Philosophy Lexicon of Arguments

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Similarity: conformity of one or more - but not all - properties of two or more objects.

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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I 89 f
Number/Frege: is an abstract object - not a property (see below).
Equality of Numbers/Numerical Equality/Equality: is a term (not a subject).
I 94
Equality/Frege: if a = b is true can be found out by introducing a third element: a mark - is there a c, for which the following applies: a = c and b = c? - ((s) tertium comparationis) - ((s) here: E.g. equality in terms of numbers).
I 95
Equality/Frege: ((s) Equality of Numbers/Numerical Equality/(s) is a concept, not an object - we need it here.)
Frege: assuming equality simpliciter would demand that it would have to be re-explained in any case, by establishing an equation.
I 95
Direction/Frege: we can obtain the concept of direction from the parallelism of straight lines - by conceiving a II b as an equation. - From this we abstract the concept of direction. - Also with parallelism the concept of equality is established first. - ((s) But not the equality of direction).
III 96
Direction/Frege: cannot be distinguished from the straight.
I 102
Equality of Numbers/Numerical Equality/Numbers/Definition/Frege/(s): Quantity can be defined by numerical equality, because there is no need to count for numerical equality! - E.g. assigning knives to plates without counting.

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.

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 2018-02-19