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Full Idea
In the Identity of Indiscernibles, one speaks about properties, and the notion of a property is by no means clearly fixed and formalized in modern symbolic logic.
Gist of Idea
The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles
Source
C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.60
A Reaction
The unclarity of 'property' is a bee in my philosophical bonnet, in speech, and in metaphysics, as well as in logic. It may well be the central problem in our attempts to understand the world in general terms. He cites intensional logic as promising.
| 18763 | Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA] |
| 18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA] |
| 18765 | Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA] |
| 18766 | 's is non-existent' cannot be said if 's' does not designate [Anderson,CA] |
| 18767 | Free logics has terms that do not designate real things, and even empty domains [Anderson,CA] |
| 18768 | We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA] |
| 18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA] |
| 18769 | Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA] |
| 18770 | We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA] |