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.
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I 110
0/1/zero /one/numbersn/Frege: 0 is the object which falls under the term "equal to 0" - so a 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.

G. Frege
Die Grundlagen der Arithmetik Stuttgart 1987

G. Frege
Funktion, Begriff, Bedeutung Göttingen 1994

G. Frege
Logische Untersuchungen Göttingen 1993

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Ed. Martin Schulz, access date 2017-05-26