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Full Idea
In the quantification '(∃)(x=a)', it is the existential quantifier, not the 'a' itself, which carries the existential import.
Gist of Idea
Existence is implied by the quantifiers, not by the constants
Source
Willard Quine (Existence and Quantification [1966], p.94)
Book Ref
Quine,Willard: 'Ontological Relativity and Other Essays' [Columbia 1969], p.94
A Reaction
The Fregean idea seems to be that the criterion of existence is participation in an equality, but here the equality seems not more than assigning a name. Why can't I quantify over 'sakes', in 'for the sake of the children'?
2611 | It is currently held that quantifying over something implies belief in its existence [Ayer] |
19486 | We can use quantification for commitment to unnameable things like the real numbers [Quine] |
16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
5747 | "No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
12440 | If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni] |