Tractatus Logico Philosophicus

Short take: What the actual f*$k.

Paraphrasing my law on Godel: Anyone who says they understand the Tractatus doesn’t understand the Tractatus; Anyone who says they do not understand the Tractatus understands the Tractus. (I can’t figure out if I understand any of it or not.)

The Tractacus is a fairly short work, 80 or so pages in all, that seeks to address the limits of language (I think). Wittgenstein tackles language in a similar way that Russell and Whitehead attacked mathematics—to make it constrain to the rules of logic and thus he seems to want to reduce language to logic in the same way that Russell and Whitehead reduced mathematics to logic in the Principia Mathematica (famously taking some 600 pages to prove that 2+2=4). He uses the same framework (although with what seem to be a few important exception i.e. p and not p and the idea of not using =’s) and further builds and references the work of Frege. To really understand all the consequences and the logic you’d need to have an understanding and have read Frege (have not) and maybe the Principia (which is just nuts, lets be honest).

While short, the work is incredibly dense and hard to interrupt. I kept thinking a class would not be enough, one could spend an undergraduate degree working through the text. While I don’t begin to claim to understand the details, my understanding is that Wittgenstein wanted to describe the limits of language (and thus of philosophy). For Wittgenstein, language can only represent reality (i.e. objects and facts). Language is thus a way of projecting reality (facts) into your mind (as pictures or thoughts).

What’s interesting and perplexing is that he seems to be saying that language (he calls propositions) can only describe reality. He specifically says that language can only describe the natural sciences and can not have anything to say about typical philosophical questions (he calls the mystical). Yet, in his 80+ pages of language he has shown us in effect what philosophy can not be and thus what it can be.

In fact, he goes to great length to show and discuss that p and “not p” are in effect the same idea. For, as defined by Wittgenstein, defining p is effect defining what it is not as well. By saying the sky is blue, you are also saying the sky is not red or green or yellow. Further, assigning a variable to anything a = b for instance, is meaningless as there is just the thing—assigning a equals b is just changing the name of the symbol that represents the thing—just say the thing. In this way the exploration of the Tractacus which defines language and its limits, by his own logic defines what it is not, and thus gives us insight into something, which by his definition, is unknowable and outside of reality. This is why the second to last sentence is so interesting:

[INSERT]

What he’s done is build a rigorous and logical scaffolding over the last 80+ pages, but it’s as if when he started he tied a rope around the bottom corner support and then just as he gets to the top—and places the last piece—the rope goes tight and pulls it out from under him (the pull up the ladder analogy).

If natural science can be described through language and thus philosophy can not be described through language, what is the “p”—the fact—the thing that encapsulated both p and not p (i.e. natural science and philosophy)—what is the thing that he has shown us—all of knowledge and it’s two compartments? and how do we think about the idea that he rigorously and logically “proved” that language could not tell us about the other to tell us about the other?

Other questions…

And in this last way, it feels relational to Godel—circular, using itself to prove itself (or disprove itself)—what is this relation? is there a relation?

ChatGPT: Wittgenstein's Tractatus Logico-Philosophicus and Gödel's incompleteness theorems are both important contributions to the foundations of mathematics and logic, but they address different issues and have different implications. The Tractatus is primarily concerned with the limits of language and its ability to represent reality, while Gödel's incompleteness theorems concern the limits of formal systems and their ability to prove all true statements within their own framework. However, both works have been interpreted as showing that there are limits to human understanding and that there are certain things that cannot be known or expressed.

Seems, in a way, to parallel Plato’s dialogue Meno—the dialogue in itself is showing how knowledge can be gained (what the story does with the sides of the triangle if I remember right) and what Plato is doing to us the reader through the dialogue.

ChatGPT: Both Wittgenstein's Tractatus and Plato's Meno explore the relationship between knowledge and understanding. In Meno, Socrates engages in a dialogue with a slave boy, in which he tries to help the boy discover knowledge of geometry through asking questions rather than telling him. In this way, Socrates shows that true knowledge is innate and can be brought to light through proper questioning. Similarly, Wittgenstein's Tractatus argues that true knowledge and understanding is innate in the structure of language and the world and can be revealed through logical analysis. Both works suggest that true knowledge cannot be acquired through empirical observation or instruction, but rather through a kind of intellectual intuition.

How are the limits of mathematics and the limits of language the same?

ChatGPT: Wittgenstein argues in the Tractatus that the limits of language are the same as the limits of the world, and that the limits of mathematics are the limits of logic. He states that "the limits of my language means the limits of my world." This means that the limits of what can be said and represented in language are determined by the nature of the world, and that language can only represent the facts of the world, not its essence. Similarly, the limits of mathematics are determined by the nature of logic and the way that numbers and other mathematical objects relate to one another.

This is interesting and helpful—the world is to language as logic is to math.

Wittgenstein suggests that the limits of mathematics and the limits of language are the same because they both derive from the structure of the world and the way that our minds are able to understand it. He argues that the structure of language reflects the structure of the world, and that the structure of mathematics reflects the structure of logic. Therefore, the limits of what can be said and represented in language and the limits of what can be proven and understood in mathematics are ultimately the same.

This seems to assume the limits of logic are the limits of the world—are they?

In other words, the limits of language and the limits of mathematics are the same because they are both based on the same underlying structures, and they both reflect the same underlying reality. Therefore, the limits of what can be said and known in language and the limits of what can be proven and understood in mathematics are ultimately the same thing.

Can language mirror the mind?

ChatGPT: Wittgenstein's Tractatus suggests that the structure of language mirrors the structure of the mind. He argues that the limits of language are the same as the limits of the world, and that the limits of the world are the limits of the mind. He states that "the limits of my language means the limits of my world." This means that the structure of language reflects the way that we understand and experience the world, and that the limits of what can be said in language are determined by the limits of our understanding and experience.

Unclear here what he means by facts—are they only observable?

Therefore, Wittgenstein suggests that the structure of language can be seen as a reflection of the structure of the mind. He argues that the way that we use language and the way that we understand the world are intimately connected, and that our understanding of the world is reflected in the way that we use language.

However, it's worth noting that this is a view that Wittgenstein held early in his career, later in his life he developed a different view on language and the mind, it's known as the later Wittgenstein. In this later view, Wittgenstein argues that language does not mirror the mind, but rather it is the mind that shapes and gives meaning to language. He argues that the meaning of words is determined by the way that they are used in practice, rather than by any inherent connection to the mind.

Therefore, whether language can mirror the mind or not is a matter of perspective and interpretation. While Wittgenstein's Tractatus suggests that the structure of language mirrors the structure of the mind, his later views suggest that the relationship between language and the mind is more complex and multifaceted.

Do facts have to be limited to observable things or can they be concepts as well? and if they are concepts then how do you determine if they are true or false?

ChatGPT: In Wittgenstein's Tractatus, facts are limited to what can be represented in language and correspond to states of affairs that can be observed in the world. He states that "the limits of my language means the limits of my world," and that language can only represent facts, not the essence of things. These facts are simple and atomic, they can't be broken down into further facts.

However, it is possible to interpret the Tractatus as allowing for facts that are not limited to observable things, but rather include concepts as well. Wittgenstein's distinction between what can be said and what can't be said can be seen as a distinction between facts that can be represented in language and concepts that cannot. This means that concepts like mathematical and logical concepts, for example, can be seen as facts that can't be observed but can be represented in language.

In determining if a fact is true or false, Wittgenstein argues that it is determined by the logical structure of the proposition that expresses it, and that the truth or falsity of a proposition is determined by the correspondence of the facts it represents to reality. A proposition is true if it corresponds to the facts of the world, it is false if it doesn't correspond to the facts of the world.

However, it's worth noting that Wittgenstein's Tractatus is a work that offers a specific and limited view of language, facts and truth, and it is not the only one. Other philosophers and theories of language, truth, and knowledge may have different perspectives and ways of determining truth and falsehood of facts.

Can you explain, in simple terms, Ludwig Wittgenstein's Tracatus Logico-Philosophicus?

ChatGPT: Ludwig Wittgenstein's Tractatus Logico-Philosophicus is a book of philosophy that presents a theory of language and meaning. Wittgenstein argues that the structure of language reflects the structure of the world, and that all meaningful statements can be understood as pictures of the world. The book is divided into numbered paragraphs, and each paragraph presents a different idea or concept. The book is considered difficult to understand because Wittgenstein uses complex and abstract language and reasoning, but the main idea is that language is a representation of the world and that the limits of language are the limits of the world.

Wittgenstein uses the term "picture" to describe the relationship between language and reality. He argues that a sentence is like a picture and that it can represent the atomic facts of the world. A sentence is a picture of a state of affairs and it describes how objects are related to one another in the world.

Wittgenstein argues that the meaning of a word is the object it stands for and that the limits of language are the limits of the world, meaning that we can only talk about objects that we can perceive. [This is the view that seems to change latter in Philosophical Investigations]

In summary, Wittgenstein's view is that a sentence can be seen as a picture of the world and that it represents the arrangement of objects in the world, the objects being the building blocks of reality and the limits of what can be represented by language. [And thus the limits of language are our limits of perception]

In summary, Wittgenstein's view is that propositions represent a possible state of affairs in the world, and that the meaning of a proposition is determined by its truth function, which is based on the logical relationships between the simple symbols that make up the proposition. The combination of propositions through truth functions makes it possible to form more complex propositions.

What are some of the various interpretations of the Tractatus?

ChatGPT: There are various interpretations of Wittgenstein's Tractatus Logico-Philosophicus, some of which are:

  1. The Resolute Reading: This interpretation emphasizes Wittgenstein's early view that language mirrors the structure of reality and that all meaningful statements can be understood as pictures of the world. It argues that the limits of language are the limits of the world and that the Tractatus provides a clear and complete picture of the nature of language and reality.
  2. The Mystical Reading: This interpretation emphasizes the seemingly mystical or poetic aspects of the Tractatus, such as the idea that "what can be said at all can be said clearly." It argues that Wittgenstein's ideas are meant to be understood in a non-literal sense, as an expression of a deeper, ineffable understanding of the world.
  3. The Dissolution Reading: This interpretation argues that the Tractatus is not meant to provide a positive theory of language and meaning, but rather to dissolve traditional philosophical problems by showing that they are based on misunderstandings of language.
  4. The Therapeutic Reading: This interpretation argues that the Tractatus is not meant to provide a positive theory of language, but rather to help the reader recognize and overcome confusions and misconceptions about language and meaning, similar to the idea of Wittgenstein's later work Philosophical Investigations.
  5. The Silence Reading: This interpretation argues that the Tractatus is ultimately a work about the limits of language, and that Wittgenstein is suggesting that there are certain things that cannot be said or known and that we should remain silent about them.

These are some of the main interpretations, but there are many more, and the Tractatus continues to be the subject of ongoing philosophical discussion and debate.

Wikipedia: The project had a broad goal: to identify the relationship between language and reality and to define the limits of science.

In order for a picture to represent a certain fact it must, in some way, possess the same logical structure as the fact. The picture is a standard of reality. In this way, linguistic expression can be seen as a form of geometric projection, where language is the changing form of projection but the logical structure of the expression is the unchanging geometric relationship.

We cannot say with language what is common in the structures, rather it must be shown, because any language we use will also rely on this relationship, and so we cannot step out of our language with language. [Language creates the thought but is not the thought per say?]

A philosophical treatise attempts to say something where nothing can properly be said. It is predicated upon the idea that philosophy should be pursued in a way analogous to the natural sciences; that philosophers are looking to construct true theories. This sense of philosophy does not coincide with Wittgenstein's conception of philosophy.

In turn, a logically "ideal" language cannot supply meaning, it can only reflect the world, and so, sentences in a logical language cannot remain meaningful if they are not merely reflections of the facts.

It would appear, then, that the metaphysics and the philosophy of language endorsed by the Tractatus give rise to a paradox: for the Tractatus to be true, it will necessarily have to be nonsense by self-application; but for this self-application to render the propositions of the Tractatus nonsense (in the Tractarian sense), then the Tractatus must be true.[14] [This seems like Godel but just in language]

Similarly, Michael Kremer suggested that Wittgenstein's distinction between saying and showing could be compared with Gilbert Ryle's famous distinction between "knowing that" and "knowing how".[25] Just as practical knowledge or skill (such as riding a bike) is not reducible to propositional knowledge according to Ryle, Wittgenstein also thought that the mastery of the logic of our language is a unique practical skill that does not involve any sort of propositional "knowing that", but rather is reflected in our ability to operate with senseful sentences and grasping their internal logical relations.

Core statements

  1. The world is everything that is the case. [Basically materialism right?]
  2. What is the case, the fact, is the existence of atomic facts.
  3. The logical picture of the facts is the thought. [Sentences turn facts into thoughts i.e. pictures]
  4. The thought is the significant proposition.
  5. Propositions are truth-functions of elementary propositions. (an elementary proposition is a truth-function of itself) [Builds the logic of language from axioms basically?]
  6. The general form of truth-function is: [ p E N(E) ]. This is the general form of proposition. [i.e. a truth function represents a proposition, the sum of its elementary propositions, and a sum of the negative elementary propositions). As an example: The sky is blue and clear. The sky is clear / the sky is blue and thus the sky is not clear / the sky is not blue. Limits of what we know is the truths and what the negatives imply.]
  7. Whereof one cannot speak, therefore one must be silent.

Definitions

A proposition is a sentence that can be true or false (and thus describes possible states of the perceivable world). A proposition, or a sentence, can be understood as a picture of the world (i.e. represent atomic facts). Where an atomic fact is the most basic and indivisible element of reality and are made up of objects and their properties. Atomic facts are the limits of language and the limits of what can be known about the world.

Objects (reality) > Atomic Facts > Creates propositions or sentences which are pictures of the world (atomic facts) > Propositions can be strung together into truth-functions