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Full Idea
Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables.
Gist of Idea
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables
Source
Willard Quine (Carnap and Logical Truth [1954], II)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.110
A Reaction
Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand.
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |