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Wittgenstein, while previously advocating a picture theory of semantics, later came to revoke his support of this position.
But did Wittgenstein still hold on to certain ideas of his old school?
What are the most influential of these similarities between the earlier Wittgenstein and the later Wittgenstein?
Wittgenstein never changed his opinion about Cantor's set theory.
Imagine set theory's having been invented by a satirist as a kind of parody on mathematics. – Later a reasonable meaning was seen in it and it was incorporated into mathematics. (For if one person can see it as a paradise of mathematicians, why should not another see it as a joke?) [V. 7]
If it were said: "Consideration of the diagonal procedure shews you that the concept 'real number' has much less analogy with the concept 'cardinal number' than we, being misled by certain analogies, inclined to believe", that would have a good and honest sense. But just the opposite happens: one pretends to compare the "set" of real numbers in magnitude with that of cardinal numbers. The difference in kind between the two conceptions is represented, by a skew form of expression, as difference of extension. I believe, and I hope, that a future generation will laugh at this hocus pocus. [II.22]
The curse of the invasion of mathematics by mathematical logic is that now any proposition can be represented in a mathematical symbolism, and this makes us feel obliged to understand it. Although of course this method of writing is nothing but the translation of vague ordinary prose. [V.46]
"Mathematical logic" has completely deformed the thinking of mathematicians and of philosophers, by setting up a superficial interpretation of the forms of our everyday language as an analysis of the structures of facts. Of course in this it has only continued to build on the Aristotelian logic. [V.48]
[L. Wittgenstein: "Remarks on the foundations of mathematics", Wiley-Blackwell (1991)]
The expression "and so on" is nothing but the expression "and so on". [p. 282]
There is no such thing as "the cardinal numbers", but only "cardinal numbers" and the concept, the form "cardinal number". Now we say "the number of the cardinal numbers is smaller than the number of the real numbers" and we imagine that we could perhaps write the two series side by side (if only we weren't weak humans) and then the one series would end in endlessness, whereas the other would go on beyond it into the actual infinite. But this is all nonsense. [p. 287]
"This proposition is proved for all numbers by the recursive procedure". That is the expression that is so very misleading. It sounds as if here a proposition saying that such and such holds for all cardinal numbers is proved true by a particular route, or as if this route was a route through a space of conceivable routes. But really the recursion shows nothing but itself, just as periodicity too shows nothing but itself. [p. 406]
In mathematics description and object are equivalent. "The fifth number of the number series has these properties" says the same as "5 has these properties". The properties of a house do not follow from its position in a row of houses; but the properties of a number are the properties of a position. [p. 457]
After all I have already said, it may sound trivial if I now say that the mistake in the set-theoretical approach consists time and again in treating laws and enumerations (lists) as essentially the same kind of thing and arranging them in parallel series so that one fills in gaps left by the other. [p. 461]
[L. Wittgenstein: "Philosophical grammar", Basil Blackwell, Oxford (1969)]
[...] there is no path to infinity, not even an endless one. [...] All right, the path must be endless. But if it is endless, then that means precisely that you can’t walk to the end of it. That is, it does not put me in a position to survey the row. (Ex hypothesi not.) [§ 123]
It isn't just impossible "for us men" to run through the natural numbers one by one; it's impossible, it means nothing. [...] you can't talk about all numbers, because there's no such thing as all numbers. [§ 124]
There's no such thing as "all numbers" simply because there are infinitely many. [§ 126]
The infinite number series is only the infinite possibility of finite series of numbers. It is senseless to speak of the whole infinite number series, as if it, too, were an extension. [...] If I were to say "If we were acquainted with an infinite extension, then it would be all right to talk of an actual infinite", that would really be like saying, "If there were a sense of abracadabra then it would be all right to talk about abracadabraic sense perception". [§ 144]
Set theory is wrong because it apparently presupposes a symbolism which doesn't exist instead of one that does exist (is alone possible). It builds on a fictitious symbolism, therefore on nonsense. [§ 174]
[L. Wittgenstein: "Philosophical remarks", Wiley-Blackwell (1978)]
One of the things he was famous for in the Tractatus is the idea about certain things that you can show but not say e.g. ethics. He rejects the reasoning he used in the Tractatus and rejects the idea of holding philosophical theses at all, and rejects theory-building. But his position on ethics didn't really change as far as I can tell. He also always rejected solipsism as solipsists see it. Also, he always seemed to dislike worship of the scientific method being used outside of science. I would say that there is more continuity between early and later Wittgenstein than is usually stated. His method did entirely change though.
The analytical school is often thought to have risen in opposition to much of what the positivist school assumed to be true.? or further specify what you mean by each of the terms.the assumptions of the logical positivists and the *continental school as a whole*.