Eminently sensible. I'm working on the Mongolian invasion in Civ.

This discussion led back to philosophy of maths, and I'm working my way through the Stanford article.

Do you have an opinion on the changes to W.'s views on mathematics between the Tractatus and PI?

But further, I don't see why we should reject infinite extensions. Or rather, I find it hard to understand his insistence on a division between mathematical intension and extension. It seems to me to have led him to place unnecessary restrictions on mathematics.

Roughly speaking, Wouldn't it have been consistent to treat all mathematics as the construction of rules? That is, all mathematics is intensional? Then the putting of those rules to use would be giving them an extension. That seems ot me the best way to understand 6.211.

Platonism seems to me to be quite misguided. So I;m not sure where we might go with this.

I'm just suggesting that you have an inflated view of his importance, because you're reading too narrowly. He does not 'give us anything,' he is not Jesus Christ. He was just one out of very many philosophers, in a very long tradition, many of whom long before and after him said similar things. — Snakes Alive

Yer suggestions were duly noted, but were subsequently rejected. Reason: insufficient information. Similar is not what I want, I am after same. Everything is the same, if you don't love them. So, Mr. Readmore, do you have anything to offer, other than recopulations of the same that is?

Book 3 of Locke's Essay would be a start.

Do you have an opinion on the changes to W.'s views on mathematics between the Tractatus and PI? — Banno

I haven't studied it enough to make an intelligent assessment.

Do you have an opinion on the changes to W.'s views on mathematics between the Tractatus and PI? — Banno

I believe the nature of mathematics remained unintelligible for Wittgenstein. The quest to understand it was probably his greatest philosophical unaccomplishment. However, he provides us with a range of very good perspectives as starting points, not having found the perfect (ideal) one, which he sought.

That's good. I was worried you might realise he was a finitist, even as you seem to be, and come back with something cogent.

The problem is that the nature of mathematics remains unintelligible to me as well, as it does to all philosophers. But some wrongly assume Platonic realism, insisting that mathematics consists of intelligible objects, and this is how they wrongly claim to understand infinity.

Is it of interest to you?

I'm no mathematician; but of course I have opinions.

Seems to me that mathematics is a built thing. So in that regard I'm with Wittgenstein. But I find his finitism hard to stomach.

I think it's because I do not understand why a mathematical extension must be finite. That is, I don't even understand this terminology, as he is using it, and as it is used in the Stanford article.

Have you considered an exposition on Remarks on the Foundations of Mathematics?

Have you considered an exposition on Remarks on the Foundations of Mathematics? — Banno

I have read some of his Philosophical Remarks, which I believe was written in 1931, it contains the seeds of his later writings on mathematics. I have an interest, but I am not sure I have the will.

You do understand that Wittgenstein overwhelmingly rejected Platonism...?

(I know I will regret asking).

OK. I'll have a think about an appropriate thread; perhaps a more general question about mathematical extension.

You do understand that Wittgenstein overwhelmingly rejected Platonism...? — Banno

I know, so do I, that's probably why we're both finitists. Did you read what I wrote? It's only those who assume mathematics consists of some sort of objects (Platonism), like set theory, who create the illusion that infinity is intelligible.

Did you read what I wrote? — Metaphysician Undercover

Yeah, i read it. It is just an assertion. So it's of no use.

No use for what?

Read what Wittgenstein says about formal concepts at 4.126 - 4.128. If you can decipher that couple of pages you'll be well on your way. But on your way toward recognizing that Wittgenstein represents mathematics as unintelligible.

Book 3 of Locke's Essay would be a start. — Snakes Alive

Thanks, you finally gave me something, something I could work with I mean. From here:

https://www.earlymoderntexts.com/assets/pdfs/locke1690book3.pdf

It seems to me that you have greatly misunderstood the Tractatus, which is why you believe Wittgenstein is, and I quote, "just one out of very many philosophers, in a very long tradition, many of whom long before and after him said similar things". Now how the hell to explain this. Hmm, perhaps Russell's introduction would be of some use. I quote:

In order to understand Mr Wittgenstein’s book, it is necessary to realize what is the problem with which he is concerned. In the part of his theory which deals with Symbolism he is concerned with the conditions which would have to be fulfilled by a logically perfect language. There are various problems as regards language. First, there is the problem what actually occurs in our minds when we use language with the intention of meaning something by it; this problem belongs to psychology. Secondly, there is the problem as to what is the relation subsisting between thoughts, words, or sentences, and that which they refer to or mean; this problem belongs to epistemology. Thirdly, there is the problem of using sentences so as to convey truth rather than falsehood; this belongs to the special sciences dealing with the subject-matter of the sentences in question. Fourthly, there is the question: what relation must one fact (such as a sentence) have to another in order to be capable of being a symbol for that other? This last is a logical question, and is the one with which Mr Wittgenstein is concerned. He is concerned with the conditions for accurate Symbolism, i.e. for Symbolism in which a sentence “means” something quite definite. In practice, language is always more or less vague, so that what we assert is never quite precise. Thus, logic has two problems to deal with in regard to Symbolism: (1) the conditions for sense rather than nonsense in combinations of symbols; (2) the conditions for uniqueness of meaning or reference in symbols or combinations of symbols. — Russell

In terms of how Russell laid out these 4 problems regarding language, it should be obvious that Locke, in his essay, was solely concerned with the first 3, while the fourth, the purely logical one, completely eluded him. Somewhere you write: "I think the question of intelligibility is interesting, but how words come to mean things, and what they mean or can mean, is a complicated topic not seriously addressed by the Tractatus". This is it right here! You were expecting something different from the Tractatus, or maybe you mistook his symbolical and logical approach to language to be doing something similar like his predecessors, Locke for example in his essay, or the so-called empiricists. I reckon that all your confusion and misunderstanding stems from this simple fact. The middle chapters of the Tractatus, of which I am certain that they are either of no interest to you, or you don't understand them at all, contain Wittgenstein's ideas regarding language, how you can treat it from the point of view of logic alone, using symbolism. And therefore W., in the Tractatus, has to make an exposition of logic as well. But of course, if someone takes logic to be what was traditionally thought to be, then they will understand completely nothing, if they try to make the new concepts and notions to somehow fit the old ones, because they don't, they don't fit, I mean.

But in general, Wittgenstein saw things differently, his POV was quite weird and unique, and so to say that he somehow fits in the philosophical tradition, is plain silly, he is more likely to be a philosophical freak, le freak, c'est chic. You can see for example his take on the philosophy of mathematics, which Banno is now exploring.

Anyway, just something to note regarding Locke's essay. He writes towards the end, in the chapter titled: "Chapter xi: The remedies of those imperfections and misuses":

2. I would cut a ridiculous figure if I tried to effect a complete reform of the language of my own country, let alone of the languages of the world! To require that men use their words always in the same sense, and only for determined and uniform ideas, would be to think that all men should have the same notions and should talk only of what they have clear and distinct ideas of; and no-one can try to bring that about unless he is vain enough to think he can persuade men to be either very knowing or very silent!. . . . — Locke

This echoes with W's last remark: "Whereof one cannot speak, thereof one must be silent". The difference is, and a great one, that for W., the one who knows keeps silent, and not as Locke puts it, that there are those who know and should/can use language correctly, and the others that don't and misuse it. And of course, for Wittgenstein there are no remedies. But then again, the methodologies of these two thinkers were totally different, and so were their conclusions.

So perhaps you could re-read the Tractatus in a different light.

Anyways, Wittgenstein believed and said that his work had been grossly misinterpreted. We can find this in various parts:

1. In the prologue made for the PI, that ended up in his notes known to us as "Culture and Value":

This book is written for those who are in sympathy with the spirit in which it is written. This spirit is, I believe, different from that of the prevailing European and American civilization. The spirit of this civilization the expression of which is the industry, architecture, music, of present day fascism & socialism, is a spirit that is alien & uncongenial to the author. This is not a value judgement.

...

Even if it is clear to me then that the disappearance of a culture does not signify the disappearance of human value but simply of certain means of expressing this value, still the fact remains that I contemplate the current of European civilization without sympathy, without understanding its aims if any. So I am really writing for friends who are scattered throughout the corners of the globe. It is all one to me whether the typical western scientist understands or appreciates my work since in any case he does not understand the spirit in which I write.

2. In the prologue of the PI:

Up to a short time ago I had really given up the idea of publishing my work in my lifetime. It used, indeed, to be revived from time to time: mainly because I was obliged to learn that my results (which I had communicated in lectures, typescripts and discussions), variously misunderstood, more or less mangled or watered down, were in circulation. This stung my vanity and I had difficulty in quieting it.

...

I make them public with doubtful feelings. It is not impossible that it should fall to the lot of this work, in its poverty and in the darkness of this time, to bring light into one brain or another—but, of course, it is not likely. I should not like my writing to spare other people the trouble of thinking. But, if possible, to stimulate someone to thoughts of his own. I should have liked to produce a good book. This has not come about, but the time is past in which I could improve it.

3. As reported by Von Wright, student, friend and alleged authority on Wittgenstein:

He was of the opinion ... that his ideas were generally misunderstood and distorted even by those who professed to be his disciples. He doubted he would be better understood in the future. He once said he felt as though he were writing for people who would think in a different way, breathe a different air of life, from that of present-day men.

Therefore, if we believe his sayings, we can say that his song came out completely wrong, due to misinterpretation. Nevertheless he tried to write a good book, with not much success as he admits. But that's okay, maybe one day we'll get rich! :)

So, another radical approach to Logic in the Tractatus was that it doesn't say anything about the world: logical propositions, or propositions of logic, laws of logic etc, are just tautologies, they don't say anything about what things are, or should be, they don't treat of something real. They just provide the grounds, the scaffolding with the help of which various (non-logical) propositions are built. Logic is transcendental, following Kant's phraseology. Moreover, Wittgenstein says that logic fills the world. And so, there is really no reason to make a list of those logical propositions or explain them to someone, since they already know them, or maybe they don't really know them or are aware of them, but they are nevertheless embodied of them, language itself and its structure is filled with all logic, as in we are children of logic, one cannot speak illogically, no matter how hard they tried. If there is anything that Logic wants, this is clarity, and not to be conflated with people's psychology, what people want it to be for their own reasons, it does not belong to anyone, but is shared by everyone.

Post 1

I'm currently making a video for YouTube that summarizes Wittgenstein's early and later philosophy with an emphasis on On Certainty. I'm going to add my summary of the Tractatus to this thread. The goal is to make it easy enough to understand that almost anyone with some effort can follow Wittgenstein's main points, viz., his view of the logic of language, his picture theory of language, and his truth-function theory of a proposition.

The Tractatus:

My goal is to explain, as simply as I can, the main thrust of his work, and to point out that Wittgenstein’s later thinking, on the logic of language, is a continuation of his early thinking with some important changes. What changes is his method of attacking the problems of language, and what Wittgenstein means by the logic of language changes. His early thinking is an a priori investigation, but in his later thinking is akin to an a posteriori investigation. It can be said with reasonable certainty that the early Wittgenstein did not understand where the logic of language would eventually lead, viz., that the logic of language would in his later thinking take on a social dimension. The early Wittgenstein had not grasped this social dimension, although there are hints of it in his early writing.

We know that Wittgenstein’s early thinking, especially in the Tractatus is influenced by Bertrand Russell and Gotloeb Frege. However, I’m not going to say much more about Russell and Frege’s contribution, other than to point out that they influenced Wittgenstein’s thinking, especially their emphasis on logic and language.

Wittgenstein sets the tone of the Tractatus in the preface. “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 (Tractatus, Preface p.3).” The problems of philosophy include just about every subject one can imagine, including ethics, mathematics, metaphysics, religion, mysticism, epistemology, and consciousness to name a few. Wittgenstein believes that if we understood the logic of our language, that this will put an end to philosophizing. How will he do this? Well, we express what we think about the world in language, so if he can set a limit to the expression of thoughts, which amounts to a limit to what can be said, then this will give us clarity. Clarity not only of thought but to the expression of thoughts.

Wittgenstein confines what can be said to the world of facts or states-of-affairs, and anything that tries to go beyond the world of facts is simply nonsense. It is nonsense because there are no facts (no states-of-affairs) beyond this world. This is seen in the opening statement of the Tractatus. “The world is all that is the case (T 1).” So, any proposition that tries to go beyond the world of facts is simply nonsense. The metaphysical or the mystical is important for Wittgenstein, but it is outside the world of facts. If it is outside the world of facts, then it is beyond the limit of what can be said in terms of propositions.

So, Wittgenstein sets out to investigate the essence of language, its function, and its structure (PI 92), and it is logic that will reveal this structure. What is the logical structure of language, i.e., the proposition, and how does it connect with the world of facts? Logic has supreme importance in Wittgenstein’s investigation. In PI 89 he says, “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 investigation explores the nature of all things.” With this view of logic in mind, Wittgenstein sets out to demonstrate how it is that a proposition connects to the world of facts, which again, sets a limit to what can be said.

To be continued...

Continuing with a summary of the Tractatus.

Post 2

So, what is the structure of the proposition? And how does the proposition’s structure connect to the world of facts? Wittgenstein believes that a proposition has two parts, viz., elementary propositions and names. Elementary propositions are directly connected to the world of facts, so that whether a complex proposition (our everyday propositions or statements) is true or false is a function of elementary propositions. An elementary proposition is the simplest kind of proposition, and it’s the elementary proposition that asserts the existence of states-of-affairs (facts) (T 4.21).

What is an elementary proposition? According to Wittgenstein, elementary propositions consist of names (T 4.22). These names are not what we would ordinarily think of as names, like doll, cat, pencil, car, etc., they are primitive signs (T 3.26) without parts. A name is where the propositional analysis ends, it’s the most primitive part of a proposition. Wittgenstein never gives an example of an elementary proposition or a name. He assumes based on pure reasoning (logic) that this is how it must be. He also assumes that language, which is made up of propositions, has a counterpart in the world, viz., fact, atomic fact, and object. The counterpart to a true proposition is a fact, the counterpart to the elementary proposition is the atomic fact, and the counterpart to a name is an object. So, objects like names are simples, i.e., just as a name is the simplest component of an elementary proposition, so too are objects the simplest component of atomic facts. A true proposition is a picture of a fact, i.e., it depicts the facts of the world correctly. A false proposition is also a picture, but it doesn’t correspond with any fact in the world.

The way an elementary proposition corresponds with reality is that it must have a one-to-one relationship between its parts (names) and the atomic fact (made up of objects) it describes. Think of a painting that is supposed to represent your home and the surrounding area. For the painting to represent reality correctly it must present the elements of the picture correctly. In other words, the objects in the painting must be in the correct logical order or correct relationship. The relationship of the things in the picture must correctly represent the relationship of the things in reality, viz., the facts. Think of a true proposition as a mirror image of the world, it correctly pictures a fact, or it corresponds to a fact.

Wittgenstein concludes, based on his logic, that this is how it must be. He accepts the traditional view of meaning “A name means an object. The object is its meaning (T 3.203).” The difference between what is traditionally thought of as a name and object and what Wittgenstein means by name and object is much different. Wittgenstein puts his own spin on these words. He tries to show logically how a name refers to an object. Again, remember we have no examples of what a name or an object are in Wittgenstein’s logic, other than they are simples, i.e., they are the simplest component parts of elementary propositions and atomic facts respectively.

Continuing with a summary of the Tractatus.

Post 3

So, Wittgenstein’s picture theory of language is his attempt to demonstrate how it is that a proposition has sense. It has sense in that a proposition correctly pictures a fact in the world if true, or if the proposition is false, it incorrectly pictures a possible fact. “What any picture, of whatever form, must have in common with reality, in order to be able to depict it—correctly or incorrectly-in any way at all, is logical form, i.e., the form of reality (T 2.18).” So, the logical form of the picture that a proposition represents must match the form of reality. Each name in the elementary proposition matches each object of the atomic fact in reality, it is a one-to-one correspondence.

Along with Wittgenstein’s picture theory of language is his truth-function theory of language. “A proposition is a truth-function of elementary propositions (T 5).” This means that if a complex proposition is true, then the elementary propositions that make up the complex proposition must also be true. In order to understand Wittgenstein's truth-functional theory, one would have to understand truth-functional logic, which is beyond the scope of this video.

“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).” If you had access to all true elementary propositions this would completely describe all the atomic facts of the world. All metaphysical propositions, which go beyond the world of facts, would simply be nonsense, because they do not depict any fact. This would follow given Wittgenstein’s first proposition that “The world is all that is the case (T 1).” However, to assume that Wittgenstein was anti-metaphysical would be a mistake. It was a mistake some philosophers made during the early 20’s. Wittgenstein had nothing but respect for those who tried to go beyond the limits of the world, and hence the limits of what can be said.

This is just a quick overview of Wittgenstein’s early philosophy. There is much more that could be added, but my goal is his later philosophy which grew out of his early philosophy. What I want you to remember is Wittgenstein’s idea that the meaning of a name is the object it denotes, because this traditional idea is mostly repudiated in Wittgenstein’s later philosophy. Moreover, the idea that meaning is connected to some object is the source of many philosophical misunderstandings, and misunderstandings in general.

The problems of philosophy include just about every subject one can imagine, including ethics ... — Sam26

Wittgenstein believes that if we understood the logic of our language, that this will put an end to philosophizing. — Sam26

Although the problems of philosophy include the problems of ethics, Wittgenstein does not regard ethics as a philosophical problem, which is to say he does not put an end to ethics.

Although the problems of philosophy include the problems of ethics, Wittgenstein does not regard ethics as a philosophical problem, which is to say he does not put an end to ethics. — Fooloso4

He only puts an end to ethics in the sense that there are no ethical propositions that state what is true or false in the world, i.e., no facts to picture. They are unsayable.

I haven't made my YouTube video yet, so the wording may change a bit.

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. — Sam26

One of the foremost Wittgenstein's scholars would disagree with this assessment. Norman Malcolm, in Nothing is Hidden, listed 15 positions in the Tractatus that he believes were rejected in Wittgenstein's later thinking.

"1. That there is a fixed form of the world, an unchanging order of logical possibilities, which is independent of whatever is the case.
2. That the fixed form of the world is constituted of things that are simple in an absolute sense.
3. That the simple objects are the substratum of thoughts and language.
4. That thoughts, composed of "psychical constituents', underlie the sentences of language.
5 That a thought is intrinsically a picture of a particular state of affairs.
6. That a proposition, or a thought, cannot have a vague sense.
7. That whether a proposition has sense cannot depend on whether another proposition is true.
8. That to understand the sense of a proposition it is sufficient to know the meaning of its constituent parts.
9. That the sense of a proposition cannot be explained.
10. That there is a general form of all propositions.
11. That each proposition is a picture of one and only one state of affairs.
12. That when a sentence is combined with a method of projection that the resulting proposition is necessary unambiguous.
13. That what one means by a sentence is specified by an inner process of logical analysis.
14. That the pictorial nature of most of our everyday propositions is hidden.
15. That every sentence with sense expresses a thought which can be compared with reality."

There are probably more than 15 ideas in the T. that Wittgenstein rejected, but there is also continuity between his early ideas and his later ideas. Are you saying that Malcolm didn't think there was continuity between W. early and later philosophy? I don't think that's true.

There are at least two points of continuity between W. early and later philosophy, and probably more. The two points I'm emphasizing has to do with the logic of language and that there is a limit to what can be said. I think most scholars would agree with this. Although, what is meant by the logic of language in his early thinking is much different from the logic of language in his later thinking. What seems clear is that logic has an important role in both the early and later W.

That said, you will always find disagreements about the connecting threads of his early and later philosophy. My goal is to make the T. as simple to understand as possible.

The latter Wittgenstein rejects the transcendental logic of the Tractatus. This is not a continuation but a repudiation.

The continuity is on the other side of the "what cannot be said" formulation: what can be shown, what can be seen, what can be experienced. Although he drops the terminology, the ethical/aesthetic.

The latter Wittgenstein rejects the transcendental logic of the Tractatus. This is not a continuation but a repudiation. — Fooloso4

I agree, which is why I said "what is meant by the logic of language in his early thinking is much different from the logic of language in his later thinking." However, there is still the "logic of use" in his later thinking, i.e., logic still plays a role, but not the same role. I would have thought that was clear from what I wrote.

I'm sure we have disagreements on some of this, but I'm sticking to my guns.

Without too much exaggeration, the only thing they have in common is the word 'logic'. The transcendental logic of the Tractatus is not simply the logic of language, it is the logic of the world. According to the later Wittgenstein, the rules of grammar (logic) are arbitrary (PI 497). There is no necessary or non-contingent connection between logic, language, and the world.