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Full Idea
We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory.
Gist of Idea
If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic
Source
Willard Quine (Carnap and Logical Truth [1954], II)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.111
A Reaction
Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic.
| 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] |