|Numbers: whether numbers are objects or concepts, has been controversial in the philosophical discussion for millennia. The most widely accepted definition today is given by G. Frege (G. Frege, Grundlagen der Arithmetik 1987, p. 79ff). Frege-inspired notions represent numbers as classes of classes, or as second-level terms, or as that with one measure the size of sets. Up until today, there is an ambiguity between concept and object in the discussion of numbers. See also counting, sets, measurements, mathematics, abstract objects, mathematical entities, theoretical entities, number, platonism._____________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 17
Numbers/Ontology/Mathematics/Nicolai Hartmann/Thiel: today (unjustly) almost forgotten position: the definition is based on a determination of the properties of mathematical being: "general ontology" Nicolai Hartmann and Günther Jacoby. Thesis: the mathematical objects would have a "fictitious per se existence". We do not conceive the being of mathematical objects as being real, but in analogy to that. We omit the space-time and keep only the "independence from the being meant"._____________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.
Philosophie und Mathematik Darmstadt 1995