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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism

[revival of logicism after much criticism]

15 ideas
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock]
Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock]
Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro]
We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale]
Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber]