Philosophy Dictionary of ArgumentsHome
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| Ontology: is the set of material or immaterial objects, of which a theory assumes that it can make statements about them. According to classical logic, an existence assumption must be assumed. In other fields of knowledge, the question of whether relations really exist or are merely mental constructs, is not always regarded as decisive as long as one can work with them. Immaterial objects are e.g. linguistic structures in linguistics. See also existence, mathematical entities, theoretical entities, theoretical terms, reality, metaphysics, semantic web._____________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. | |||
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Christian Thiel on Ontology - Dictionary of Arguments
Thiel I 18/19 Mathematics/Ontology/Mathematical Entities/Thiel: Def "Logicism" attributes mathematics (any object) to logic. The object of mathematics is then the object of logic. What is then the object of logic: logicism must say: actually no material object at all, but "all objects" in the sense that its statements apply to all objects in the world. We create the objects ourselves. "In itself" such an object never exists! >Mathematical entities, >Platonism. DubislavVs: Every convention must be made about something. So one must ask the conventionalist about which structures his axioms have to be regarded as consistent. >Beginning, >Axioms. I 312 In modern mathematics one speaks not only of "the" addition, but of "an addition" and introduces linking signs. For example, one writes addition as "$" if it is associative and commutative, if it is not the case, one might prefer to write the operation as multiplication "§" or something else. >Axioms/Hilbert. I 312/313 Ontology/object/mathematics/Thiel: the validity of such laws does not turn the subject area into a number area, just as the validity of any set-theoretical laws transforms the (ranges of) numbers into (ranges of) sets. >Numbers, >Sets. The recording of the possible types of operations does not provide any fundamental discipline. I 314 It may be that the universality of mathematics is based on the ever new applicability of the very general operations and not on the fact that mathematics deals with particularly general objects. >Generalization, >Generality. Although we always carry out the same set-theoretical operations in the different fields of mathematics, this does not mean that there are "sets" as autonomous objects. At most, a fundamental discipline should be envisaged that fulfils this task as a fundamental canon for "dealing with everything and everyone"._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
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Ed. Martin Schulz, access date 2024-04-18