The assimilation of tautologies and contradictions with true and false propositions respectively results from the fact that tautologies and contradictions can be taken as truth-functions just like ordinary propositions, and for determining the truth of falsity of the truth-function, tautologies and contradictions among its arguments must be counted as true or false respectively. ...Are the propositions of symbolic logic and mathematics tautologies in Mr Wittgenstein's sense?
Frank P. RamseyRelated topics
assimilation fact false falsity logic mathematics ordinary sense take truthRelated quotes
Suggestion, or rather Autosuggestion, is quite a new subject, and yet at the same time it is as old as the world. It is new in the sense that until now it has been wrongly studied and in consequence wrongly understood; t is old because it dates from the appearance of man on the earth. In fact autosuggestion is an instrument that we possess at birth, and in this instrument, or rather in this force, resides a marvellous and incalculable power.
Émile Coué
Mr. Darwin's hypothesis is not, so far as I am aware, inconsistent with any known biological fact; on the contrary, if admitted, the facts of Development, of Comparative Anatomy, of Geographical Distribution, and of Palaeontology, become connected together, and exhibit a meaning such as they never possessed before; and I, for one, am fully convinced that if not precisely true, that hypothesis is as near an approximation to the truth as, for example, the Copernican hypothesis was to the true theory of the planetary motions.
Thomas Henry Huxley
Reports to the Surgeon General... represent the final word upon the efficient and devoted sense of responsibility of our people in this obligation to our fellow citizens. Overwhelmingly they confirm the fact that the general mortality rate, infant mortality rate, epidemics, the disease rate-are less than in normal times. There is but one explanation. That is, that through an aroused sense of public responsibility, those in destitution and their children are receiving actually more adequate care than even in normal times.
Herbert Hoover
Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
David Hilbert
The truth [is in his paintings]... When they have a similar structure to and are organized in as truthful a way as nature. When I look out of the window, then truth for me is the way nature shows itself in its various tones, colours and proportions. That's a truth and has its own correctness. This little slice of nature, and in fact any given piece of nature, represents to me an ongoing challenge, and is a model for my paintings.
Gerhard Richter
