Then why does Wittgenstein talk about pictures? — Metaphysician Undercover

I dunno why, I guess this was his way.

And there we have it. The mathematical basis of the physical sciences rejected. — Banno

So here we have the heart of the issue. We use mathematics to deal with things other than logical facts and states of affairs. We use mathematics to deal with things like velocities, probabilities, statistics and predictions. These are real aspects of the world which mathematics deals with, which cannot be pictured as states of affairs. Would you agree that Wittgenstein concludes that mathematics cannot say anything about the world, because it is used to understand the difference between states of affairs, and doesn't tell us anything about any actual state of affairs?

I don't have any dislike of Wittgenstein at all. I actually like what he did, and am in broad sympathy with the Oxford / 'ordinary language' philosophy.

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.

So here we have the heart of the issue. — Metaphysician Undercover

Yes, indeed. I think we have finished. I've cut to the irrationality that lies at the core of your thinking: your rejection of the calculus. And not for the first time.

It puzzles me, since as I said you are intelligent and articulate. But there it is. If it were a mere eccentricity one might be able to pass over it in order to attend to your other comments; but it seems to pervade your writing. But there are some things that must remain a mystery, and hence be passed over in silence.

Actually I will go back to this:

Right, when you get to the end of the book, Wittgenstein admits that it's all wrong, and advises you to throw it all away. He basically says I've given you a demonstration of the wrong approach, now move along and find the right approach. But when you see from the very beginning, that it's all wrong... — Metaphysician Undercover

It seems to me that the error Meta makes here parallels the error he makes in rejecting the calculus.

See the discussion here.

Meta is apparently stuck in the first paragraph,

(x2 − 1)/(x − 1)
Let's work it out for x=1:
(12 − 1)/(1 − 1) = (1 − 1)/(1 − 1) = 0/0

failing to see past the "other way" of dealing with the problem. He's unable to kick away the ladder of in order to see how limits give us a different way of viewing the problem of finding an instantaneous velocity.

In much the same way he can't see how The Tractatus, in setting out what can be said, shows us the limits of our ability ot say things.

Yes, indeed. I think we have finished. I've cut to the irrationality that lies at the core of your thinking: your rejection of the calculus. And not for the first time. — Banno

You misunderstand. I don't reject calculus, I think it is very useful. But under Wittgenstein's stated principles, in the Tractatus, mathematics cannot say anything about the world. Mathematics doesn't picture anything, like a proposition does, so mathematics doesn't make any sense in that sense. So the expression "2+2=4" doesn't say anything about the world, it's not a fact, it doesn't picture anything. In the Tractatus, mathematics is an "operation". But how is it possible that "operations", from which propositions might be created, are not part of the world? Wittgenstein might give us coherency but he doesn't give us a true picture of "the world". The irony!

You misunderstand. — Metaphysician Undercover

I don't think I do.

I don't reject calculus, I think it is very useful.

yet,

Do you accept that one can find the instantaneous velocity of an accelerating body?
— Banno

No, of course not, that's completely illogical. — Metaphysician Undercover

I know you try to finesse this contradiction into some semblance of coherence. We've been there before. Those musings are an indictment of your thinking. Hence,

"2+2=4" doesn't say anything about the world — Metaphysician Undercover

Well, yes, it does tell us about the world; but you can't see that because your notion of meaning is referential, and you can't see a "real" 2 to add to another "real" 2. But meaning is best seen in use, not reference, and hence 2+2=4 tells us about something we can do in the world - adding things together.

SO all that is evident is your mis-phrasing of the very question. Mathematics is embedded in the world, in much the same way as is language. That's what is meant by

(1) “The world is all that is the case.”

Thanks, @Sam26.

Anything to add about truth tables?

nothing.

The bottom part isn't right – one of the main points of the Tractatus is that logical truths don't tell us about the world, but 'show' its transcendental structure. 'All that is the case' is one way the world can be among others, but logical truths including mathematical ones don't distinguish one way the world can be among others (I'm speaking in Tractatus W's voice here).

(I'm speaking in Tractatus W's voice here). — Snakes Alive

Yep, you are right. My defence is that I am speaking in a voice that attempts to parse Wittgenstein into something that Meta might understand. Lies to children, as it were. Notice that above that I tell another lie about meaning as use, which of course has no place in the Tractatus.

But that raises the interesting question of how the view of mathematics implicit in the Tractatus might differ from that found in the later Wittgenstein.

6.211 Indeed in real life a mathematical proposition is never what we want. Rather, we make use of mathematical propositions only in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics. (In philosophy the question, ‘What do we actually use this word or this proposition for?’ repeatedly leads to valuable insights.) 

Here, interestingly, is much the same point I was making to Meta. I suppose the point might be better phrased as: while 2+2=4 does not say anything about the world, its use tells us a great deal about the world.

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.

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.

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. — Sam26

I wouldn't say that this is new, he distinctly says in the Tractatus that language pictures reality. The reality referred to is empirical reality, the world. That a priori thoughts cannot possibly be sensible, is clearly explained in the 3's and 4's. This is what excludes mathematics from being able to say anything sensible. Mathematics involves internal relations, relations of order, which he distinguishes from proper relations (spatial relations which can be pictured).
"2.225 There are no pictures which are true a priori.
3 A logical picture of facts is a thought.
3.001 'A state of affairs is thinkable': what this means is that we can picture it to ourselves.
3.01 The totality of true thoughts is a picture of the world"

Following this he proceeds to discuss what sort of existence an a priori thought might have, and it follows that it must not have any sense. But then he wants to give the a priori some kind of reality as a "logical form", and the logical form would have to comprise some sort of object. But logical forms are presented by philosophers as propositions, and such propositions are nonsensical. In keeping with the picture analogy, Wittgenstein insists that a proposition must show us something, rather than saying something, and this is what gives the proposition some sort of sense, by showing. But the proposition can't show us anything other than its logical form, and this produces the distinction between showing and saying. It's now determined that a proposition cannot say anything. It only makes any sense by showing us its own logical form.

The problem is that he has turned the picture analogy around, so now the picture (proposition) doesn't say anything about the world, it just shows us something, and what it shows us is only its logical form, what turns out to be internal relations. This leaves us with no means for saying anything sensible about the world

You left out the first page of the Tractatus, the most important part.

I think the main problem with Tractatus is self contradiction. The main thesis of Tractatus is the idea that only logical propositions and empirical propositions are truth apt. In other words, all the rest of statements which includes moral commands, metaphysics, aesthetic etc, are senseless and not truth apt. The thesis itself also falls under the category of senseless statements as it isn't a logical statement nor an empirical one , it is a meta ontological statement, bordering on metaphysics, so we do not know what to conclude. Throw away the ladder or everything ?

The picture theory also doesn't help us at all and Wittgenstein gave us his famous rabbit/duck picture to highlight how weak picture theory is. The reduction of statements into their individual components doesn't help at all as even the elementary propositions which we supposedly cannot further separate are not simple but complex, so the very idea that we can analyze the whole by studying the components still causes problems.

An interesting question which Wittgenstein posed in Investigation is what does a picture of the general prototype of a tree look like. We cannot help but only picture a specific example. The picture theory cannot give us a general meaning ( it should ) and perhaps there isn't a general meaning or a definition which covers all examples. There is only a resemblance between different uses of a word.

What specifically are you referring too?

The page that starts with the title, "Tractatus Logico-Philosophicus", and then continues with "DEDICATED".

Quine famously argued for the existence of abstract objects like sets,numbers etc along with physical objects we find in the universe. It is argued that they both have equivalent ontological commitments.

A theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true ~ Quine
I wonder how Wittgenstein would refute Quine as he was against platonism of all forms. Quine wasn't a full blown platonist as he didn't think hyper real sets existed. His more controversial ideas would be modifying math based on how effectively it describes the world when used in science/empirical endeavors. He emphasized a minimum modification.

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

No, before that, I was talking about the motto.

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

The motto, yes. What does Fann say about it? What? Nothing? Why is that, you think?

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

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. — Sam26

Well maybe it's not, but vital to really understanding the Tractatus. After all, it seems like a combination of epistemology and a proposition that has sense.

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. — Sam26

:razz: I am sorry, I didn't know u were in serious business, or else I wouldn't have imposed! But everyone needs a break, once in a while. Maybe you'll come back, like Wittgenstein did. Take care.