Editor’s / Author’s Introduction1
- In 'The Julius Caesar Objection: More Problematic than Ever' Fraser MacBride further explores issues surrounding the identity and individuation2 of numbers from a Fregean point of view.
- According to Frege it is a requirement upon the introduction of a range of objects into discourse that identity criteria are supplied for them — criteria that determine whether it is appropriate to label and then relabel an object on a different occasion as the same again.
- In order to introduce cardinal numbers into discourse Frege therefore proposed the following principle — Hume's Principle that specifies necessary and sufficient conditions for the identity of cardinal numbers: the number of Fs = the number of G's iff there is a 1-1 correspondence between the Fs and the Gs. Famously, however, Frege became dissatisfied with Hume's Principle as a criterion of identity, maintaining that it failed even to settle whether (e.g.) the number two was identical or distinct to an object of an apparently quite different sort (e.g.) the man Caesar.
- MacBride subjects this difficulty — the so-called 'Julius Caesar Objection' — to critical examination, arguing that beneath the superficial simplicity of the problem that bedevilled Frege there lies a welter of distinct difficulties.
- These may be arranged along three different dimensions.
- (A) Epistemology: does the identity criterion supplied for introducing numbers into discourse provide warrant for the familiar piece of common-sense knowledge that numbers are distinct from persons?
- (B) Metaphysics: does the identity criterion given determine whether the things that are numbers might also be such objects as Caesar?
- (C) Meaning: does the identity criterion supplied bestow upon the expressions that purport to denote numbers the distinctive significance of singular terms?
- It is because, MacBride argues, these different problems and the interrelations between them often fail to be disentangled that (in part) the different (purported) solutions to the Julius Caesar — neo-Fregean and supervaluationist solutions — fail.
- MacBride concludes by suggesting that Frege may have been too strict in imposing the requirement that objects introduced into discourse have identity criteria, noting that not even sets have identity criteria in the strict sense Frege required.
- What is the ‘Caesar Problem’?
- 2.1 Frege
- 2.2 Dimensions of the Caesar Problem
- 2.3 The Epistemological Caesar Problem
- 2.4 The Metaphysical Caesar Problem
- 2.5 The Meaning-Theoretical Caesar Problem
- Two Solutions
- 3.1 The Supervaluationist Solution
- 3.2 The Neo-Fregean Solution
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