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Full Idea
Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant.
Gist of Idea
Logicism might also be revived with a quantificational approach, or an abstraction-free approach
Source
B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2)
Book Ref
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.167
A Reaction
Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting.
| 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] |