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Number/Frege: is an abstract object - not a property (see below).
Equality of Numbers/Numerical Equality/Equality: is a concept (not a subject).
Equality/Frege: if a = b is true, is 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).
Equality/Frege: - ((s) Number Equality/Numerical Equality/(s) is a concept, not an object - this is what we need here.) - Frege: assuming equality simpliciter would require re-explaining it in any case by establishing an equation.
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 the first thing to be established. - ((s) but not equality of direction).
Direction/Frege: cannot distinguish from the straight line.
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.
Die Grundlagen der Arithmetik Stuttgart 1987
Funktion, Begriff, Bedeutung Göttingen 1994
Logische Untersuchungen Göttingen 1993