|Similarity: conformity of one or more - but not all - properties of two or more objects.|
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Number/Frege: is an abstract object - not a property (see below).
Equality of Numbers/Numerical Equality/Equality: is a term (not a subject).
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).
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.
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).
Direction/Frege: cannot be distinguished from the straight.
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