Gottlob Frege on One (Number 1) - Philosophy Lexicon of Arguments

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Philosophy Lexicon of Arguments


One, number 1: in modern logic it is not possible to introduce the number one directly. It must be introduced indirectly, via existential quantification ("for at least one x ...") and universal quantification ("for all x ..."). In addition, identity is needed. See also definition, identity, logic, elementary logic, number theory, numbers. _____________ 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.

Frege, Gottlob	One (Number 1)	I 110 0/1/zero/one/numbers/Frege: 0 is the object which falls under the term "equal to 0". - So an object (zero) falls under the concept. - Because an object falls under the concept, the concept is the number one (1 object, zero). - In contrast 0: no object falls under the term "equal to 0 but not equal to 0". - Hence, 0 is the number which belongs to the concept. _____________ 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.	F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993

> Counter arguments against Frege

Ed. Martin Schulz, access date 2018-06-21