Rational truths and factual truths

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The truths of reason and truths of fact - vérités de raison et vérites de fait - designate two types of truths in Leibniz .

The truths of reason are necessary, but the truths of fact cannot be ascertained without a comparison with reality. A factual truth can be: “It's raining outside” - you have to see whether that is “the case”. The laws of logic are among the primary truths of reason. Leibniz calls the rational moments identical, because they are the repetition of the same thing without telling people anything new about things.

Ludwig Wittgenstein developed the areas of different claims to truth established by Leibniz's thesis in his writings Tractatus Logico-Philosophicus (1922) and About Certainty (first published posthumously in 1969). Under point 6.1 in the Tractatus he writes , "The propositions of logic are tautologies, [6.11:] The propositions of logic therefore say nothing (they are analytic propositions)." In About Certainty , Wittgenstein added illustrative questions about the truth content of mathematical equations to these considerations. That the sentence “12 × 12 = 144” is true does not follow from a look at reality; it follows the basic assumptions according to which the number system is defined. If you define that, that's the result. The observation: “a white mold” is similar: it is no more true than the observation “a mold”. After all, a gray horse is already the definition of a white horse. It would therefore be better not to speak of an "observation" and a "factual truth" established in it, but of a tautological statement.

In Wittgenstein's view that the laws of logic are not a reflection of reality, Rudolf Carnap and other neopositivists agreed . Carnap distinguished two types of truths:

• logical, necessary, built on meaning and
• empirical, accidental, dependent on the facts of the world

With regard to the logical truths, it is sufficient to understand the statement in order to determine its truthfulness. Beyond the linguistic facts, nothing else is assumed here. According to Carnap, the analytical judgments (ie the tautologies) do not provide any information about the world and the synthetic judgments provide certain information.