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.

I'm in the middle of WoW I've lost interest in philosophy. :lol: I need a break. People in here take themselves to seriously, including moi.

I don't remember him saying anything about it. I don't think there is much to it. It seems silly to me.

Oh, the motto, that's a strange motto. :gasp:

After he dedicates the book to his friend Pinsent, then comes the preface written by Wittgenstein, is that what you're referring too?

What specifically are you referring too?

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.

Anything to add about truth tables? — Banno

I tried to sum up the Tractatus into what I thought was important. Obviously there is a lot that I left out, and his use of truth-tables was one of those things. Wittgenstein is credited with developing truth-tables.

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...

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 I didn't leave too much out. Maybe this will give you some understanding of how his picture and truth-function theory works.

I'll debate anyone who wants to, on the subject of whether there is evidence that consciousness survives death. I'll debate them formally in the debate thread with a moderator.

He said the world is made up of facts or states-of-affairs. A true proposition is one that pictures states-of-affairs in the world. All propositions, whether they are known or unknown, true or false, imaginary or not, represent pictures, and we can understand them because they are pictures.

Of course what is unknown is part of reality, unless you're referring to that which is outside the world, the metaphysical, this goes beyond the world, or beyond what can be said. However, there is that which is unknown in the world, and this can be pictured too. All the facts in the world, known or unknown, are what we can talk about. Wittgenstein mapped out what can be talked about (at least in theory).

So can we conclude that Wittgenstein's description, or definition of "the world" is unacceptable, and "the world" as we know it is quite different from this? — Metaphysician Undercover

I don't find his idea of the world a problem, but his ideas of how language connects to the world. Moreover, his idea that there is a limit to language, this idea is not only a part of the Tractatus, but also the PI.

And the afterlife is one of many imaginaries. To say personal experience is evidence for it (as per Sam26) is no more coherent than saying my memory of my dream is evidence my dream really happened. — Baden

This is what someone would say who never examined the evidence. First, dreams, hallucinations, or delusions don't describe real events as do NDEs. One can verify the accuracy of NDE testimonial evidence by talking to doctors, nurses, and family members who can verify or corroborate the evidence. This kind of response also shows a particular bias, because they don't respond to the arguments, they just give their uneducated opinions.

Post 10 (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)."

No, this isn't about religion. I'm not religious, but I do think there is plenty of testimonial evidence that supports the idea of an afterlife. If you have the time read all of my posts.

I wrote a thread on this very subject. There is plenty of evidence of an afterlife.

https://thephilosophyforum.com/discussion/1980/evidence-of-consciousness-surviving-the-body/p1

Perhaps that is what is nascent in ↪Gregory. — Banno

Perhaps.

Okay that should be enough for now.

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)."

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.

If propositions can only picture facts in the world, then it would seem to make sense that propositions of metaphysics, which go beyond the world of facts, can't picture anything. There is nothing for the proposition to picture. Right?

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.

I guess I should get busy and post a little more.

Banno quit making things up. :joke:

We haven't even scratched the surface of all that is in the Tractatus, not that I'm going to go into that much depth.

Is there anything praiseworthy? Yes, its originality, and based on Wittgenstein's premises it follows logically. It also led to Wittgenstein's critique of the work, and to a better way of looking at how language functions. I also like the idea of propositions picturing facts or states-of-affairs, because I think it is true of many propositions (although not in the way of names connecting to objects). There is much in this work, i.e., many novel ideas, besides his picture and truth-function theories, that could be thought through. What I mean is that there are a lot of side issues that he touches on that might deserve a look at. What I find interesting, is where his thoughts led him in the end. And, ya, we might find some of his ideas silly today, but that's true of many subjects that are over 100 years old.

Is everyone bored, like MU? :wink:

This phrase seems to have two possible interpretations: attempts to say things about what kinds of things are not able to be said, vs attempts to say things which attempts are doomed to fail because the things one is attempting to say cannot be said. — Pfhorrest

In other words, it attempts to go beyond the world of language. Language, in terms of making sense, is language that describes the world. So ya, your latter interpretation.

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).”

Right, when you get to the end of the book, Wittgenstein admits that it's all wrong — Metaphysician Undercover

This is incorrect. Wittgenstein is NOT admitting that it's all wrong. He says at the beginning of the Tractatus, "On the other hand the truth of the thoughts that are here communicated seems to me unassailable and definitive (T. p. 4)."

"My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them [metaphysical propositions] as nonsensical, when he has used them--as steps--to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) (T. 6.54)."

Wittgenstein's famous last words have caused more problems for those who read the Tractatus than any other passage. Philosophers from Bertrand Russell to present day philosophers have misunderstood the significance of this passage. After all, Wittgenstein seems to have said a great deal about what cannot be said according to Russell. There have been other accusations that Wittgenstein was illuminating nonsense, according to Pitcher in the Philosophy of Wittgenstein. Ramsey also had some remarks about this passage in the following: "And again we must then take seriously that it is nonsense, and not pretend as Wittgenstein does, that it is important nonsense (F. Ramsey, The Foundations of Mathematics (London, 1931), p. 263)!"

My understanding of this passage is the following: By examining the propositions in the Tractatus, the reader comes to understand that he/she must transcend the propositions (metaphysical propositions) in order to see the world aright. Once this is done, one can then discard the process because Wittgenstein will have accomplished his purpose - that of showing you the way. Once you see enough of what is nonsensical, hopefully, you will have a clear picture of what can be said and what cannot be said - i.e., what propositions have sense. So, the question now becomes, how do the propositions of the Tractatus show us the truth contained therein? One might answer the question this way - just as music and art show us something important, so do the propositions in the Tractatus.

Wittgenstein defines for us which propositions have sense, and which do not. He demonstrates both in the Tractatus. There is a difference between saying and showing. Once we understand the difference between those propositions which have sense, those that refer to states-of-affairs, then we are able to have a clear view of those propositions that are senseless, viz., those that go beyond the limit of language according to the Tractatus.

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).”

Tractatus is best viewed as a poem. It is elegantly written and tells a story, it describes a framework of ideas. But it is not strictly logical nor does it solve any problems, at least none that are not contrived. — A Seagull

Nowhere is there evidence that Wittgenstein thought of the Tractatus as a poem, and he sure didn't wish us to think of it as a kind of poem. And, the idea that the Tractatus is "not strictly logical" belies all the logic in the book.

I'll discuss more of this later.

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.

Thanks Banno.

Because you said that he solved all philosophical problems by analyzing propositions via their truth-functions. Philosophical propositions, pertaining to philosophical problems, and according to him, do not have a truth-function, they are neither true or false, right or wrong, but nonsensical, and so the best one can do with them, is to get rid of them. For example, the critique of pure reason by Kant, is a fine example of a nonsensical book. — Pussycat

Remember I'm talking mainly about the Tractatus, and it's clear if you read what he said about that book, that he believed he solved all the major problems of philosophy. It's in the Tractatus that Wittgenstein puts forward his theory of truth-functions, which I'll be talking more about as we go along.

I don't really see any major disagreement.

Yet, somehow, from this, positivism then says that 'all metaphysics is meaningless' and that therefore the only meaningful statements are those which can be validated with respect to sensible experience. Which is pretty well the exact opposite of Wittgenstein's attitude, in my opinion. — Wayfarer

Ya, the Vienna Circle got it wrong, as many did back then when reading Wittgenstein.

He believed in god, although not the sot that is found hereabouts. When asked if he believed in god, he replied "yes, I do, but the difference between what you believe and what I believe may be infinite". — Banno

Can you reference that Banno? I've read quite a bit, but never came across anything like that.

If you think that why are you in here posting?

:up: It is just a lot of confusion.

I don't think you could say Wittgenstein was religious, maybe in his very early years, but definitely not in his later years. He never ridiculed religion, and in fact, he admired some religious writings. He definitely had a mystical bent to his personality. Some misinterpreted this side of Wittgenstein as religious, but I would say not. The mystical for Wittgenstein would best be expressed between the ideas of saying and showing. He didn't think the mystical could be expressed, but only shown in our actions (e.g. praying and meditating). The mystical goes beyond what can be expressed in language. Wittgenstein believed that language has a boundary, beyond which is that that is senseless (not nonsense, but senseless). I'll talk about this later in my posts.