Philosophy Dictionary of ArgumentsHome
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| Numerals: numerals are symbols used to represent numbers. There are different systems of building numerals according to the supply of elementary symbols for the construction of the numerals. Examples are the Roman numerals and the Arabic numerals, but also the binary system, decimal system, hexadecimal system. It is necessary that there are fewer elementary symbols than numbers, as it would otherwise be impossible to learn them and to calculate with them. The properties of the numerical systems influence our numeracy. These properties are not to be confused with the properties of the numbers, which are independent of their representation in numerical form. See also numbers, counting, symbols, names, numeric names, numeric words._____________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 Numerals - Dictionary of Arguments
I 131 Abstraction/Mathematics/Frege/Thiel: Abstraction is a purely logical process, an operating with statements whose logical character is revealed by the change from the structure of the complicated initial statement to the structure of the new statement. >Abstraction, >Structures. Frege was the first to understand this. Statements not only about numbers, but also about quantities, functions, concepts, state of affairs, meaning and truth value of a statement, about structures. I 133 Numbers/Numerals/Number Names/Names/Mathematics/Thiel: The philosophical point of the transition from general statements about numerals to arithmetical statements lies in the fact that, although we have introduced speech about numerals in addition to speech about numbers, we have introduced speech about numbers as a way of speaking, as a facon de parler, the possibility of which does not depend on there being abstract objects beyond the concrete numerals, which we call "numbers". >Numbers, >Mathematical entities. I 134 We also had no reason to regard the numerals as "names" of numbers, so that about 4, IV, and |||| would denote the same number Four, as probably assumed in the traditional philosophy of numbers._____________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 2024-04-20