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2 ideas
| 16416 | The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber] |
| Full Idea: The inferential role of the existential quantifier in first order logic does not carry over to the existential quantifier in English (we have empty names, singular terms that are not even in the business of denoting, and so on). | |
| From: Thomas Hofweber (Ambitious, yet modest, Metaphysics [2009], 2) |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |