“A tautology's truth is certain, a proposition's possible, a contradiction's impossible.”

— Ludwig Wittgenstein, book Tractatus Logico-Philosophicus

Certain, possible, impossible: here we have the first indication of the scale that we need in the theory of probability.
4.464
Original German: Die Wahrheit der Tautologie ist gewiss, des Satzes möglich, der Kontradiktion unmöglich
Source: 1920s, Tractatus Logico-Philosophicus (1922)

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Ludwig Wittgenstein228

Austrian-British philosopher 1889–1951

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“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. Ramsey (1903–1930) British mathematician, philosopher

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“Tautologies and contradictions are not real propositions, but degenerate cases. …Clearly, by negating a contradiction we get a tautology, and by negating a tautology a contradiction. …A genuine proposition asserts something about reality, and it is true if reality is as it is asserted to be. But a tautology is a symbol constructed so as to say nothing whatever about reality, but to express total ignorance by agreeing with every possibility.”

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“The best paradoxes raise questions about what kinds of contradictions can occur—what species of impossibilities are possible.”

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“Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.) (5)”

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“If he will not be satisfied with truth in the form of tautology, that is to say, if he will not be content with empty husks, then he will always exchange truths for illusions.”

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It is only by means of forgetfulness that man can ever reach the point of fancying himself to possess a "truth" of the grade just indicated. If he will not be satisfied with truth in the form of tautology, that is to say, if he will not be content with empty husks, then he will always exchange truths for illusions.

“Possible impossibility emerges from an impossible possibility, or possibly, impossible possibility blooms from the impossibly possible impossibility.”

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“After defining semantical concepts like logical truth and related ones, I proposed to interpret the modalities as those properties of propositions which correspond to certain semantical properties of the sentences expressing the propositions. For example, a proposition is logically necessary if and only if a sentence expressing it is logically true.”

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“It is quite impossible for a proposition to state that it itself is true.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

4.442
Original German: Ein Satz kann unmöglich von sich selbst aussagen, dass er wahr ist.
1920s, Tractatus Logico-Philosophicus (1922)

“A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions”

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“There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible.”

Gottfried Leibniz (1646–1716) German mathematician and philosopher

Il y a aussi deux sortes de vérités, celles de Raisonnement et celle de Fait. Les vérités de Raisonnement sont nécessaires et leur opposé est impossible, et celles de Fait sont contingentes et leur opposé est possible.
La monadologie (33).
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“A tautology's truth is certain, a proposition's possible, a contradiction's impossible.”

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Ludwig Wittgenstein228

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