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2 ideas
| 21647 | Logicism makes sense of our ability to know arithmetic just by thought [Hofweber] |
| Full Idea: Frege's tying the objectivity of arithmetic to the objectivity of logic makes sense of the fact that can find out about arithmetic by thinking alone. | |
| From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.1) | |
| A reaction: This assumes that logic is entirely a priori. We might compare the geometry of land surfaces with 'pure' geometry. If numbers are independent objects, it is unclear how we could have any a priori knowledge of them. |
| 21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |
| Full Idea: A major flaw of the neo-Fregean program is that it is more impressed by the technical result that Peano Arithmetic can be interpreted by second-order logic plus Hume's Principle, than empirical considerations about how numbers come about. | |
| From: Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.3) | |
| A reaction: This doesn't sound like a problem that would bother Fregeans or neo-Fregeans much. Deriving the Peano Axioms from various beginnings has become a parlour game for modern philosophers of mathematics. |