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Single Idea 8787

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem ]

Full Idea

The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?)

Clarification

This refers to Frege's Grundlagen §66

Gist of Idea

The Julius Caesar problem asks for a criterion for the concept of a 'number'

Source

B Hale / C Wright (Logicism in the 21st Century [2007], 3)

Book Ref

'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.179

A Reaction

One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right.

The 23 ideas from B Hale / C Wright

10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
10626 Objects just are what singular terms refer to [Hale/Wright]
10630 Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
10631 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
10627 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
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]
12223 It is a fallacy to explain the obscure with the even more obscure [Hale/Wright]
12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
12226 The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright]
12227 Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright]
12228 Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright]
12231 Reference needs truth as well as sense [Hale/Wright]
12229 Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright]
18443 A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright]
12230 Singular terms refer if they make certain atomic statements true [Hale/Wright]