Philosophy Dictionary of ArgumentsHome
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| 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. | |||
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Gottlob Frege on One (Number 1) - Dictionary of Arguments
I 110 0/1/zero/one/numbers/Frege: 0 is the object that falls under the term "equal to 0". This means that an object ((s) the number zero) falls under the term. ((s) Because an object falls under the term, the number 1 (1 object, namely zero) is assigned to the term). ((s) Precondition: the distinction between concept and object, the distinction between number and number-of (amount), as well as the concept of falling under a term). ((s) In contrast, zero/0: falling under the concept "equal to 0 and not equal to 0" does not include an object. Therefore, 0 is the number of (the amount of) objects that fall under the (contradictory) term). >Concept, >Object, >Numbers, >Zero/Frege, >Number-of/Frege._____________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. |
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 |
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> Counter arguments against Frege
> Counter arguments in relation to One (Number 1)
Ed. Martin Schulz, access date 2024-04-27