstein says that ”.. there .. have to be objects and states of affairs” (2.021 , 3.203 , 3.3 , 4.031 , 4.064 , 4.2211) , he has his reasons.

The true meaning of picture theory, as an implication of independence, as an expression of provably and consistently ”true or false” propositions is that a well-formed proposition ”.. must have something in common .. with reality in order to be able to represent it .. rightly or falsely ..” (2.16 , 2.161 , 2.17 , 2.18 , 2.21) , a n d  this ”something in common”  HAVE  TO  BE  CONTAINED  IN  A  PROPOSITION  I T S E L F ! Simply because of ”independence” (2.024 , 4.061). An evident, logical place ”to contain” is ”objects” , they constitute propositions, and since ”.. only in the context of a proposition has a name meaning” , logical places ”to contain” are ”objects .. in the context of .. propositions represents such and such a state of affairs” (2.014 , 2.021 , 3.203 , 3.3 , 4.031). Therefore Wittgenstein says, concludes  –

”Objects contain the possibility of all states of affairs” (2.014)

And Wittgenstein continues fortwith ! self-referring  –

”The possibility of its occurrence in atomic facts is the form of the object”. (2.014 , 2.0141)

”Objects” refer to themselves, in ”u – language” , not only as expressions of ”.. all possible states of affairs ..” (2.0121 , 2.0124 , 2.021 , 3.203 , 3.3) , but ! precisely also as containing  a l l  the possibilities of ”.. the agreement or disagreement .. with reality ..” (2.014 , 2.06 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 2.21 ,  2.222 , 3.02 , 4.25 , 5 , 5.01)  of these ”all possible states of affairs” , made by ”objects” themselves ”.. in the context of a proposition ..” (3.3).

And it is precisely  THESE  a l l  the possibilities of ”.. the agreement or disagreement .. with reality ..” (2.014 , 2.06 , 2.1 , 2.11 , 2.201 , 2.202 , 2.203 , 2.21 ,  2.222 , 3.02 , 4.25 , 5 , 5.01)  of these ”all possible states of affairs” , made by ”objects” themselves ”.. in the context of a proposition ..” (3.3) , W H I C H … ”.. i s  the form of the object” (2.0141) , and is precisely  –  t h e  object  of ! Wittgenstein’s ”fundamental thought” (3.221 , 4.0311 , 4.0312 , 4.128 , 5.55 , 5.5571).

”One name stands for one thing, and another for another thing, and they are connected together. And the whole, like a living picture, presents the atomic fact”. (2.021 , 3.203 , 3.3 , 4.0311 , 4.0312)

It is this totality of ”living pictures” , i. e. all possibilites of ”objects” to occur ”in atomic facts” (2.0124 , 2.014 , 2.0141) , which is the object of Wittgenstein’s ”fundamental thought” (4.0312).

Wittgenstein’s doctrine of ”the substance of the world”* (2.021)  is not easy to grasp. It is (to realise) throughout ”its”* second layer, which ”.. cannot be said” (4.0312 , 4.1212 , 4.128) , although it, ! the proof-theoretical meaning of the ”sense” / (4.2) ,   ”.. can be shown” (4.022 , 4.023 ,  4.1212 , 4.2).

Wittgenstein’s doctrine of ”the substance of the world”* (2.021)  is not easy to compehend because ”its”* meaning can be expressed only .. so to say .. in the ”Mirror – Hall” of self-reference : Not only ”if all objects aren given, then at the same time all possible states of affairs are given” (2.0124 , 2.014 ) , but also ! at the same time, ”objects” are ! self-referring to ”themselves” so that , all possibilites of ”objects” to occur ”in atomic facts .. are given” (2.0124 , 2.014 , 2.0141 , 2.021 , 3.203 , 3.3 , 3.31 , 3.311) ; precisely ! d u e  t o  this to correspondence theory of truth necessary quality of ”containing”.

What I am trying to say is this, suppose that there is not yet given any theory of truth, i. e. here the correspondence theory, b u t still nothing else but ”.. all objects are given .. in the context of a proposition ..” (2.0124 , 2.021 , 3.203 , 3.3). Then we have anyway, already ”.. all possible states of affairs .. given” (2.0124) , that is ”.. every sense ..” (4.002)  is expressible simply by the grammar of in question of language / ”u – language”. Every, in princible and practice, possible sentence is given, including those, which (as possible propositions) are claiming ”something” to be or not to be the case. It is by a computer to be done, every possible sentence.

Wittgenstein speaks about ”external” and ”internal qualities, properties” of ”objects” (2.01231 , 4.1221 , 4.123) , and in my abovesaid ”thinking experiment” it is only ”external properties” , which are given : The correspondence theory is not yet present, given and not until with it ”.. an internal property .. is unthinkable that its object does not possess it” (4.1221 , 4.123).

”In order to know an object, I must know not its external but all internal qualities”. (2.01231 , 4.1221 , 4.123)

”An internal property of a fact we also call a feature of this fact”. (2.01231 , 4.1221 , 4.123)

”A property is internal if it is unthinkabbe that its object does not possess it”. (2.01231 , 4.1221 , 4.123)

W h y  correspondence theory presupposes this ”.. internal property of a fact ..” (2.01231 , 4.1221 , 4.123) ?

Simply, because of if  this ”.. internal property of a fact ..” (2.01231 , 4.1221 , 4.123)  is missing, then it is not thinkable any proposition to be provably ”true or false” , which means that in practice our theory of truth is next to nothting, and only to put to wastebasket.

The essential, r e a l  cause of this ”must” of ”.. internal property of a fact ..” (2.01231 , 4.1221 , 4.123) , i. e. that ”objects contain the possibility of all states of affairs” (2.014)  i s  independence.

The fact that a ”.. proposition represents such and such a state of affairs” (4.031)  independent of reality (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063 , 2.024 , 4.061)  comes along not until the logic of the correspondence theory.

Independence !  What is needed to overcome, or rather to circumvent, bypass it ?  That propositions can be shown to be provably ”true or false” (2.223 , 3.05) , and correspondence theory rescued.

”In order to be a picture a fact must have something in common with what it pictures”. (2.16 , 2.161 , 2.17 , 2.18 , 3.12 , 3.14 , 4.01 , 4.06)

”In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all”. (2.16 , 2.161 , 2.17 , 2.18 , 3.12 , 3.14 , 4.01 , 4.06 , alleviivaus jatkuu (2.17) )

”What the picture must have in common  w i t h  reality  in order to be able represent it after its manner – rightly or falsely  –  is its form of representation”. (2.16 , 2.161 , 2.17 , 2.18 , 3.12 , 3.14 , 4.01 , 4.06)

”What every picture, of whatever form, must have in common  w i t h  reality in order to be able to represent it at all  –  rightly or falsely  –  is the logical form, that is, the form of reality”. (2.16 , 2.161 , 2.17 , 2.18 , 3.12 , 3.14 , 4.01 , 4.06)

”Something in common, identical with reality (2.16 + 2.161 + 2.17) ?  ”Every picture must have the logical form of reality” (2.18) ?

So, to bypass independence every provably ”true or false” proposition ”must have the logical form of reality” (2.18) , and in order to say ! what is this ”logical form” it is inevitable that reality has to be determinated, conceived.  –  ”Picture of ! ”what”” !  –  ”Logical form of ! ”what ”” !

And not (at all) strange enough, or to be circular argument, Wittgenstein determinates reality by means of correspondence theory, that is throughout the same theory, which asks to conceive reality.

To do the determination of reality by means of correspondence theory itself, and here we are again doing with self-reference, is (an advantage) to avoid the dilemma of ! what is the relation between correspondence theory* and that ”theory” , which would do  o u t side of it* the conception of reality. By means of correspondence theory we are in same nexus, catecory.

Why is ”the determination of reality by means of correspondence theory itself” not circular argument ?

”The existence and non-existence of states of affairs is reality. (We call the existence of states of affairs a positive fact, and their non-existence a negative fact.)”. ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031)

This, ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031) , take place ! to wit in the ”u – language” independent of reality.  –  Hence, there is not a single proposition, which one can point and say, assert proposition to be (provably) ”true or false”.  –  To compare is not (yet) possible,

Thus, ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031)  is a tautology. It is a tautology to say that .. ”the reality” is a totality of true ”positive” and true ”negative” propositions (1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.21 , 2.221 , 2.222 , 4.031 , 5.5151)  because it is to say nothing more, nothing less than, for example .. ”it’s raining or not”.

The determination of reality by means of correspondence theory itself must be a tautology in that sense that the determination said is only prequisite, first step to prove correspondence theory adequate.  –  Otherwise, if not tautology, the determination said would be a circular argument.

If one premises correspondence theory of truth, then the self-referential determination said is intuitive, ! given that it is a tautology.

Anyway, having said that fact of tautology, one must add that the result to prove correspondence theory valid cannot be ! anymore a tautology ; if so, one have ! ended up to a circular argument, unto itself.  –  We would be in the situation of Sisyfos.

The question was of ”the logical form of reality” (2.18) , which a proposition presupposes in order to be ”a picture of reality” (4.01) , i. e. to be provably ”true or false” (4.06 , 5 , 5.01). Now, the answer seems to be .. idling, that is .. no answer at all but repeat the question. The answer is as well .. ”the logical form of reality” , which a proposition presupposes to be provable ”true or false” (2.18 , 4.01 , 4.06 , 5 , 5.01) .. i s  ”the logical form”  j u s t  that of .. a proposition to be provable ”true or false”.

OK !  Let’s ask then, w h a t  i s  that ”logical form” , and ! where  –  if somewhere  –  it  e x i s t ?

”The picture represents what it represents, independently of its truth or falsehood, through the  f o r m of representation”. (2.22 , 4.06 , 4.1)

”Das bild stellt dar, was es darstellt, unabhängig von seiner Wahr-  oder Falschheit, durch die  F o r m der Abbildung”. ( (2.22 , 2.222 , 4.06 , 4.1) , original ”die Form der Abbildung” relate up ! (2.22 / 4.06) )

”Independently” , of course, no doubt : ”The form of representation” is not until ! ”.. the expression of .. truth-conditions” (2.22 , 4.06 , 4.1 , 4.431).

So, the answer .. ”the logical form of reality” , which a proposition presupposes to be provable ”true or false” (2.18 , 4.01 , 4.06 , 5 , 5.01)  is ”the logical form” just that of .. a proposition to be provable ”true or false” .. i s  anyway right : ”Die form der Abbildung” / ”the form of representation” (2.22)  i s  as well ! ”the logical form” .. a proposition to be provable ”true or false” (2.18 , 2.22 , 4.01 , 4.06 , 5 , 5.01).

The answer is anyway right. Let us to remember, that Wittgenstein conceives ”the reality” throughout the correspondence theory. Thereby ”the logical form of reality” (2.18)  is ”the logical form” of true ”positive” and true ”negative” propositions.

And notwithstanding the determination of ”the reality” , the ! insisted relation between ”u – language” and reality means, is the prequisite, a proposition to be provable ”true or false”. By this ”relation” we face anyway ”truth and falsehood”.

The insisted relation between ”u – language” and reality,  as an expression of ”.. the logical form .. of reality” (2.18) , is the core of the PToL.

The answer to the second question  –  ”where ”the logical form” e x i s t ?”  –  respond to that of, if one is still wondering ”idling” , that is, Wittgenstein seems nothing but repeat himself  –

”If the form of representation is the logical form, then the picture is called a logical picture” (2.16 , 2.161 , 2.17 , 2.18 , 2.181 , 2.182)

”Every picture is also a logical picture”. (2.16 , 2.161 , 2.17 , 2.18 , 2.181 , 2.182)

The reason, why .. ”every picture is also a logical picture” (2.182) , comes along with the respond to the question ”where ”the logical form” exist?” :

A proposition as ”a picture of reality” contains the quality, which  m a k e s  proposition ”a picture of reality” (2.06 , 2.11 , 2.201 , 2.203 , 4.01 , 4.25).

9 .     ”The existence of an internal relation” (4.125)

W h a t  is needed to overcome, bypass or circumvent independence (so that propositions can be shown to be provably ”true or false” (2.223 , 3.05) , and correspondence theory rescued)  i s ”the existence of  an  i n t e r n a l  relation” (4.125)  BETWEEN  ”U – LANGUAGE”  AND  REALITY.

Why this relation is ”internal” ?

Plainly, needless to say, because of the external relation is already occupied by independence. And because of there is no other place than ”u – language” where to be, it is ”a logical necessity” (6.375) that ”the existence of an internal relation” (4.125)  stands in ”u – language”.

There must be relation, i. e. connection, conjuntion or connexion, in between ”u – language” versus reality. If not, it is ”a logical impossibility” (6.375) ! to compare ”.. what the picture represents .. with reality ..” (2.221 , 2.222 , 2.223 , 4.031) , and thereby to show ”.. its truth or falsity ..” (2.222).

To recall : ”The picture is a model of reality” (2.06 , 2.1 , 2.11 , 2.12) , constructed in ”u – language”. In a self-referential way, simulating the truth-  and proof-theoretical relation between ”u – language” and ”reality” , as it is valid throughout the logic of correspondence theory of truth.

”To the proposition belongs everything which belongs to the projection ; but not what is projected. Therefore the possibility of what is projected but not this itself. In the proposition, therefore, its sense is not yet contained, but the possibility of expressing it. (”The content of the proposition” means the content oh the the significant proposition.) In the proposition the form of its sense is contained, but not its content”. ( (2.18 , 2.22 , 2.221 , 2.222)  ←  3.13)

Thus, ”.. in the proposition the form of  .. representation .. is contained, but not .. what the picture represents ..” (2.17, 2.18 , 2.22 , 2.221 , 3.13).

”The proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand”. (4.022 , 4.03)

”Der Satz  z e i g t  seinen Sinn. Der Satz  z e i g t, wie es sich verhält, w e n n er wahr ist. Und er s a g t , d a s s  es sich so verhält”. (4.022 , 4.03)

”A proposition must communicate a new sense with old words. The proposition communicates to us a state of affairs, therefore it  must be  e s s e n t i a l l y  connected with the state of affairs. And the connexion is, in fact, that it  i s  i t s  logical picture. The proposition only assert something, in so far as it is a picture”. (4.022 , 4.03)

”A proposition must communicate a new sense with old words ..” (4.03) , i. e. it is the case that ”a new sense” , in a new situation, have to be  –  its meaning  –  explained ”with old words”.

”Ein Satz muss mit alten Ausdrucken einen neuen Sinn mitteilen. Der Satz teilt uns eine Sachlage mit, also muss er  w e s e n t l i c h  mit der Sachlage zusammenhängen. Und der Zusammenhang ist eben, dass er  i h r  logisches Bild  i s t. Der Satz  s a g t  nur insoweit etwas aus, als er ein Bild ist”. (4.022 , 4.03)

A well-formed proposition is a ”logical picture” of ”the connexion” between a proposition and reality so that ”the agreement or disagreement with reality” of what a proposition (in question) represents, i. e. ”its sense” , can be said, provable. (2.221 , 2.222 , 2.223 , 4022 , 4.03 , 4.031 , 4.125 , 5 , 5.01).

”The existence of an internal relation between possible states of affairs expresses itself in language by an internal relation between the propositions presenting them”. (4.125)

”Das Bestehen einer internen Relation zwischen möglichen Sachlagen drückt sich sprachlich durch eine interne Relation zwischen den sie darstellenden Sätzen aus”. (4.125)

Thus, the abovesaid ”connexion”* (4.022 , 4.03)  is expressed in ”u – language” , and ”it”* is simulating  the truth-  and proof-theoretical relation between ”u – language” and ”reality” , as it is valid throughout the logic of correspondence theory of truth.

W h a t  i s  all about, ! the  c o r e , of this self-referential well-formed proposition throughout the correspondence theory of truth ?

Here I will go in for, exercise straightforward, literal, even pedantic, and comparative reading. For example ”contain” is to contain .. like a bottle of wine contains its liquid. Reading with a ’cavalcade’ of Wittgenstein’s paragraps, (brief) notes in between. Looking for similarities, equivalences. Taking into account what I have said, interpreted hitherto.

”The picture presents the facts in logical space, the existence and non-existence of atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , ! 2.11 , 2.12 , 2.201 , 2.202 , ! 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”The facts in logical space” (1.13 , 2.11)  of the correspondence theory (2.21 , 2.221 , 2.222 , 3.12 + 3.12 , 4.06).

”Das Bild stellt die Sachlage im logischen Raume, das Bestehen und Nichtbestehen von Sachverhalten vor”. (2.11)

In my book ”die Sachlage” / ”the facts” and ”das Bestehen und Nichtbestehen von Sachverhalten” / ”the existence and non-existence of atomic facts” are synonyms, with a meaning that is the same. Thus ”die Sachlage” / ”the facts” is going to be substituted by ”das Bestehen und Nichtbestehen von Sachverhalten” / ”the existence and non-existence of atomic facts” in paragraph 2.203 ( , and so on .. ! 4.25 .. ).

”The picture is a model of reality”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”Model of reality” (2.12)  throughout the correspondence theory  –  applying it in ”u – language”.

”The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Recall the detemination of ”reality”* (2.06) , and substitute ”it”* here (2.201)  by ”the existence and non-existence of atomic facts”.

”The picture represents a possible state of affairs in logical space”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”The picture  c o n t a i n s  the  p o s s i b i l i t y  of the state of affairs which it represents”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , ! 2.11 , 2.12 , 2.201 , 2.202 , ! 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Let us remember here the synonyms in paragraph 2.11 , and perhaps look at the original text.

”Das Bild  e n t h ä l t  die  M ö g l i c h k e i t  der Sachlage, die es darstellt”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , ! 2.11 , 2.12 , 2.201 , 2.202 , ! 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Hence, in my book, by substituting ”the facts” with ”the existence and non-existence of atomic facts” we get, can conclude :

”The picture  c o n t a i n s  t h e  p o s s i b i l i t y  of  the  existence  and  non-existence  of atomic facts”. (2.11 + 2.203)

And here (2.11 + 2.203 + 3.02 + ! 4.25)  it is not only as if for fun to compare original text in German with translations, but to show what is the case. By original text we get, can conlude :

”Das Bild  e n t h ä l t  die  M ö g l i c h k e i t  das  Bestehen  und  Nichtbestehen  von  Sachverhalten, die es darstellt”. (2.11 + 2.203)

(The form ”.. das Bestehen und ..” (2.11 + 2.203)  may be not right according to german grammar, anyway here is  the thought essential. )

”The thought contains the  p o s s i b i l i t y  of the state of affairs which it thinks. What is thinkable is also possible”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

What’s ahead !  Here (2.11 + 2.203 + 3.02 + ! 4.25)  is already a clue, why the consistency of PToL must to be shown. And also a clue why Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  is what it is. In a well-formed proposition as ”a picture of reality” (4.01)  independence  m u s t  still stand. For the sake of correspondence theory to be further consistent.

Thus its ! s t a t e  changes : Independence becomes or turns out so that ”logical forms” cannot be expressed, said by the means of any logic(al method) ”.. beforehand .. on one occasion ..” (2.18 , 4.12 , 4.121 , 4.1212 , 5.47).

If both independence and relation must stand, independence being the necessary first, between ”u – language” and reality, then the totality of ”pictures of reality” (4 , 4.001 , 4.06)  are undecided. In fact, not a single ”picture of reality” can be derived.

”I conceive the proposition  –  like Frege and Russell  –  as a function of the expressions contained in it”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the ”whole theory of types”)”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01 , underline continues (3.333) )

”A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself ..”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

What ”no proposition can say .. about itself ..” (3.332)  i s ”the sense .. about itself” (3.332 , 4.2) , just because every (well-formed) proposition ”.. already  c o n t a i n s .. the possibilities of the existence and non-existence of atomic facts” (2.11 , 2.203 , 3.332 , 3.333 + 4.2) , i. e. it  i s ! n o t  possible to a proposion to say ! (anymore) ”.. its agreement and disagreement with the possibilities of the existence and non-existence of atomic facts” (4.2). If it could, then indeeed a proposition should ”contain itself” in order to be able to ! compare itself with that ”already contains”. I f  this ”contain itself” possible, t h e n  correspondence theory of truth would contradict its spitit, essence ! let alone correspondence theory would be driven to real contradiction, and also the law of identity would be broken  –

”.. If, for example, we suppose that the function F(x) could be its own argument, then there would be a proposition ”F(F(fx) )” , and this outer function F and the inner function F must have different meanings ; for the inner has the form φ(f x) , the outer the form ψ(φ(f x)). Common to both funktion is only the letter ”F” , which by itself signifies nothing. ..”. (3.333)

As a laymen’s example maybe such ”experiment” , that would it be possible a definite circle contain itself so that both circles, the outer and the inner, be the same, have the same (value of) surface area or the same size, dimension of  perimeter? I think not.

The spirit, essence of correspondence* theory is not that (of solipsism, that) the valid language of it* contains reality, to which then propositions are to be compared ! by the language itself .. to itself .. to .. .

”A proposition presents the existence and non-existence of atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Recall the self-referential, by independence (2.024)  possible, determination of ”reality” throughout the correspondence theory of truth ( (1 , 1.1 , 1.11 , 1.12 , 2 , 2.06 , 2.063)  ←  2.221 , 2.222 , 4.031).

Here ”a proposition presents .. the reality” (2.06 + 4.1) , i. e. a proposition in guestion is well-formed as ”a picture of reality” (4.01)  b y  presenting  b o t h .. ”.. the existence  a n d  non-existence of atomic facts” (4.1) , s i n c e  ”BOTH – AND”  must be possibble in order a proposition .. ”.. c a n  be true  o r  false ..” (4.06). IF  there is ! not yet a single ”true or false” proposition, T H E N  to have ”true or false” propositions, b o t h  ”true”  a n d  ”false”  m u s t  be possible in order to .. e i t h e r  truth value ”true”  o r  ”false” can be fulfilled, actualize. B o t h  ”the agreement with reality”  a n d  ”the disagreement with reality” of ”the sense” of ”a proposition” must be possible in order to ”.. the agreement or disagreement of .. sense with reality ..” (2.221 , 2.222 , 4.031)  can be fulfilled, actualize.

”The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Let’s remember that the meaning of the term ”sense” has two sides, layers. The first is that of trivial, overall on behalf of (existence of) the meaningful language. Paragraph 4.2 says the second : How a (well-formed) proposition assert ”.. the agreement or disagreement of .. sense .. with reality ..” (2.22 , 2.221 , 2.222 , 4.031 , 4.2)  so that the ”truth or falsity” of a proposition in question can be provable (2.223). And ! recall, that this not trivial second truth-  and proof-theoretical meaning of the ”sense” is expressed in ”u – language” modelling, simulating the relation between ”u – language” and ”reality” , as it is valid throughout the logic of correspondence theory of truth. And ! recall, which is the case with paragraps (2.11 + 2.203). Here / 4.2  it is again something to place / (2.11 + 2.203 + 4.2)  in between : ”The sense of a proposition is its agreement and disagreement with the ”proposition in itself containing” possibilities of the existence and non-existence of atomic facts” (2.11 + 2.203 + 4.2).

So, what ”no proposition can say .. about itself ..” (3.332)  i s  the truth-  and proof-theoretical ”.. sense .. about itself ..” (2.18 , 3.13 , 3.332 , 4.022 , 4.12 , 4.121 , 4.1212 , 4.128 , 4.2).

”If the elementary proposition is true, the atomic fact exist ; if it is false the atomic fact does not exist”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”Ist der Elementarsatz wahr, so besteht der Sachverhalt ; ist der Elementarsatz falsch, so besteht der Sachverhalt nicht”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

If we now compare paragraphs 2.11 , 2.203 and 4.25 , original text in German being again most convincing, w h a t  is the conclusion of this (2.11 + 2.203 + 4.25)  reading ?  –  Focus on the paragraph 2.203.  –  W h a t  ”Das Bild enthält” ?

”Das Bild stellt die Sachlage im logischen Raume, das Bestehen und Nichtbestehen von Sachverhalten vor”. (2.11)

”Das Bild enthält die Möglichkeit der Sachlage, die es darstellt”. (2.203)

”Ist der Elementarsatz wahr, so besteht der Sachverhalt ; ist der Elementarsatz falsch, so besteht der Sachverhalt nicht”. (4.25)

If you ask me, the result of (2.11 + 2.203 + 4.25)  reading is ; let it be first, consequently in German  –

”Das Bild  e n h ä l t  d i e  M ö g l i c h k e i t  ”der Wahrheit  u n d  der Falschheit  der Elementarsätze””. ( (2.11)  →  2.203  ←  (4.25) ).

And in Englisch the conclusion of this ”equation” ( (2.11)  →  2.203  ←  (4.25) )  is  –

”The picture  c o n t a i n s  the  p o s s i b i l i t y  of  ”the truth  a n d  falsity of the elementary propositions””.

”The truth-possibilities of the elementary propositions mean the the possibilities of the existence and non-existence of the atomic facts”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Thus / 4.3  one can add ( (2.11)  →  2.203  ←  (4.25 + 4.3) )

”A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

This 4.4 is the definition of well-formed proposition throughout correspondence theory, without saying what ”a proposition” contains, which is the object of ”the expression of agreement and disagreement” , and is the way to Wittgenstein’s ”fundamental thought” (4.0312).

”The truth-possibilities of the elementary propositions are the conditions of the truth and falsehood of the propositions”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Recall, the situation in the beginning, that there where not yet a single proposition (expressed) in ”u – language” , which can be said to be consistent and provable ”true or false”. The situation was ! in fact in the beginning that there where not yet a single proposition (expressed) in ”u – language” to devote any truth value at all : Since the independence-relation between ”u – language” and reality. Hence, when Wittgenstein says ”.. reality must therefore be completely descriped by the proposition ..” (4.023) , it is actually a question ! of all possible truth values / (4.46) ; not only propositions as ”pictures of reality” (4.06) , but ”the sense of a proposition is its ..” (4.2)  all possible truth values.

”Among the possible groups of truth-conditions there are two extreme cases. In one of these cases the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological. In the second case the proposition is false for all the truth-possibilities : the truth-conditions are contradictory. In the first case we call the proposition a tautology ; in the second a contradiction”. (4.25 , 4.3 , 4.41 , 4.46 , 5 , 5.01)

Thus, if we add 4.41 to our ”equation” ( (2.11)  →  2.203  ←  (4.25 + 4.3 + 4.41) ) , then the conclusion can be said, simply  –

”The picture  c o n t a i n s  the  p o s s i b i l i t y  of  ”i t s  truth  a n d  falsehood””.

Thus, the essence of a well-formed proposition throughout correspondence theory is that it contains the possibility, ! all the possibilities, of ”truth and falsehood” of itself.

”The expression of the agreement and disagreement with the truth-possibilities of the elementary propositions expresses the truth-conditions of the proposition. The proposition is the expression of its truth-conditions”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

Here it is to repeat the paragraph 3.318 to get the almost final meaning of ”the existence of an internal relation” (4.125)  –

”I conceive the proposition  –  like Frege and Russell  –  as a function of the expressions contained in it”. (3.318)

When paragraps 3.318 and 4.431 are placed and read together, side by side, the result is  –

”.. The proposition .. is .. a function .. of  i t s  truth-conditions .. c o n t a i n e d  in it” (3.318 + 4.431).

In original text, in German the result will be, I do not write anything but the essential, without any dots in between  –

”Den Satz fasse ich als funktion der in  i h m  e n t h a l t e n e n  Wahrheitsbedingungen auf” (3.318 + 4.431).

”Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

”The elementary propositions are the truth-arguments of propositions”. (1 , 1.13 , 2 , 2.06 , 2.063 , 2.1 , 2.11 , 2.12 , 2.201 , 2.202 , 2.203 , 3 , 3.02 , 3.13 , 3.318 , 3.332 , 3.333 , 4.1 , 4.125 , 4.2 , 4.25 , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01)

That is the truth values of propositions depend on truth values of ”the truth-arguments of propositions” (4.46 , 5 , 5.01).

Hence, the final meaning of ”the existence of an internal relation” (4.125)  will be a ”equation”  –

”The picture  c o n t a i n s  the  p o s s i b i l i t y  of  ”the truth  a n d  falsity  of the truth-arguments of the picture itself ”” ( ( (2.11)  →  2.203  ←  (4.25 + 4.3 + 4.41 + 5.01) ).

But, if .. ”the picture contains the possibility of its ”truth and falsehood”” .. then the question hanging around must to be answered is  –

10 .     The consistency of picture theory / (4.0641)

If already under ”independence” (2.024 , 4.061)  one wonders how to bypass ”it” in order to (rescue) correspondence theory to be applicaple, and also its consistency not to be a thing of faith, now the challenge may seem overwhelming. Independence must stand, otherwise correspondence theory is not consistent. But now, with ”the existence of an internal relation” (4.125) , in order to be possible to prove a proposition ”truth or false” ,  we .. ! re-encounter the question of consistency.

It is really to show , ! prove that the correspondence theory of truth is consistent. Both independence and connexion, conjunction have to stand.

How to bypass that a well-formed proposition contains the possibility of both ”truth and falsehood” of itself ?  –  What is a clear contradiction!  –  Are we not up to here (in) quagmire.  –  How on earth a contradiction can circumvent ! itself.

Anyway, the trick is not at all so strange. Instead of saying ”falsehood” , one can say .. ”the truth of an another proposition”. Hence we get  –

A well-formed proposition contains the possibility of both ”truth” of itself  a n d  the ”truth” of an another proposition.

”The proposition determines a place in logical space : the existence of this logical place is quaranteed by the existence of the constituent parts alone, by the existence of the significant proposition”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641 , underline continues (3.411) )

Recall  –  ”a place in logical space” throughout correspondence theory.

”The propositional sign and the logical co-ordinates : that is the logical place”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641)

”The geometrical and the logical place agree in that each is the possibility of an existence”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641)

”Every proposition must already have a sense ; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641)

”One could say, the denial is already related the logical place determinated by the proposition that is denied. The denying proposition  d e t e r m i n e s  a logical place  o t h e r  than does the proposition denied. The denying proposition determines a logical place, with the help of the logical place of the proposition denied, by  s a y i n g  that  i t  lies  o u t side the latter place. That one can deny again the denied proposition, shows that what is denied is already a proposition and not merely the preliminary to a proposition”. (3.4 , 3.41 , 3.411 , 4.064 , 4.0641)

”.. The denying proposition  d e t e r m i n e s  a logical place  o t h e r .. with the help of the logical place of the proposition denied, by  s a y i n g  that  i t  lies  o u t side the latter place ..” (4.0641).

So  –  ”.. a place in logical space .. is the possibility of an existence .. a logical place other ..” (3.4 + 3.411 + 4.0641) , when ”a sense” of a ”proposition” is denied, that is to say ”.. the agreement .. of its sense with reality ..” (2.221 , 2.222 , 4.031)  is denied by the denying ”proposition” itself. For example proposition ”Finland is not a kingdom” denies itself the truth of ”its” positive form / ”Finland is a kingdom”.

What is the trick in this (notwithstanding its numerical weight pivotal) paragraph 4.0641 to overcome, erase the abovesaid    contradiction    ?

H o w  –  ”.. a logical place  o t h e r ..” (3.4 , 3.41 , 3.411 , 4.0641) , i. e. an o t h e r  ”.. proposition with a sense” (3.4 , 3.41 , 3.411 , 4 , 4.064 , 4.0641)  i s  the key correspondence theory to be correct ?

An another proposition  –  ”.. a logical place other ..” (4.0641)  –  is necessary. Otherwise it would be not possible to say, assert a proposition to be ”true  o r  false” , i. e. t o ! d e n y  the truth of a proposition.

The key, plain and (beautiful) simple, is that the ”truth” of an another proposition  r e p r e s e n t s, is an exression or a manifestation of the  p o s s i b i l i t y  of a(nother) proposition to be ”false”.

Recall part 6. (of my paper).

So  –  ”.. a place in logical space .. is the possibility of an existence .. a logical place other ..” (3.4 + 3.411 + 4.0641) , when the possibility of ”falsehood” of a proposition is in question.

Hence, ”.. a logical place other .. with the help of the logical place of the proposition denied ..” (4.0641) is an expression of self-reference, that is ”the proposition denied”  r e f e r ( e n c e ) s  throughout  ”i t – self”  t o ”a logical place  o t h e r” , in order to be possible ”falsehood” by the ”truth” of that ”logical place other” , which ”.. lies outside the latter place” , i. e. ”.. outside .. the proposition denied ..” (4.0641).

”Outside” , that is to say  –  independent.

Recall, by the logic of correspondence theory, the consequence, if there is not ”something” in reality which the ”sense” of the ”false” proposition agrees not (2.21 , 2.221 , 2.222 , 4.031) ; which necessary ”something” is expressed by another, ! ”true” proposition / ”.. its sense .. in the agreement .. with reality ..” (2.221 + 2.222).

Recall  –  the correspondence theory of truth as a truth theory of (ontological) realism.

The consequence would be that there is ”nothing” in reality which the ”sense” of the ”false” proposition agrees not, i. e. the ”false” proposition” expresses nothing but what is the ”truth” in the whole reality !

If a ”false” proposition is an expression of the ”truth” of the whole reality, then  t h i s  –  ”.. contradiction fills the whole logical space and leaves no point to reality ..”. (4.463)

”The truth of tautology is certain, of propositions possible, of contradiction impossible. (Certain, possible, impossible : here we have an indication of that gradation which we need in the the theory of probability.)”. (4.464)

What is then to conclude from the ”.. logical necessity ..” (6.375) , that the ”truth” of an another proposition  r e p r e s e n t s, is an exression or a manifestation of the possibility of a(nother) proposition to be ”false” ?  To conclude from the point of view of  ”the aim of the book” (Preface / (4.112 , 4.114) ) , i. e. in the last line to express ” the totality of propositions” , which ”can be true or false” as ”pictures of reality” (Preface / ( (3 , 3.12 , 4)  ←  4.001  ←  (4.06 , 4.112 , 4.114) ) ).

To conclude, that Wittgenstein’s aim, effort cannot succeed. Why not?  –

”The totality of propositions” , which provable ”can be true or false” as ”pictures of reality” (4.001 , 4.06)  is actually ”the totality of propositions” , which provable ”can be true” , and  i s  a totality, which ! i n clude ”propositions”* , which  e x clude  the expression of ”each other”*  B Y  R E P R E S E N T I N G ”EACH  O T H E R ’ S”*  POSSIBILITY  TO  BE  ”FALSE” : ”The totality of propositions” , which (provable) ”can be true or false” as ”pictures of reality” (4.001 , 4.06)  cannot be said, ”cannot be represented” (4.0312).  –  If law of noncontradiction stands. Or even notwithstanding of that law, since from a ”true” propostion one cannot derive a ”false” one , i. e. this well-formed ”the totality of propositions” include ”propositions”* , which ! contradict ”each other”* , ! b u t .. which contradiction .. ”.. cannot be said” (4.1212) , i. e. !  a l s o  the  n o n – contradictory this well-formed ”the totality of propositions .. cannot be said” (2.18 , 4.001 , 4.06 , 4.12 , 4.121 , 4.1212).  –  (Cf. Gödel’s second incompleteness theorem.  –  Suppose, you can say this ”non-contradictory” .. and you are in a situation that not a single well-formed ”proposition” can be ”false” , i.e. all well-formed ”propositions” are necessarily ”true” , i. e. ! ”tautologies” .. and so ! picture theory / correspondence theory fails as a theory of contingency. )

This (abovesaid) is not to say that every well-formed proposition exclude every other, but there are ”anumerical” (4.128)  sets of propositions, which comport with, fit together ( , and perhaps these ”sets” are not ”without number” (4.128)  if .. P = NP ..).

So, ergo : What is the trick to bypass that a well-formed proposition contains the possibility of both ”truth and falsehood” of itself ?  –  The trick is that  –

The well-formed ”propositions”* as ”.. pictures of the reality” (4.01 , 4.06)  show, point ”.. from within through ..” (4.114) ! ”t h e m selfs”*  o u t side of  ”t h e m selfs”*  l y i n g  AN O T H E R  WELL – FORMED  ”PROPOSITIONS”* .

That is to say, that  –

WELL – FORMED  ”PROPOSITIONS”*  ARE  ”.. from within through ..” (4.114) ! ”T H E M – SELFS”*  INDEPENDENT  OF  ”EACH  OTHERS”* .

It is already in the beginning of Tractatus when said this fact of the logic of the correspondence theory of the truth : If expressed ”in logical space” of correspondence theory + the three laws of (classical) logic, applied in ”u – language” , then ”the world” constitutes .. in the end of ”ladders” .. as a totality of ”anumerical” well-formed ”propositions”* independent of ”each others”* (1.13 , 2.06 , 2.061 , 2.061 , 2.063 , 2.21 , 2.221 , 2.222 , 3.12 + 3.12 , 4.001 , 4.06 , 4.128 , 6.54)  –

”States of affairs are independent of one another”. (1.13 , 2.06 , 2.061 , 2.062 , 2.063 , 3.12 + 3.12 , 4.06)

”From the existence of one state of affairs it is impossible to infer the existence or non-existence of another”. (1.13 , 2.06 , 2.061 , 2.062 , 2.063 , 3.12 + 3.12 , 4.06)

Thus, the actual world , i. e. ”the world .. that is the case” (1)  by the use of methods of natural science (6.53) , is a (eternal jigsaw) puzzle formulated, put together ”piece” by ”piece” , little by little ; throwing ”false positives” out.

Eternal jigsaw puzzle even if ”the world” as ”facts in logical space” (1.13)  of correspondence theory + the three laws of (classical) logic applied in ”u – language” may be, or rather ! is to be, seen ”sub specie aeterni” as existence of (eternal) platonic ”whole” (3.42 , 6.45).

That ”independence” is to say, t h a t  –

THE  TOTALITY*  OF  THESE  WELL – FORMED  ”PROPOSITIONS .. CANNOT  BE  SAID” , IT*  I S  ”ANUMERICAL” / ”W I T H O U T  NUMBER”  BY  ANY  MEANS  OF  LOGIC  ”.. BEFOREHAND .. O N  ONE  OCCASION ..” (2.18 , 3.12 + 3.14 , 4.001 , 4.0312 , 4.06 , 4.12 , 4.121 , 4.1212 , 4.128 , 5.47 , 6.4321).

The question was about the consistency of picture theory / correspondence theory. Ergo, what is the answer, are the answers ?

Is the correspondence theory of truth, and thereby picture theory, consistent ?  Yes  –  it is, they are.

That ”anumerical”  is to say, t h a t  –

WELL – FORMED  ”PROPOSITIONS”*  EXCLUDE  (by ”their”* logical nature)  THE  EXPRESSION  OF  ”EACH  OTHERS”*  by any means of logic ”.. beforehand .. on  o n e  occasion ..” (5.47).

The question was about the consistency of picture theory / correspondence theory. Ergo, what is the answer, are the answers ?

Is the correspondence theory of truth, and thereby picture theory, consistent ?  Yes, it is ; they are. To wit, the way independence stands, alonside connexion or conjunction between ”u – language” and reality, is ! just that all ”logical forms” cannot ”.. be said beforehand .. on one occasion ..” (2.18 , 4.128 , 5.47).

The necessary condition of independence of the correspondence* theory of truth, to be consistent, stands  a l o n g s i d e  i t s*  sufficient condition, i. e. ”the existence of an internal relation” (4.125)  B Y  WAY  OF  –

”THE  TOTALITY  OF  PROPOSITIONS”  A S  ”PICTURES  OF  REALITY”  IS  UNDECIDED. (4.001 , 4.06)

Thus, by way of this (2.18 , 3.12 + 3.14 , 4.001 , 4.0312 , 4.06 , 4.12 , 4.121 , 4.1212 , 4.128 , 5.47 , 6.4321) , the correspondence theory is coherent, correct and applicaple.

And if some here is (some kind of) paradox, it may the logical fact that correspondence theory is coherent just because ! its coherency cannot be proved by derivying all (throughout it) provable ”true or false” propositions .. ! just because of  t h i s ”derivying”  w o u l d  lead  non – coherency.

Also it may be a reason of (some kind of) paradox or ”mystical” , that at the same when ”the totality of propositions” as ”pictures of reality” is undecided one can be convinced of the logical fact that there are ”propositions” , which are necessarily ”true” : If not, then there is ”nothing” in reality which the ”sense” of the ”false” proposition agrees not, and a ”false” proposition would be an expression of the ”truth” of the whole reality.

The undecidable result of ”propositions” , that can be provable ”true or false” is interrelated with the result that there are, exist ”truths” , which are ”.. inexpressible .. cannot put into words” (4.1212 , 6.552). A result which in my book resembles Kurt Gödel’s firts incompleteness theorem in 1931, and then few years later in 1936, Alain Turing’s negative result of Entscheidungsproblem.

Only what you have to do to get this undecidable result is to suppose that the correspondence theory of truth with the laws of (classical) logic is right, sufficient to conclude in the end of the analysis the existence of ”truths” , which are ”.. inexpressible .. cannot put into words .. beforehand .. on  o n e occasion ..” (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 5 , 5.01 , 5.47 , 5.55 , 5.551 , 5.5571 , 6.552 ) , i. e. ! these ”truths” are not be said forever undecidable, but there are, will be (allways) ”truths” to be decided.

Recall, that Wittgenstein’s aim  –  ”.. to draw a limit .. to the expression of thoughts ..” (Preface)  –  was to decide a priori in logic (5.55 , 5.551 , 5.552) , by its means, the question of ! ”.. the form of  a l l  propositions ..” (4.001 , 5.47)  which provable and consistent ”.. can be true or false ..” (2.18 , 3 , 3.12 , 4 , 4.06 , 4.211 , 5 , 5.01) ; throughout the logic of correspondence theory (2.024 , 2.21 , 2.221 , 2.222 , 2.223 , 4.031 , 4.061) , by the laws of (classical) logic.

”It is clear that everything which can be said beforehand about the form of all propositions at all can be said on one occasion ..”. (5.47 , 5.551 , 5.552 , 5.5521)

”Our fundamental principle is that every question which can be decided at all by logic can be decided off-hand. (And if we get into a situation where we need to answer such a problem by looking at the world, this shows that we are on a fundamentally wrong track.)” (5.47 , 5.551 , 5.552 , 5.5521)

”The ”experience” which we need to understand logic is not that such and such is the case, but that something is ; but that is no experience. Logic precedes every experience  –  that something is so. It is before the How, not before the What”. (5.47 , 5.551 , 5.552 , 5.5521)

”And if this were not the case, how could we apply logic? We could say : if there were a logic, even if there were no world, how then there be a logic, since there is a world?” (5.47 , 5.551 , 5.552 , 5.5521)

Paragraph 5.5521 is a kind of ! ”koan” , with a positive (logical) meaning / ”.. since there is a world ..” (5.5521)  expressed by the logic of correspondence theory by the fact that ”the totality of propositions” as ”pictures of reality” is undecided ; and ! thereby to show, not only the possibility of ”true or false” propositions but the (necessary) existence of ”true” propositions as representives that ”.. the world ..is”  (6.44 , 6.522).

And so, although his effort fails .. ! throughout just this failing .. Wittgenstein shows the ! necessary ! ! possible existence of ”truths” , and conclude (in my book) with a sense of humour  –

”For an answer which cannot be expressed the question too cannot be expressed. The riddle does not exist. If a question can be put at all, then it can also be answered”. (6.5 , 6.51)

”Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked. For doubt can only exist where there is a question ; a question only where there is an answer ; and this only where something can be said”. (6.5 , 6.51)

To wit, the fact that ”.. The riddle does not exist ..” (6.5) , that is to say ! since ”.. the world .. exists” (5.5521 , 6.44) , be it ”mystical” or not, is precisely because of what Wittgenstein have asked, answered and thus anyway said  –  with extra vigour of denying ”the said”.

11 .     ”The logical forms are anumerical ..” (4.0312 , 4.128 , 6.4321)

Wittgenstein’s ”fundamental thought” (4.0312)  with more respect to his doctrine of ”of the substance of the world”  –

”Objects form the substance of the world. Therefore they cannot be compound”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

Recall : ”The facts in logical space are the world”. ( (1.13)  ←  2.021  →  (3.12 + 3.14 , 4.06 , 5 , 5.01) )

Recall, ”the facts in logical space” are to be constructed ”in logical space” of the correspondence theory of the truth. (1.13  →  (2.21 , 2.221 , 2.222 , 2.223)  →  (3.12 + 3.14 , 4.031 , 4.06) ) , with the laws of (classical) logic. So, there is not a single ”fact” yet, until ”we make ourselves pictures of facts” (2.1) , and the fact that ”the picture is a fact” (2.141 , 3.12 + 3.14 , 4.06)  simply because to show ! the possibility of facts existing in reality of (ontological) realism  p r e s u p p o s e s  to show the possibility of ”pictures of facts” , i. e. ”pictures of the reality” ( ( (1 , 1.1 , 2.024 , 2.06 , 2.063)  ←  3.12 + 3.14 , 4.06)  ←  4.061).

Hence, ”the facts” in question are all propositions, which ”can be true or false” throughout the logic of the correspondence theory ; consistent and provable (3.12 + 3.14 , 4.06 , 4.211 , 5 , 5.01)

Hence, ”the substance” in question is for these well-formed propositions.

”The simple signs employed in propositions are called names”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

”The name means the object. The object is  i t s  meaning. (”A” is the same sign as ”A”)”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

”The postulate of the possibility of the simple signs is the postulate of the determinateness of the sense”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

”Only the propositon has sense ; only in the context of a proposition has a name meaning”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

Thus  –  ”.. the simple signs is the postulate of the determinateness of the sense .. of a proposition ..” (3.23 + 3.3).

Recall that abovesaid already concers ”a fact” , i. e. ”a proposition” as ”a picture of reality” (3.12 + 3.14 , 4.01 , 4.06) , that is to say ”.. not merely the preliminary to a proposition” (4.064 , 4.0641) ; not anymore a question of the conditions of an arbitrary (declarative) sentence representing the first layer of  ”the substance of the world” (2.021)  to be well-formed proposition  throughout correspondence theory + the laws of (classical) logic, but what it is to be a  well-formed proposition  –

”The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of atomic facts” (4.2).

So, what is the place in pragraph 4.2 where ”.. the simple signs .. postulate .. the determinateness of the sense” (3.23) ?

The place where ”objects” as ”simple signs” , that is ”their” simple meanings (2.021 , 3.202 , 3.203) , are situated, i s  –  ”.. with the possibilities of the existence and non-existence of atomic facts” (4.2).

AND  NOW .. let us to recollect ! the pivotal thing of the logic of correspondence theory when the place of  ”the existence of an internal relation” (4.125)  is in question :

” Objects contain the possibility of all states of affairs”. (2.014 .. 4.2 .. 5.01)

Not to repeat all that ’cavalcade’ of Wittgenstein’s paragraps, what I have said in chapter 8. , but only the last conclusion to see, comprehend the role of the ”objects” , first in the determination of well-formed propositions as ”pictures of the reality (4.06) , and then, secondly in the context of Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  –

”The picture  c o n t a i n s  the  p o s s i b i l i t y  of  ”the truth  a n d  falsity  of the truth-arguments of the picture itself”” ( ( (2.11)  →  2.203  ←  (4.25 + 4.3 + 4.41 + 5.01) ).

”The name occurs in the proposition only in the context of the elementary proposition”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01 , underline with bolding continues (5.01) )

”Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

”The elementary propositions are the truth-arguments of propositions”. (2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

Thus, the question here to answer is : The role, meaning of the ”objects” in the derermination of well-formed propositions as ”pictures of the reality ( (4.06)  ←  3.3 , 4.23 , 5 , 5.01) ?

In my book the role, meaning of the ”objects” , as ”the substance of the world” ( (1.13)  ←  2.021  →  (3.12 + 3.14 , 4.06 , 5 , 5.01) )  is clearly that of  –

The  p o s s i b i l i t y  of ”the truth  a n d  falsity  of the truth-arguments of the picture itself””  i s  contained  i n ”the meanings of simple names” which constitute ”the  truth-arguments of propositions” ( (1.13)  ←  2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.2 , 4.23  →  (3.12 + 3.14 , 4.06 , 5 , 5.01) ).

T h u s, ”the meanings of simple names” (2.021 , 3.202 , 3.203) , which are present ”.. in the proposition only in the context of .. the truth-arguments of propositions” (3.3 , 4.23 + 5.01)  a r e  e x p r e s s i o n s  of the  p o s s i b i l i t y  of ”the truth  a n d  falsity of the truth-arguments” (3.31 , 3.311 , 3.318 , 4.2).

”I call any part of a proposition that characterizes its sense an expression (or a symbol). (A proposition is itself an expression.) Everything essential to their sense that propositions can have in common with one another is an expression. An expression is the mark of a form and a content”. (3.31 , 3.311 , 3.318)

”An expression presupposes the forms of  a l l  the propositions in which it can occur. It is the common characteristic mark of a class of propositions”. (3.31 , 3.311 , 3.318)

Why  –  ”an expression presupposes the forms of all the proposition in which it can occur ..” (3.311) ?

S i n c e : ”Objects contain the possibility of  a l l  states of affairs”. (2.014 , 2.0141)

And  s i n c e .. ! self-referring : ”The possibility of its occurrence in atomic facts is the form of the object”. (2.014 , 2.0141 , 2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

H e n c e, paragraps (2.014 , 2.0141)  are interrelated. They have to be read together, with help of forthcoming paragraps. To say that ”objects contain the possibility of all states of affairs” (2.014)  is to say concurrently, at the same time that ”objects contain the .. possibility of its occurrence in .. all state of affairs” ( (2.014 + 2.0141)  ←  2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 4.23 , 5 , 5.01)

Recall that ”a proposition” as ”a picture of reality” (4.01)  must have ”internal relation” (4.125 , 4.1251)  to reality, i. e. ”relation” which is cointained in ”a proposition” itself, the ”external relation” being already occupied by independence, and ! thus, actually by definition, ”a proposition” as ”a picture of reality” contains ! necessarily all ”its” possible truth-values. By definition not only because of the determination of reality (2.06) , but already by definition of  the concept of ”truth” by correspondence theory. If a proposition or sentence has (to have) to itself contained relation to reality, it must by definition of the correspondence theory of truth have some truth-value, and since any truth-value cannot be beforehand excluded all truth-values must be present ( , including the possibility that ”truth-values” turn over, refute one another).

”I conceive the proposition  –  like Frege and Russell  –  as a function of the expressions contained in it”. (3.31 , 3.311 , 3.318)

T H U S, ”the meanings of simple names” (2.021 , 3.202 , 3.203)  a r e  e x p r e s s i o n s  of the  ALL the  p o s s i b i l i t i e s  of ”the truth  a n d  falsity of the truth-arguments of propositions” (2.014 , 2.0141 , 2.021 , 3.202 , 3.203 , 3.23 , 3.3 , 3.31 , 3.311 , 3.318 , 4.2 , 4.23 , 4.25 , 4.3 , 4.41 , 5 , 5.01)

The in my book (again) simple reason, why ”the substance of the world” is what is, is the undeniable fact that there is no language ! without ”meaning”* ; so that concept* is a common maker to all languages and thereby a good subject to contain.

S O, in total, to consummate : What is the role of ”objects” in the context of Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321) ?  –  In the context of fact, t h a t  –

WELL – FORMED  ”PROPOSITIONS”*  E X CLUDE  THE  EXPRESSION  OF  ”EACH  OTHERS”* .

In the context of fact, t h a t  –

”THE  TOTALITY  OF  PROPOSITIONS”  A S  ”PICTURES  OF  REALITY”  IS  UNDECIDED. (4.001 , 4.06)

”Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is”. (3.221 , 5.55 , 5.5571)

”We must now answer a priori the question as to all possible forms of the elementary propositions. The elementary proposition consists of names. Since we cannot give the number of names with different meanings, we cannot give the composition of the elementary proposition”. (3.221 , 5.47 , 5.55 , 5.551 , 5.5511 , 5.5571 , underline continues (5.5571) )

”If I cannot give elementary propositions a priori then it must lead to obvious nonsense to try to give them”. (3.221 , 5.47 , 5.55 , 5.551 , 5.5511 , 5.5571)

What is the reason Wittgenstein to say  –  ”.. I cannot give elementary propositions a priori ..” (5.5571) ?

W h y  –  ”.. we cannot give the number of names with different meanings ..” ( (4.128)  ←  5.55) ?

W h y  –  ”.. it is senseless to speak of the number of all objects ..” ( (4.1272 , 4.128)  ←  5.55) ?

S I N C E , to the (total)  s e t ”of names with different meanings” (5.55)  would  i n h e r e  also ! the ”names” , WHICH  CONSTITUTE  the  p o s s i b i l i t i e s  of ”the truth  a n d  falsity of the truth-arguments of propositions”  A N O T H E R ! ”l o g i c a l  forms” (4.128)  –  ”.. a logical place  o t h e r ..” (3.4 , 3.41 , 3.411 , 4.0641)  –  that is  the ! ”.. propositions .. w h a t .. c a n n o t  be said” (2.022 , 2.023 , 2.18 , 4.12 , 4.121 , 4.1212 , 4.128).

Ergo, if the (total) set ”.. of names with different meanings .. the truth-arguments of propositions .. cannot put .. into words ..” (2.021 , 3.202 , 3.203 , 3.221 , 3.23 , 3.3 , 4.23 , 5 , 5.01 , 5.55 , 5.5571 , 6.522) , t h e n  the (total) set of propositions, that can be provable ”true or false” is not possible to say (2.18 , 4.001 , 4.0312 , 4.06 , 4.12 , 4.121 , 4.1212 ,  4.128 , 6.4321).

”The sense of a proposition .. being .. a picture of reality .. is .. inexpressible ..” (4.01 , 4.06 , 4.2 , 6.522).

Thus, even if it would be possible ”.. the propositional sign .. be contained in itself ..” (3.332) , it would be not possible ”.. the propositional sign .. be its own argument ..” , that is to say, be ”.. expression of the agreement and disagreement with the truth-possibilities of .. the truth-arguments of propositions” (3.332 , 3.333 , 4.431 , 5.01) , because the effort of ”the propositional sign”  t o  e x p r e  s  s ! ”its agreement with the truth-possibilities of  ! i t s  own truth-arguments”  WOULD  BY  ”.. l o g i c a l  necessity ..” (6.375)*  S H O W  ”.. A  LOGICAL  PLACE  O T H E R .. O U T SIDE ..” (3.4 , 3.41 , 3.411 , 4.0641)  of this  e f f o r t , b e c a u s e  o f* the law of non-contradiction and the law of identity. So, it is an ”effort” that denies itself.  –  (You may look at appendix 1. )

And above said in fact agrees that said in paragraps 3.332 and 3.333 as a logical consequence of the pivotal fact of  throughout correspondence theory well-formed propositions are ! already  c o n t a i – n i n g  their ”truth-conditions” , since  –

”.. If, for example, we suppose that the function F(x) could be its own argument, then there would be a proposition ”F(F(fx) )” , and this outer function F and the inner function F must have different meanings ; for the inner has the form φ(f x) , the outer the form ψ(φ(f x)). Common to both funktion is only the letter ”F” , which by itself signifies nothing. ..”. (3.332 , 3.333)

But, what is then .. if anything .. in the fact that a valid ”language” / ”u – language”* by correspondence theory of ”truth” with the laws of (classical) logic is undecidable, i. e. cannot be derived in ”its”* totality by any means of logic ! that Wittgenstein calls  –

12 .     ”Das Mystische” / ”The mystical” (6.44 , 6.45 , 6.522)

In the beginning of my paper I said the reason why Wittgenstein’s aim ends up ! ”Das Mystische” / ”The mystical” (6.44 , 6.45 , 6.522)  to be that the logic of correspondence theory* , ”the facts” being based on it* , ”cannot be represented” (4.0312) , and ! nevertheless it* is correct .. j u s t  because of ! (4.0312) , i m p l y i n g .. ”truths” , that are ”.. inexpressible .. cannot .. put into words” (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.552).

Anyway, it is not quite so, the reason why Wittgenstein’s aim ends up to ”.. the mystical feeling” (6.45). It is rather and ! more a question of the ”limited whole” , an intertwined question with ”limited whole”.

”Not how the world is, is the mystical, but that it is”. (6.44 , 6.45 , 6.522)

”The contemplation of the world sub specie aeterni is its contemplation as a limited whole. The feeling that the world is a limited whole is the mystical feeling”. (6.44 , 6.45 , 6.522)

”There is indeed the inexpressible. This shows itself ; it is the mystical”. (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321  →  (6.44 , 6.45 , 6.552) )

However, Wittgenstein says, reminds nothing of ! the cause* , the  m a d e – up of the ”limited whole” :

”The contemplation of the world sub specie aeterni is its contemplation as a limited whole .. is the mystical feeling” ( ( (1.13)  →  3.12 + 3.14 , 3.42 , 4.001 , 4.06)  ←  6.45 )  i s  made up throughout the correspondence theory* + the laws of (classical) logic* ( (2.222 , 4.031) + (2.21 , 3.203 , 4.211) ).

Applying these things* to or in the ”u – languge” the conclusion will be that the ”u – language” , as containing, having ”from within” (4.114) , a relation to the reality, contains*  a l l  possible truth-values of propositions (possible to form) in the ”u – language” (1.1 , 1.11 , 1.13 , 2.06 , 2.063 , 2.1 , 2.11* , 2.12 , 2.201 , 2.202 , 2.203* , 3.02* , 3.318 , 4.1 , 4.25* , 4.3 , 4.4 , 4.41 , 4.431 , 5 , 5.01) , and ! concurrently point at, refer  o u t s i d e* ! of the ”u – language” (3.4 , 3.41 , 3.411 , 4.0641).  –  This ! virtual* incongruity is the gist of ”the mystical”.

Recall the fact : ” The facts in logical space are the world”. (1.13  ←  (6.44 , 6.45 , 6.522) )

Recall the fact what these ”facts” (1.13)  are, i. e. that they are ”propositions” as ”pictures of the reality” , and ! recall for what logical reason (they are) : ”Propositions can be true or false only by being pictures of reality” (1.13  →  (2.141 , 3.12 + 3.14 , 4.06)  ←  6.44 , 6.45 , 6.522).

And thirdly, recall the fact that ”the facts in logical space ..” are constructed ”in logical space” of the correspondence theory* of the truth (1.13  →  (2.21 , 2.221 , 2.222 , 2.223)  →  (3.12 + 3.14 , 4.031 , 4.06) ) , with the laws of (classical) logic* ; by applying these* in ”u – language” , which Wittgenstein calls  ”the substance of the world” (2.0124 , 2.021 , 3.203 , 3.3 , 4.002 , 4.031 , 4.0311) , i. e. ”the substance of the” all well-formed propositions as ”pictures of the reality” ( (1.1 , 1.13 , 2.06 , 2.063)  ←  3.12 + 3.12 , 4.06). ”U – language” is ! simply the necessary (2.0211 , 2.0212 , 4.2211)  material, stuff ”.. from within .. we make ourselves pictures of facts” (2.1 , 3.12 + 3.12 , 4.001 , 4.06 , 4.114) , throughout the correspondence theory of truth + the laws of (classical) logic. It is the logic of correspondence theory, the first rule or in fact ! axiom of that theory of truth, which make to do ”.. ourselves pictures of facts” , i. e. ”pictures of reality” (1.1 , 1.11 , 2.06 , 2.063 , 2.1 , 4.06). The axiom is that of independence of the ”u – language” of the reality (1.12 , 2.021 , 2.024 , 2.06 , 3.203 , 3.3 , 4.031 , 4.061) , which says that if ”u – language” is not, in the first place, independent of reality, then correspondence theory will be in the case of a proposition to be ”true” a ! circular argument and in the case of a proposition to be ”false” a ! ! contradiction. All the same the axiom of independence raises immediately ! the question of the possibility of a proposition at all to be ”true or false” throughout correspondence theory. The question concerns to (how be able to) compare a proposition or what it represents with reality! If only independence stands, then ”to compare with reality” is prohibited : ”U – language” and reality cannot be expressed together, in order to be able to compare propositions* or what propositions of the ”u – language” represent* with reality and so to show them* ”true or false”.  It is a question of ”provability” ; (how) to prove a proposition ”true or false” , to prove that a proposition or what it represents agree or disagree with reality. Wittgenstein’s answer is PToL (2.16 , 2.161 , 2.17 , 2.18 , 2.21 , 2.221 , 2.222 , 2.223 ,  4.01 , 4.031 , 4.06).

Hence the abovesaid ”construction” so, that the contingent ”truth or falsity” of a proposition can be proven, consistently (2.21 , 2.221 , 2.222 , 2.223 , 4.031 , 4.1 , 4.211 , 4.25 , 5 , 5.01). The conclusion of this ”make-up” of the well-formed propositions is the virtual, ”containing” and ”refer outside” , incongruity.

All the more, to take into account Wittgenstein’s aim (Preface / ( (3 , 3.12 , 4)  ←  4.001  ←  (4.06 , 4.112 , 4.114) ) ) , and its conclusion ; his ”fundamental thought” (4.0312 , 4.128 , 6.4321). If the first two parts of this paper where for, in by book, undeniable facts of Tractatus / PToL , then the abovesaid facts are undeniable facts of (trying to) comprehend the ”mystical” (6.44 , 6.45 , 6.522). Thus ”the mystical” is one aspect, point of Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321) , the impossibility to ”.. delimit .. the thoughts .. limit .. from within the thinkable” (4.112 + 4.114).

What is ”the mystical” , in my book book yet virtual, point in the fact that by means of any logic it is not possible to say, express ”.. beforehand .. on  o n e  occasion ..” all the propositions that can be provable and consistent ”true or false” (1.1 , 1.12 , 1.13 , 2.06 , 2.063 , 2.21 , 2.221 , 2.222 , 2.223 , 3.12 + 3.14 , 4.001 , 4.031 , 4.06 , 4.1 , 4.2 , 4.211 , 4.25 , 5.01 , 5.47 , 5.55 , 5.551 , 5.5571) ?

In order to fullfil ”the object of philosophy” (Preface / ( (3 , 3.12 , 4)  ←  4.001  ←  (4.06 , 4.112 , 4.114) ) ) , Wittgenstein has to determine the conditions of a proposition to be ”true or false”. He needs a theory of truth, determination of the concept of ”truth” ; correspondence theory* (2.21 , 2.221 , 2.222 , 2.223 , 4.031). Accompanied by the laws of (classical) logic* (2.0233 , 2.02331 , 2.17 , 2.18 , 2.21 , 3.203 , 4.06 , 4.211 , 5.53 , 5.5303). To apply these* in ”u – language” tells what are the conditions of a proposition to be ”true or false” , i. e. the conditions of the propositions (possible to form) in the ”u – language” to be provable and consistent ”true or false”. And the last line of that ”applying” ( , which entire story I don’t repeat, ) tells inevitable, it is ”.. a logical necessity ..” (6.375) , that the conditions of these well-formed propositions* as ”pictures of reality” (4.06)  are such  t h a t  they* presuppose each others* (1.13 , 3.12 + 3.14 , 3.4 , 3.41 , 3.411 , 3.42 , 4.01 , 4.06) , BUT  IN  A  WAY  THAT  IT  IS  N O T  POSSIBLE , it is ”.. a logical impossibility” (6.375)  to  s h o w  a l l  these well-formed propositions* as ”pictures of reality” (4.001 , 4.06 , 5 , 5.01 , 5.47 , 5.55 , 5.551 , 5.5571). That well-formed propositions* presuppose each others* means actually that ! not a single such a proposition can be expressed, said ; it would ! as well necessitate another proposition, ”.. a logical place other ..” (1.13 , 3.12 + 3.14 , 3.4 , 3.41 , 3.411 , 3.42 , 4.01 , 4.06 , 4.064 , 4.0641) , which would then perhaps have further another proposition different than the first, and so on .. . As you may remember, the reason of that well-formed propositions* presuppose each others* is that they* , a proposition to another proposition, represent, i. e. substitute each others*  p o s s i b i l i t i e s  to be ”false” by that another proposition being ”true”. So that there is ”something” in reality (that is possible) to disagree with ; what a ”false” proposition represents do not agree (with that) what a(nother) ”true” proposition represents. Hence, it is ”.. a logical necessity ..” (6.375)  that these each others* ”true or false” – possibilities representing, substituting propositions* ”.. cannot be said” (4.1212)  s i n c e  they* d i s a g r e e  with each others* , and by law of non-contradiction  t h e y* e x c l u d e  the expression of each others* , which is the same as to say that from a ”true” proposition* it not allowed to derive a ”false” one* , even so (the existence of) a ”false” proposition* presupposes (the existence of) a ”true” one*.

So, Wittgenstein’s aim (Preface / ( (3 , 3.12 , 4)  ←  4.001  ←  (4.06 , 4.112 , 4.114) ) )  fails :

”The totality of propositions” as ”pictures of reality” in undecided. ( (4.001 , 4.06)  ←  2.18 , 3.12 + 3.14 , 4.0312 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.522)

B u t ”.. the mystical feeling” (6.45)  in that failior ?  It is already in Wittgenstein’s aim! It is already in the question to show, not only all propositions but a single proposition that can provable and consistent be ”true or false” throughout the correspondence theory of truth + the laws of (classical) logic. The cause of ”the mystical” is literally built-in to correspondence theory, in spite of standing, not depending of the laws of (classical) logic. To wit, I think that the laws of (classical) logic depends on the truththeory in question. If we suppose that correspondence theory hold true, then first independence is to be approved. If not approved, then we do not need any correspondence theory since at once, at the same time with a proposition* we have  b o t h  its* ”truth and falsehood”. If not independence stands , then at the same time by ”.. a proposition with a sense” (2.221 , 4 , 4.031)  there is also ! the reality present, ”a sense” to agree or disagree with (2.21 , 2.221 , 2.222 , 4.031) , i. e. both to agree and disagree with reality are present. The mess, confusion is not only that ”truth and falsehood” / ”a sense” of a proposition ”to agree and disagree with reality” can be seen ! right away, i. e. there is no need ”to compare” , but (the mess is) ! also that to see the difference, differentiate ”a sense” of a proposition and reality. It is the question that ”something”* is in agreement and disagreement with ! ”itself”* ; the question of circular argument and contradiction.

But ! .. if ”we do not need any correspondence theory” , then we do not have any truth-values either. Perhaps any values at all. Still, here with Tractatus is not possible to avoid ! to make a difference ; not possible to avoid to concider that the correspondence theory stands, holds true. Thus, independence must stand, between language* and reality ; be it* ”u – language” , as Wittgenstein’s aim presupposes, or not. Thus, we seem to confront a puzzle. That independence is necessary to correspondence to be not (both) circular argument and contradiction  m i s match the possibility to prove the agreement or disagreement with reality what a proposition represents, since to compare what a proposition represents with reality is not possible. Yes, by independence correspondence theory of truth is not circular argument and contradiction. But ! yet, only by independence it is useless, in a nonworking condition, or we have to count on to independence as an axiom and .. draw lots consistent ”true or false” propositions. Still, as said, here with Tractatus is not possible to avoid to concider that the correspondence theory stands, holds true also with the possibility that the ”truth or falsehood” of a proposition is both consistent and provable. Thus independence between ”u – language” and reality is not enough. Hence, axiom of independence is relative to that there is something in common with ”u – language” and reality, which ”something in common” accomplish to compare ”u – language” and reality, i. e. to compare what a proposition represents with reality, and so to prove a proposition in question ”true or false” by showing, demonstrating the agreement or disagreement of the ”sense” what a proposition in question represents with reality (2.12 , 2.16 , 2.161 , 2.17 , 2.18 , 2.21 , 2.221 , 2.222 , 2.223 , 4.01 , 4.031).  –  To be continue ..

In itself Wittgenstein’s ”fundamental thought” (4.0312 , 4.128 , 6.4321)  is not strange, enigmatic. That ”the logical forms are anumerical ..” (4.128) , i. e. that it is not possible to express all well-formed propositions by means of any logic ”.. beforehand .. on one occasion ..”. (5.47) , is consequent with the idea of correspondence theory as truth-theory of (ontological) realism. At least in my book correspondence theory presupposes (ontological) realism. And in order to this sine qua non to hold true it is not enough that the totality of propositions as ”pictures of reality” are undecided, but there must exist ”truths” , that are ”.. inexpressible .. cannot put into words” (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.552). To wit these in ”u – language” existing ”truths” which however ”.. cannot be said .. beforehand .. on  o n e  occasion ..” (4.1212 + 5.47)  by means of any logic represent the of any (human) mind, consciousness or whatsoever observation independent existing reality.

And, one may try to think any (human) mind, consciousness or whatsoever observation without some ”language”. These in ”u – language” unspeakable, but to the non-contradiction of the correspondence theory + the laws of (classical) logic necessary, ”truths” represent  the of ! ”u – language” independent existing reality ; which ! independence of reality of ”u – language” has to be shown in ”u – language” itseself, ”from within” (4.114).  –  How it is shown ?

Recall that when trying to fullfil his aim, throughout the correspondence theory + the laws of (classical) logic, Wttgenstein was forced to simulate, make a model of the valid relation between ”u – language” and reality. A simulation that has to be done ! in ”u – language” itself. In the beginning of the analysis of the valid relation between ”u – language” and reality there exists nothing else but ”u – language” , since in order to be (not circular argument and) non-contradictory ”u – language” must be independent of reality (1.1 , 1.11 , 1.12* , 2.0124 , 2.021 , 2.024* , 3.203 , 3.3 , 4.002 , 4.061). Hence in order to that independence to hold true it must to have its place also in that simulation, in the ”u – language” itself. So, what is the place* of that independence in the simulation, model of the valid relation between ”u – language” and reality ?  It* is ! n o w  the non-contradiction of that model to stand, by pointing out the impossibility of Wittgenstein’s aim to ”.. limit the thinkable .. from within ..” (3 , 3.12 , 4 , 4.001 , 4.06 , 4.112 , 4.114). The totality of well-formed propositions* made by the correspondence theory + the laws of (classical) logic include members* which exclude each others. Thus, to say inversely ”.. there is .. a logical impossibility” (6.375)  to construct the totality of well-formed propositions. Any such effort would eventually ! to blow up by trying to enumerate propositions* , which exclude (to express) each others*. In other words the algorithm to ”.. make to ourselves .. the totality of .. pictures of reality” (2.1 , 2.141 , 3.12 + 3.12 , 4.001 , 4.06)  would be, end up in infinite loop, run forever or if stops, then by contradiction.

Hence, no algorithm, manual to express ”the totality of .. pictures of reality” (4.001 + 4.06) , which represent the existence of the world. Hence, ”.. the world .. is” (6.44) , exists independent of the ”u – language”* ; expressed in ”it”* itself by ”truths” , that are ”.. inexpressible .. cannot .. put into words” (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.552).

These in ”u – language” unspeakable ”truths”* represent the existence of the world simply by being ”true” propositions according to the correspondence theory (2.21 , 2.221 , 2.222 , 2.223 , 4.031) : ”They”* presuppose ”.. the world .. that .. is” (6.44) , to agree with.

So, if there is anything mystical from the point of view of the logic of the correspondence theory with the laws of (classical) logic in the undecidability of ”the totality of .. pictures of reality” (4.001 + 4.06) and in the existence of ”truths” , that are ”.. inexpressible .. cannot put into words” (2.18 , 4.12 , 4.121 , 4.1212 , 4.128 , 6.4321 , 6.552) , what is then ”the mystical” (6.44 , 6.45 , 6.522) ?

“To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.”
― William Blake, Auguries of Innocence

”Although a proposition may only determine one place in logical space, the  w h o l e  logical space must already be given by it”. ( (1.13 , 3.12 + 3.14 , 3.42 , 4.06)  ←  6.44 , 6.45 , 6.522)

Wittgenstein’s mysticism is that of well-known, to see ”All” in ”One”.  –  But, featuring by ! Logic.

To be continue ..

Appendix 1 :  ”The sense of a proposition” (4.2 , 4.46).

Appendix 2 :  The enumeration of paragraps used.

Epilogue

References