|Theories: theories are statement systems for the explanation of observations, e.g. of behavior or physical, chemical or biological processes. When setting up theories, a subject domain, a vocabulary of the terms to be used and admissible methods of observation are defined. In addition to explanations, the goal of the theory formation is the predictability and comparability of observations. See also systems, models, experiments, observation, observation language, theoretical terms, theoretical entities, predictions, analogies, comparisons, evidence, verification, reduction, definitions, definability._____________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. |
|Thiel I 73
Theory/Mathematics/Thiel: The term "meta mathematics" had already appeared in a different meaning in the 19th century, reformulated by Hilbert.
Hilbert had proved that in Euclid not all of the properties used in the geometric propositions are really developed from the basic properties recorded in the axioms. So it was incomplete.
After Cantor's work at the end of the 19th century, it looked as if one could actually find a complete axiom system. Admittedly, no meta mathematics would have been necessary for this.
Meta mathematics makes a difference between the proof that a statement A cannot be refuted (the proof that its opposite is not justifiable) and a "positive" justification of A. The first is a rebuttal of ~A thus a proof of ~~A, the second a proof of A.
New: in meta mathematics the existential statements are interpreted more strictly. Anyone who now claims the existence of evidence must also indicate a verifiable way of constructing such evidence. Def "effective" or "constructive" assertion of existence._____________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