Something about Wittgenstein

–     heading adopted from Francesco Berto’s Gödel book.

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), as reference.

Otherwise references simply with Wittgenstein’s notation (1 , 1.1 , 1.11 , 2 .. 7). Quotes I take both Ogden and Pears/McGuinness. Sometimes also in German (to compare). Underlines and boldings mine. As also spaces, excect propositions (4.0312 , 4.128).  –  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 University of Cambridge.  –  With Bertnard Russell.  –  With turbulence around the philosophy of mathematics and logic!

And, of course :  Ludwig Wittgenstein

–   –   –   –   –

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 concequence of Russell’s paradox

4 .     Language / ”Universal – language”

5 .     The correspondence theory of truth

6 .      The logic of the correspondence theory

7 .     Picture theory as an implication of independence

….

Foreword

To make throughout the correspondence theory of truth propositions that can be provably and consistent ”true or false”.  –  Is it then possible, in logic to express the totality of these well-formed 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 go on. Step by step, until the last part ”Das Mystische” / ”The mystical” (6.44 , 6.45 , 6.522).  –  Now and then short interludes and comments on, what is to come up.

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)

This  –  ”.. 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 ”gödelian” insight.  –  If nothing else in the beginning of my journey with Tractatus to conceive, then ! ”hold on” .. proposition ! (4.0312) .. Kurt Gödel ?

As soon as you understand 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 reality”. (3.12 , 3.14 , 4.06)

Thus, combining paragraphs (3.12 , 3.14 , 4.06) , we get the two-part meaning of the ”facts”  –  second part being a consequence of first (part) :

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

(This result reading, that ”projektive relation to the world” is synonym to ”picture of reality”.)

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” / ! Russell’s paradox.

Now, / 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 ”proposition” to be ”true or false” rest on the correspondence theory of truth.  –  And as said (in my Preface) , PToL is ! yet 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 ”the book will” / ”the object of philosophy” (Preface , (4.112 , 4.114) ) , i. e. to show all the propositions, that can be ”true or false” (4.001 , 4.06 , 5 , 5.01).

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 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  –  ”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  c o r r e c t .. j u s t  because of .. ! (4.0312) , i m p l y i n g .. ”truths” , that are ”.. inexpressible .. cannot put into words” (4.128 , 6.4321 , 6.552).

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 pf 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)

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

Keyword is ”thought” , i. e. ”.. the propositional sign .. in its projektive relation to the world”. (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)

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

It is not so ☺ bold to assume that ”propositon with a sense” indicates ”in its projektive relation to the world”.

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

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

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

The thinkable” (4.114)  is therefore every ”propositional sign” , that is formed so, ”.. that its elements, the words, are compined in it in a definite way ..” (3.12 , 3.14a s ”pictures of reality” implicating, t h a t ”propositions  c a n  be true or false” (4.06).  –  And as it is, all the same, at least Wittgenstein seems to think, as a corollary of Russell’ s pradox, that there is anymore, not yet any such a well-formed propositon, that (as ”picture of reality”) can be ”true or false” , in princible every possible sentence, that can be done in a language is a possibility, possible place of (thinking of) well-formed proposition. That’s why Wittgenstein says  –

”.. Logic treats every possibility, and all possibilities are its facts ..”. (2.0121)

Anyway one needs a language to say  –

”We make ourselves pictures of facts”. (2.1)

It is not (even Wittgenstein) possible to ”.. make .. pictures of facts” ! n o where, not as if  .. but ! literally from ”nothing”.  –  Thus, it is simply because of one needs a language, when Wittgenstein argues : ” .. It will .. only be in language that the limit can be drawn .. from within ..” (Preface, (4.112 , 4.114).

That the possibility of proposition to be ”true or false” means provable and consistent (4.211 , 5 , 5.01) can here yet not to be considered. It is the question of necessary terms of correspondence theory of truth.  –  It is to be considered the inevitable question of the logic (6.375)  of that theory of truth!

Thus  –  ( 1.  / if and only if  2. )  –  the possibility of proposition to be ”true or false” i s  provable, and ! yet the contistency of correspondence theory of truth is to be proven.

(Some moves ahead both questions, i. e. ”provable” and a bit later ”consistent” ,  are to be answered. )

Correspondence theory of truth, as it’s logic entails, throughout ”picture theory” , is Wittgenstein’s method to take up the challence for propositions, which ! altogether  c a n  be ”true or false”.

And (of course) as a logician Wittgenstein will ”draw a limit .. to the expression of thoughts” (Preface) , that is to say, that ! Wittgenstein will ”draw a limit .. to the expression of propositions” , which as ”pictures of reality .. can be true or false” (3 , 3.12 , 4 , 4.06).  –  What is (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. 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 would be ”good apples” versus ”rotten apples”. )

Wittgenstein will express  –

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

It’s possible to understand Wittgenstein’ s aim as such, that he asks : ”Is it possible to express in logic all the propositions, which can be provably, consistently ”true or false” ?  –  Without the question why ”the object of philosophy” (4.112 , 4.114)  is determined as it is.

Why ”the aim of the book” (Preface / (4.112 , 4.114) ) ?

3 .     A concequence 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 Campridge.

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. It seems (to me) , that Wittgenstein interpret Russell’s paradox quite simply, get to the ! point, so that there is anymore, not yet .. not ! a single proposition, that can (be said to) be ”true or false” ; provable and contistent.

”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) )  Russell’s paradox can be overcome.

Actually, by taking into account the value of concept ”truth” in logic , Wittgensteins effort is to rebuild the whole logic  –  and / or (at least) show its right place  –  from the very beginning.

(It is perhaps justifiable to say, that so called tree law of thought stand, i. e. law of excluded middle, law of noncontradiction and law of identity. )

If  ”the totality of propositions is a language” (4.001) , in which every proposition is provable and consistent ”true or false” , can be formed, then  –  ”.. Russell’s paradox vanishes” (3.333)  –  and if not (can be formed) , as it is (4.0312 , 4.128 , 6.4321) , even then both the consictency of logic and that logic is ”truth” – preserving stand troughout the logic of correspondence theory of truth.

So, what is needed to accomplish the abovesaid task?  –  What tools ore prequisites are needed?

4 .     Language / *”Universal – language”

*From now on  –  ”u – language.”

”Man possesses ability to construct languages capable of expressing every sense ..”. (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. Thus Wittgenstein’s task ”draw a limit” have to be done in the same space, together with ”the expression of thoughts”.  –  Especially when ! ”the thoughts” (3 . 3.12 , 4 , 4.06)  must first to be done ; in some language (2.1).

What is not (at all) self-evident, tvial is that the language involved must be ”u – language”. If not, then there can be no steps on the ”ladders” (6.54).  –  Why not?  –  If language involved is not assumed to be language as ”u – language” , i. e. where everything ”that can be in principle said” is possible to express, then it is from the very beginning impossible to fullfil the task : Express in logic all the propositions, which can be provably, consistently ”true or false”.

Thus, before Wittgenstein can say his last paragraph (7) , he must ”speak” , express the (very) ”whereof .. one must be silent”.  –  In the beginning, beforehand there can be no limit!

Although Wittgenstein does not state direcly that ”language” has to be ”u – language”* , if not in paragraph (4.002) , his aim imply it*. Not to mention to what Wittgenstein says of ”objects” and ”things” : His ! doctrine of ”of the substance of the world” (2.021).  –  (While Wittgenstein talks a lot, in many paragraphs* , ”objects” and ”things” , I take most of them* with only by numerical sign. If at all. )

”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 to fulfil ”the aim” , it is logical that Wittgenstein at first comprises, determines ”the world” , ”the reality” (2.06 , 2.063). And not only because ”reality” is a concept of the theory, but precisely because of the logic of the correspondence theory (4.061) !  –  And by reason of 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 ”logical space” needed is 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, stranded (as .. Tractatus itself) part of the paper.

Simply : If notu – 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 notu – 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” to 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 precise. Otherwise ”.. 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 , 4.23 , 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 at least ”language” , if not ”u – language” , which ”form the substance of the world” ; the one side or layer of Wittgenstein’s doctrine of the ”substance”.

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

5 .     The correspondence theory of truth

If there is still evident, undeniable facts, along with (the meaning of) ”facts” , ”thougts” and ”draw a limit” , in Tractatus, 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 inulanguage”.

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 , 2.1 , 3.5 , 4.01 , 4.2211).

”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 rightly, 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” 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 ”sense”. )

With respect to PToL Tractatus is actually an analysis of applying the correspondence theory of truth in ”u – language” to get eventually 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).  –  (To 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 it is ”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 constitute, ! model ”the world” (2.063).

And, indeed, Wittgenstein (can) determine, conceive ”the reality” with the correspondence theory 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 ( , an inevitable question) !

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)  then there 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 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 ..” .. b o t h .. ”.. such and such a state of affairs” , which (an) o t h e r ! ”.. a g r e e s  with reality ..” , (an) o t h e r , then ! ”.. n o t ..” (2.21 , 2.221 , 2.222 , 4.031).

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 the law of noncontradiction stands : 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” then 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 space  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.

The concequence of independence is that it is not possible 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 the supposed corollary of Russell’s paradox is the first move of analysis of correspondence theory.  –  Be it for better or worse with Russell’s paradox ( , as a corollary of it).

So, 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 is ! 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 is as for the (valid) relation between ”u – language” and ”reality” , postulated by correspondence theory.

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 logic 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” is obliged to ”.. have something in common ..” (2.16 , 2.161 , 2.17 , 2.18 , 2.21).

First there are nothing else than (pure) 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, then there is still the question concerning the requisite of provability.

Thus, the meaning of the term ”sense” has two sides, layers. The first is purely dealing with the (existence of) theory of truth. The second, and the ! point, deals with how to assert ”.. the agreement or disagreement of .. sense .. with reality ..” (2.222 , 4.031)  so that ”.. its truth or falsity ..” (2.222)  can be consistent and  provable. (2.223).

These two sides, layers of ”sense” are the subtle, but not ☺ .. ”stranded” , 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”.

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 .. ”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 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) / vicious circle.

Hence  –

”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)

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” (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 ! 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). Threfore Wittgenstein says, concludes : ”Objects contain the possibility of all states of affairs” (2.014) , and 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” (4.0311 , 4.0312 , 4.128 , 5.55 , 5.5571).

”If all objects are given ..” (2.0124)  we have already ”.. in the context of a proposition ..” (2.021 , 3.203 , 3.3)  expressions of ”.. all possible states of affairs ..” (2.0124) , i. e. ”.. every sense ..” (4.002) , without being yet affected by independence of reality.

The fact that a ”.. proposition represents such and such a state of affairs” (4.031)  independent of reality comes along not until the logic of the correspondence theory.

 

To be continued ..

 

(And as said  –  this will take some time.)

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