|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. |
Number expression/numerals/Frege: names of certain objects ("abstraction").
Abstraction/Frege: to explain the use of new expressions by the old expressions._____________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.
Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994
Expressive Vernunft Frankfurt 2000
Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001
Begründen und Begreifen Frankfurt 2001