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Single Idea 13664

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

Full Idea

It is claimed that aiming at a universal language for all contexts, and the thesis that logic does not involve a process of abstraction, separates the logicists from algebraists and mathematicians, and also from modern model theory.

Gist of Idea

Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 7.1)

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.176

A Reaction

I am intuitively drawn to the idea that logic is essentially the result of a series of abstractions, so this gives me a further reason not to be a logicist. Shapiro cites Goldfarb 1979 and van Heijenoort 1967. Logicists reduce abstraction to logic.

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]