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Single Idea 10580

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism ]

Full Idea

Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.

Gist of Idea

Mathematics is both necessary and a priori because it really consists of logical truths

Source

Stephen Yablo (Abstract Objects: a Case Study [2002], 10)

Book Ref

-: 'Nous' [-], p.237

A Reaction

Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.

The 15 ideas with the same theme [revival of logicism after much criticism]:

21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
18144 Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock]
18147 Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock]
7804 Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
13899 The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
13896 The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
9224 Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
13664 Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro]
18167 We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
19295 Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale]
21648 Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber]