|Knowledge: Knowledge is a conscious relationship to sentences or propositions, which legitimately attributes to them truth or falsehood. What is known is true. Conversely, it does not apply that everything that is true is also known. See also knowledge how, propositional knowledge, realism, abilities, competence, truth, facts, situations, language, certainty, beliefs, omniscience, logical knowledge, reliability_____________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. |
Knowledge/Geometry/Mathematics/Thiel: the classical derivation, e.g. of the Thales Theorem, is based on intuition. (Of course not the measurement of things of the body world.) We conclude and even calculate a bit. Of course, this is not an axiomatic procedure.
Where does the insight come from that a certain geometric theorem is correct?
Knowledge/Thiel: knowledge about the sum of angles in the triangle comes from the knowledge that when two parallel lines are intersected by a third line, the resulting Z angles (alternating angles) are equal.
But how do we know that the Z angles are equal? It is shown in a figure. According to the parallel postulate of Euclid. Also counterfactual assumptions, which are refuted._____________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.
Philosophie und Mathematik Darmstadt 1995