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Full Idea
It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other.
Gist of Idea
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
Source
B Hale / C Wright (Logicism in the 21st Century [2007], 8)
Book Ref
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.196
A Reaction
It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading.
8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |