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Full Idea
'Numerical identity' implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical.
Gist of Idea
It is controversial whether only 'numerical identity' allows two things to be counted as one
Source
Harold Noonan (Identity [2009], §1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
Noonan cites Geach, presumably to remind us of relative identity, where two things may be one or two, depending on what they are relative to. The one 'guard on the gate' may actually be two men.
| 16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
| 16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
| 16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
| 16020 | Identity can only be characterised in a second-order language [Noonan] |
| 16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
| 16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
| 16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
| 16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |