Explaining the Tractatus Logico-Philosophicus

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Sam26
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Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

A Summary of the Tractatus Logico-Philosophicus

I’m going to try to condense the Tractatus, which hopefully will help those of you with an interest to better understand its contents.

The Tractatus is the culmination of Wittgenstein’s early philosophy. It was completed before he was 30 years old. He covers a wide range of philosophical ideas, including, the nature of the world, the properties of language, the nature of logic, the nature of mathematics, and remarks on the philosophy of science, ethics, religion, and mysticism (Wittgenstein’s Conception of Philosophy, by K. T. Fann, p. 3).

Without a doubt the Tractatus is one of the most difficult works in philosophy to understand. One of the reasons for this is the way the book is written, i.e., the style of the book. It consists of very short concise numbered remarks. Another reason the Tractatus is difficult, is that the subject matter itself is difficult. It is common even amongst philosophers to generally misunderstand the contents therein. Even Bertrand Russell misunderstood the contents of the Tractatus, and he wrote the introduction. Today, though, we're in a much better position to understand the contents of the Tractatus.

In the preface to the Tractatus Wittgenstein tells us what the book is all about. “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 thought, 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 therefore 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, p. 3).”

One of the other goals of this thread is not to critique Wittgenstein’s statements, but just to give a general understanding of its contents.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 2

One of the common misunderstandings of Wittgenstein’s later writings is that he rejected the Tractatus. And while it’s true that Wittgenstein did reject some of his earlier premises (e.g., that there was a one-to-one correspondence between names and simple objects in the world – more on what names and simple objects are later), he did not reject the Tractatus in total. This is not to say that he wasn’t a harsh critic of the Tractatus, because he was. It’s only to say that there is a continuity of thought between Wittgenstein’s early and later thinking. That continuity consists in answering the questions of the nature, job, and method of doing philosophy. One can think of Wittgenstein’s early method of doing philosophy, as the traditional method, and in his later works he introduces a new method of analysis (one could look at his early method as an a priori method, and his later method as a posteriori – although this is not written in stone), in both methods he is still thinking about the logic of language, just in different ways.

According to K. T. Fann the basic assumptions behind the Tractatus has to do with the structure of language being revealed by logic, and that the function of language is to describe the world. Wittgenstein deals with two major questions, according to Fann, “(1) What is the nature of logic? And (2) How is language related to the world? (Wittgenstein’s Conception of Philosophy, p. 5).”

The Tractatus is divided into seven major parts, the seventh part, though, only consists of one statement. The following is a list of these seven parts:

(1) “The world is all that is the case.”
(2) “What is the case—a fact—is the existence of states of affairs.”
(3) “A logical picture of facts is a thought.”
(4) “A thought is a proposition with a sense.”
(5) “A proposition is a truth-function of elementary propositions.
(An elementary proposition is a truth-function of itself.)
(6) In six Wittgenstein gives the general form of a truth-function.
(7) “What we cannot speak about we must pass over in silence.”


Each of these numbered divisions are numbered to establish a hierarchy. For instance, remark 1.12 is an elaboration on 1.11, which is an elaboration on 1.1, etc., etc. His remarks are put down as if they were unassailable and definitive, with no argument, or very little argument.

Each of these seven divisions can be further broken down into three main topics, logic, language, and the world.

I will continue…
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 3

Logic seems fundamental to Wittgenstein’s thinking, however, how logic fits into his thinking in both his early and later thinking is a bit different, but not always. A difference can be seen, for example, in his thinking about propositions. Propositions are a mirror image of the world in the Tractatus. Propositions have a one-to-one correspondence with the world, viz., with facts. One can think of meaning in the Tractatus as a kind of pointing to, i.e., propositions point to facts in the world, names as part of propositions point to objects which are the smallest parts of facts. This logic is much different from the logic that is seen in his later philosophy (Philosophical Investigations). In the Philosophical Investigations he uses the language-game and use (of words, of propositions) within the social context to show the logic behind language. A vague proposition in the Tractatus is no longer vague when fully analyzed. In the PI, a vague proposition is still vague when analyzed, but it has a kind of logical use, a social use, that incorporates its vagueness into its social function.

The logic in the Tractatus contains an exactness that is disposed of in the PI (at least for the most part). It’s this exactness, I believe, that leads Wittgenstein to believe that he has solved all the philosophical problems (in the T.) in one fell swoop. How has he solved all the philosophical problems? Well, if as Wittgenstein supposes one can analyze all propositions via their truth-functions (more on this later), and these line up with facts in the world, then we can determine what’s true and what’s false based on Wittgenstein’s a priori analysis. This is probably why Russell thought that Wittgenstein was creating a logically perfect language.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 4

Wittgenstein saw logic as something sublime in the Tractatus. “For there seemed to pertain to logic a peculiar depth—a universal significance. Logic lay, it seemed, at the bottom of all the sciences.—For logical investigations explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that (PI, 89).” Wittgenstein’s view of logic drove him in a particular direction, viz., the logical connection between the proposition (thought) and the facts (states-of-affairs in the world). For the Wittgenstein of the Tractatus there was an a priori order to the world, and that order would show itself in the connection between the proposition and the world. “The great problem round which everything that I write turns is: Is there an order in the world a priori, and if so what does it consist in (Nb, p.53)?”

In later posts we will see how Wittgenstein uses logic to connect the dots. Connecting the dots was an investigation into the structure of the proposition, and the structure of the world, and again, it’s logic that will reveal that structure.

“This order of investigation [in the Notebooks], however, is roughly the reverse of the order of presentation in the finished text [in the Tractatus]. In the Tractatus Wittgenstein starts with the proposition: ‘The world is all that is the case’ (T. 1.0). ‘The world is the totality of facts, not of things (T. 1.1).’ Though these statements stand at the beginning, they are best regarded as conclusions from what follows. The account of the nature of the world is given first because it anticipates and is required by the theory of language which comes later. The meaning of these metaphysical statements cannot be fully appreciated until his account of the nature of language is understood (Wittgenstein’s Conception of Language, by K. T. Fann, pp. 6, 7).”
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 5

Language

“My whole task consists in explaining the nature of the proposition. That is to say, in giving the nature of all facts, whose picture the proposition is (Nb, p. 39).” Out of this idea springs Wittgenstein’s picture and truth-function theories of language. These theories will answer the questions, how are propositions related to the world, and how are they related to one another.

Wittgenstein’s premise is that if we can talk about the world, then there must be propositions directly connected to the world. He determined that since these propositions (speaking of elementary propositions, which are a subset of ordinary propositions) are connected to the world, then their truth or falsity is determined by the world, and not other propositions. So, the question arises, how are they connected to the world?

“It is obvious that the analysis of propositions must bring us to elementary propositions which consists of names in immediate combination.

“This raises the question how such combination into propositions comes about (T. 4.221).”

Elementary propositions are further broken down into names, and names are the smallest parts of elementary propositions (T. 4.22). So, what you have are propositions broken down into elementary propositions, and further broken down into names. If an elementary proposition is true, then the state-of-affairs obtains or exists, if the elementary proposition is false, then the elementary proposition is false and the state-of-affairs fails to obtain or exist (T. 4.25). The truth or falsity of elementary propositions is dependent on the world, which is made up of facts or states-of-affairs. If you were able to list all true propositions you would have a complete description of the world.

Wittgenstein was convinced that in order for language to work there had to be this one-to-one correlation between language and the world. He is still operating under the old assumption that meaning is associated with the object it denotes. Hence, the idea that names (the smallest constituent part of elementary propositions) is directly connected with objects (the smallest constituent part of atomic facts). In fact, all true propositions are a mirror image of the world. It’s these ideas that Wittgenstein argues against in the Philosophical Investigations.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

I already have much of this written out, and I should be able to complete it in about 10 posts (roughly).
Last edited by Sam26 on Tue May 12, 2020 3:46 am, edited 1 time in total.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 6

I want to give credit to K. T. Fann (Wittgenstein’s Conception of Philosophy), because I’m using his book as a guide through this, along with, of course, the Tractatus.

The question arises, what are names? Wittgenstein does not mean names like chair, cat, or Socrates. His idea is that a name is a primitive sign, i.e., something that cannot be analyzed any further by means of a definition (T. 3.26). A name is something simple, not complex. For Wittgenstein, this idea comes about by logical necessity.

Wittgenstein never gives us an example of a name, or for that matter, an elementary proposition. He did not think it was his job as a logician to give such examples. However, Wittgenstein was not unaware of the problem. “Our difficulty was that we kept on speaking of simple objects and were unable to mention a single one (Nb. p. 62).”

Remember, Wittgenstein holds to the traditional view at this point in his life, that names refer to objects. “A name means an object. The object is its meaning (‘A’ is the same sign as ‘A’ (T. 3.203).” The configuration of names in an elementary proposition conforms to the configuration of objects in atomic facts. There is a one-to-correspondence to the facts in logical space, which is why propositions are pictures of facts. If we use Wittgenstein’s logic, “A propositional sign is a fact (T. 3.14).” This is why all true propositions (all empirical propositions, propositions of natural science) are equal to particular facts in the world.

“In a proposition a name is the representative of an object.

“Objects can only be named. Signs are their representatives. I can only speak about them: I cannot put them into words. Propositions can only say how things are, not what they are.

“The requirement that simple signs be possible is the requirement that sense be determinate (T. 3.22, 3.221, 3.23).”
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 7

More on what can and cannot be said according to the Tractatus.

You can think of it this way. First, you have the world, and that includes all that we can talk about sensibly. Next you have what’s beyond the limit of the world, and that’s what cannot be spoken of, the mystical.

Language is a mirror image of the world, and the terms sense, senseless, and nonsense are related to saying, i.e., propositions. Within the boundaries of language (saying) we say things with sense. If we attempt to talk about the limit or the boundaries of language, then we are saying things that are senseless. However, if we attempt to go beyond the boundary, then the result is nonsense. The failure to understand these three categories (sense, senseless, and nonsense) results in misunderstandings of the Tractatus. Early interpretations failed to understand the distinction between senseless (sinnlos) and nonsense (unsinnig), and this can be seen in the first translations of the Tractatus. The distinction between senseless and nonsense was lost on many who first read the Tractatus.

An example of senseless propositions are the propositions of logic, they say nothing (T. 6.11). However, they are not nonsensical for they show “…the formal logical properties of language and the world, i.e., they show us the limit of language and the world (T. 6.12, and K. T. Fann, p. 23).

According to Wittgenstein the propositions of philosophy are not empirical propositions (propositions of natural science). They are attempts to say what cannot be said (for the most part). Wittgenstein believed that most of the propositions of philosophy are not false but nonsensical. They are attempts to say how reality is. Philosophical propositions are similar to asking if the good is more or less identical with the beautiful (T. 4.003).

Wittgenstein also believed that the reasons for why we misunderstand the differences between these propositions (those that make sense, vs those that are senseless, vs those that are nonsense), is that we misunderstand the logic of our language, viz., the logic displayed in the Tractatus.

“Religion, ethics, art, and the realm of the personal are, like metaphysics, concerned with what cannot be said—that which transcends the world (K. T. Fann, p. 23, 24).”
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 8

In previous posts I talked about names being the simplest component of elementary propositions, and that names referred to objects, and objects make up atomic facts. The question came up about how we could make sense of a proposition if there were no corresponding objects, and thus, no corresponding facts. According to the Tractatus a proposition pictures reality, so if we are to understand a proposition that refers to unicorns, it is because the proposition displays a picture, and that picture either matches up with reality or it does not. If it correctly mirrors reality, then it is true, if it does not mirror reality, then it is false. So, to understand the sense of a proposition it is a matter of picturing the proposition, and this occurs quite apart from there being a corresponding facts in reality.

A picture or proposition presents a fact from a position outside of it, or separate from the fact it is displaying. Just as a picture of the White House presents the White House from a position outside it, or quite separate from reality or the state-of-affairs. Any picture either accurately or inaccurately presents a certain state of affairs (T. 2.1). And as we keep repeating, propositions are pictures according to the Tractatus. For example, consider any painting that displays a picture, the picture may or may not actually match up with a corresponding state of affairs (shown in the picture), and yet whether it does has no bearing on whether we understand the picture.

"The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way. Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture (T. 2.15)."

The pictorial form is the form a picture shares with a fact. The form of the picture has to do with the arrangement of the elements in the picture. "What a picture must have in common with reality, in order to be able to depict it--correctly or incorrectly--in the way it does, is its pictorial form. A picture can depict any reality whose form it has. A spacial picture can depict anything spacial, a coloured one anything coloured, etc. A picture cannot, however, depict its pictorial form: it displays it (T. 2.17 - 2.172)."

There is a shared logic between the picture and the fact (T. 2.18).

How does a proposition correspond with reality? "Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture.

"That is how a picture is attached to reality; it reaches right out to it.

"It is laid against reality like a measure (T. 2.151-2.1512)."

Each person, truck, bridge, house in the picture represents those things in the world.

So how do we tell if a proposition is true or false? We must compare it with reality (T. 2.223).

The sense of a picture is the arrangement of the things in the picture, which supposedly correspond to the arrangement of things in the world (T. 2.221).

The way one verifies the correctness of a proposition is by inspecting the proposition to see if it indeed reflects reality (T. 2.223).

According to Wittgenstein a thought is a logical picture (Wittgenstein does not believe that we can think illogically), it uses the form of logic to represent a fact (T. 3 and 3.03).

"In a proposition a thought finds an expression that can be perceived by the senses (T. 3.1)." So the logical picture is made by logical units, such as, visual marks or auditory marks.

Therefore, a proposition says that 'a' is in a certain relation to 'b', i.e., 'aRb'. For instance, Sam is standing next to Jane.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

In the Notebooks Wittgenstein says the following: "In the proposition a world is as it were put together experimentally (Nb, p. 7)." This idea apparently occurred to Wittgenstein when he observed or read about a model of a car accident that was used in a Paris court of law, that is, they used dolls and other objects to represent the facts of the case. The model was a picture of reality; and so it is with the proposition, it is a model of reality as we imagine or picture it (T. 4.01).

Before I end this post, I just want to say that I believe that many of our propositions are pictures of reality, but again, this is not the only way propositions state the facts. Many people think Wittgenstein repudiated this idea, but I think he merely was saying that language does more than this. Just as language does more than use the ostensive definition model.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 9

As we've said the other central idea presented in the Tractatus is the truth-function theory. It goes hand-in-hand with the picture theory. "A proposition is a truth-function of elementary propositions (T. 5)." Therefore, if you are given all elementary propositions, then you can construct every possible proposition, which fixes their limits (T. 4.51). My understanding is that this sets the limit of language, or sets a limit to what can be said.

A full appreciation of this thesis requires an understanding of truth-functional logic. It suffices for our purpose to point out merely that a compound proposition, compounded of the propositions P1, P2,....,Pn, is a truth-functional compound of P1, P2,..., Pn if and only if its truth or falsity is uniquely determined by the truth or falsity (the truth-values) of P1,..., Pn. In other words, the truth-value of a compound proposition is completely determined by the truth-values of its components--once the truth-values of is components are given, the truth-value of the compound proposition can be calculated. Wittgenstein claims that all propositions are related to elementary propositions truth-functionally (K.T. Fann, p. 17).

Therefore, what follows is this: "If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by giving all elementary propositions, and adding which of them are true and which false (T. 4.26)."
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 10

We know that Wittgenstein thought that all propositions were truth-functions of elementary propositions. Therefore, if a proposition X is analyzed into elementary propositions p and q, and they are connected by the truth-functional connective and, then the truth-value of X is determined by p and q. If you took logic, then you should remember truth-tables. For example...

Code: Select all

P        Q           X
___________________________

T        T          T

T        F          F

F        T          F

F        F          F
So, if X is true, both p and q have to be true. If not, then it is false. X is dependent upon the truth-values of p and q, i.e., its component parts. So X qualifies as a genuine proposition - X has sense. Wittgenstein demonstrated using truth-tables, that for any proposition, when analyzed into elementary propositions, we can determine whether it has sense or not (T. 4.31).

According to Wittgenstein there are two extreme cases amongst the possible groups of truth-conditions. In one of these cases, the proposition is true for all truth-possibilities of elementary propositions; and thus, we say that the truth-conditions are tautological. In the second case the proposition is false for all truth-possibilities, which then yields a contradiction (T. 4.46).

"Propositions show what they say: tautologies and contradictions show that they say nothing.

"A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.

"Tautologies and contradictions lack sense.

"(Like a point from which two arrows go out in opposite directions to one another.)

"(For example, I know nothing about weather when I know that it is either raining or not raining.) (T. 4.461)."

"Tautologies and contradictions are not, however, non-sensical. They are part of the symbolism, much as '0' is part of the symbolism of arithmetic (T. 4.4611)."

Wittgenstein goes on to say that tautologies and contradictions are not pictures of reality, since they do not represent possible situations or states of affairs. Tautologies show all possible situations or states of affairs; and contradictions show us no possible situations or states of affairs (T. 4.462). These are not propositions in the strict sense, but are degenerate propositions; and any proposition that is not subject to truth-value analysis is considered non-sense, or a pseudo-proposition.

"Summarily then, language consists of propositions. All propositions can be analyzed into elementary propositions and are truth-functions of elementary propositions. The elementary propositions are immediate combinations of names, which directly refer to objects; and elementary propositions are logical pictures of atomic facts, which are immediate combinations of objects. Atomic facts combine to form facts of whatever complexity which constitute the world. Thus language is truth-functionally structured and its essential function is to describe the world. Here we have the limit of language and what amounts to the same, the limit of the world (K. T. Fann, p. 21)."

Maybe some of you can see why the Logical Positivists latched onto Wittgenstein's theory, and tried to make it support their own view of reality.

Hopefully this will give you some understanding of how his picture and truth-function theory works.
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

Post 11 (Final post of summary, as incomplete as it is.)

To conclude this basic summary of the Tractatus is to conclude that philosophy is not one of the natural sciences. Philosophy is above or below the natural sciences, but not beside them (T. 4.111). This follows from 4.11, "The totality of true propositions is the whole of natural science." This conclusion is was arrived at long before the publication of the Tractatus in 1918. It goes back to 1913 in his Notes on Logic given to Russell.

Wittgenstein is saying that philosophy gives us no truths. "Philosophy aims at the logical clarification of thoughts. [It] is not a body of doctrine but an activity (T. 4.112)."

Even in the Philosophical Investigations Wittgenstein is still aiming at the logical clarification of thoughts. Albeit, a different logical method is used. His later method in the PI isn't as rigid as that of the Tractatus, but is more flexible, which is more in conformity with how language works.

"Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries (T. 4.112).

"Philosophy settles controversies about the limits of natural science (T. 4.113).

"It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards to what cannot be thought (T. 4.114).

"It will signify what cannot be said, by presenting clearly what can be said (T. 4.115)."

Understanding what Wittgenstein is doing should clarify what he means in 6.54, i.e., he has shown us what cannot be said, by setting a limit to language, so, you can throw away the ladder that reaches beyond the world of sense into the world of the senseless, and even further into the realm of nonsense.

For Wittgenstein the only facts are the facts in the world, there are no metaphysical facts for language to grasp hold of. If someone tries to say something metaphysical, you would show him using Wittgenstein's picture theory and his truth-function theory that he has not managed to say anything; they've gone beyond the boundaries of the world, beyond the boundaries of language. This is why Wittgenstein says, "What we cannot speak about we must pass over in silence (T. 7)."
Sam26
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Re: Explaining the Tractatus Logico-Philosophicus

Post by Sam26 »

After writing the Tractatus Logico-Philosophicus Wittgenstein abandoned philosophy for a few years, and in 1920 he became an elementary school teacher in Austria until he resigned in 1926. There is evidence that this period of time had an affect on his thinking. Apparently he taught children reading, writing, and arithmetic, and also compiled a dictionary of several thousand words for young children.

How do we know if a child has learned to use a word correctly - is it because they can define the word? No, we observe how they use the word. It seems that this time of teaching brought Wittgenstein's philosophy down to earth, i.e., his observations of the way children learn words probably played a part in his later view of language.

In the late 1920's Wittgenstein attended a lecture in Vienna on the Foundations of Mathematics, and this apparently began to stir his thinking once again. He returned to Cambridge early in 1929 and registered as a student. It seems he wanted to work toward his PhD. However, as it turns out, he was allowed to present the Tractatus as his thesis, and if I remember correctly, he presented it before Russell and Moore.

Soon after he returned to England he wrote a paper for the Aristotelian Society called Some Remarks on Logical Form, and in this paper it is clear that he still subscribed to many of the doctrines of his earlier work. However, there is a short remark in the paper that seems to point in a new direction ("...we can only arrive at a correct analysis by what might be called, the logical investigation of the phenomena themselves, i.e., in a certain sense a posteriori, and no[t]: by conjecturing about a priori possibilities."). This seems to hint at a new method of inquiry (an a posteriori method of analysis), which is reflected in his later work.

This methodological turn in his mind is what differentiates the early Wittgenstein from the later Wittgenstein. It is not that he repudiates all of what he wrote in the Tractatus, but his method of analyzing propositions shifts; and it is this more practical or pragmatic approach that becomes the hallmark of his philosophical inquiry until his death in 1951.
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Re: Explaining the Tractatus Logico-Philosophicus

Post by uwot »

Sam26 wrote: Mon May 11, 2020 9:17 am...all true propositions are a mirror image of the world. It’s these ideas that Wittgenstein argues against in the Philosophical Investigations.
Thanks Sam26. It's a long time since I read Wittgenstein, but for me the above is the crucial point. It seems of a piece with the shift away from any notion of 'logical atomism' or positivism in the middle of the 20th century. I'll have to read your entries a few more times to properly get my head round it.
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