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Single Idea 18147
[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
]
Full Idea
The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else.
Gist of Idea
Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number
Source
David Bostock (Philosophy of Mathematics [2009], 9.A.2)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.272
Related Ideas
Idea 18145
Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock]
Idea 9046
Our definition will not tell us whether or not Julius Caesar is a number [Frege]
The
15 ideas
with the same theme
[revival of logicism after much criticism]:
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21718
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Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets
[Russell, by Linsky,B]
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18144
|
Neo-logicists agree that HP introduces number, but also claim that it suffices for the job
[Bostock]
|
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18147
|
Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number
[Bostock]
|
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7804
|
Wright has revived Frege's discredited logicism
[Wright,C, by Benardete,JA]
|
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13899
|
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals
[Wright,C]
|
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13896
|
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes
[Wright,C]
|
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10622
|
The neo-Fregean is more optimistic than Frege about contextual definitions of numbers
[Hale/Wright]
|
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8783
|
Logicism might also be revived with a quantificational approach, or an abstraction-free approach
[Hale/Wright]
|
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12225
|
Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment
[Hale/Wright]
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10580
|
Mathematics is both necessary and a priori because it really consists of logical truths
[Yablo]
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9224
|
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment
[Fine,K]
|
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13664
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Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions
[Shapiro]
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18167
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We can get arithmetic directly from HP; Law V was used to get HP from the definition of number
[Maddy]
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19295
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Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers
[Hale]
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21648
|
Neo-Fregeans are dazzled by a technical result, and ignore practicalities
[Hofweber]
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