|Analytic/synthetic: achieved by decomposition or by composition. In philosophy analytically true = true according to the meaning of the components - synthetic insight = substantial expansion of knowledge._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Mill and Mach claimed that mathematical propositions were of empirical origin,
Kant, the arithmetic and geometrical propositions are synthetic judgments a priori.
Poincaré: although arithmetic propositions are synthetically a priori, but the geometric ones are analytical.
Frege: the arithmetical ones are analytical, the geometric ones are synthetic.
Russell: all mathematical propositions are analytical.
Today (1947) it is often said that logic is a system of tautologies and mathematics is a >part of logic._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976