@misc{Lexicon of Arguments,
title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024},
author = {Frege,Gottlob},
subject = {Equality},
note = {I 89 f
Number/Frege: the number is an abstract object - not a property (see below).
Equality of Numbers/numerical equality/equality: equality is a concept (not a subject).
>Numbers, >Objects.
I 94
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).
I 95
Equality/Frege: ((s) number equality/numerical equality/(s): number equality 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.
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 the first thing to be established. ((s) but not equality of direction).
>Concepts.
I 96
Direction/Frege: direction cannot distinguish from the straight line.
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.
>Definition.},
note = { 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
},
file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=729012}
url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=729012}
}