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Full Idea
A cursory examination shows that mathematicians have no aversion to saying that this-or-that mathematical entity exists. But is this a different sense of 'existence'?
Gist of Idea
Do mathematicians use 'existence' differently when they say some entity exists?
Source
C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.72
A Reaction
For those of us like me and my pal Quine who say that 'exist' is univocal (i.e. only one meaning), this is a nice challenge. Quine solves it by saying maths concerns sets of objects. I, who don't like sets, am puzzled (so I turn to fictionalism...).
| 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] |