It is quite impossible for a proposition to state that it itself is true. (4.442)
Ludwig Wittgenstein
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Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
Bertrand Russell
A tautology's truth is certain, a proposition's possible, a contradiction's impossible. (Certain, possible, impossible: here we have the first indication of the scale that we need in the theory of probability.) (4.464)
Ludwig Wittgenstein
The criterion which we use to test the genuineness of apparent statements of fact is the criterion of verifiability. We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express — that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject it as being false.
Alfred Jules Ayer
What is true is that I have at times earned my own crust of bread, and at other times a friend has given it to me out of the goodness of his heart. I have lived whatever way I could, for better or for worse, taking things just as they came. It is true that I have forfeited the trust of various people, it is true that my financial affairs are in a sorry state, it is true that the future looks rather bleak, it is true that I might have done better, it is true that I have wasted time when it comes to earning a living, it is true that my studies are in a fairly lamentable and appalling state, and that my needs are greater, infinitely greater than my resources. But does that mean going downhill and doing nothing?
Vincent van Gogh
What is true is that I have at times earned my own crust of bread, and at other times a friend has given it to me out of the goodness of his heart. I have lived whatever way I could, for better or for worse, taking things just as they came. It is true that I have forfeited the trust of various people, it is true that my financial affairs are in a sorry state, it is true that the future looks rather bleak, it is true that I might have done better, it is true that I have wasted time when it comes to earning a living, it is true that my studies are in a fairly lamentable and appalling state, and that my needs are greater, infinitely greater than my resources. But does that mean going downhill and doing nothing?
Vincent Van Gogh
Wittgenstein, Ludwig
Wodehouse, P. G.
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