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" "Frege ridiculed the formalist conception of mathematics by saying that the formalists confused the unimportant thing, the sign, with the important, the meaning. Surely, one wishes to say, mathematics does not treat of dashes on a bit of paper. Frege’s idea could be expressed thus: the propositions of mathematics, if they were just complexes of dashes, would be dead and utterly uninteresting, whereas they obviously have a kind of life. And the same, of course, could be said of any proposition: Without a sense, or without the thought, a proposition would be an utterly dead and trivial thing. And further it seems clear that no adding of inorganic signs can make the proposition live. And the conclusion which one draws from this is that what must be added to the dead signs in order to make a live proposition is something immaterial, with properties different from all mere signs.
But if we had to name anything which is the life of the sign, we should have to say that it was its use.
Ludwig Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-born philosopher who spent much of his life in England.
Biography information from Wikiquote
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Logic pervades the world: the limits of the world are also its limits. So we cannot say in logic, "The world has this in it, and this, but not that." For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well. We cannot think what we cannot think; so what we cannot think we cannot say either. (5.61)
The truly apocalyptic view of the world is that things do not repeat themselves. It isn’t absurd, e.g., to believe that the age of science and technology is the beginning of the end for humanity; that the idea of great progress is delusion, along with the idea that the truth will ultimately be known; that there is nothing good or desirable about scientific knowledge and that mankind, in seeking it, is falling into a trap. It is by no means obvious that this is not how things are.
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