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Single Idea 10548

[filed under theme 7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment ]

Full Idea

The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them.

Gist of Idea

The context principle for names rules out a special philosophical sense for 'existence'

Source

Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)

Book Ref

Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.497

A Reaction

He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims.

The 23 ideas from 'Frege Philosophy of Language (2nd ed)'

10320 If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale]
19168 Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson]
10549 Since abstract objects cannot be picked out, we must rely on identity statements [Dummett]
10516 A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale]
10547 Abstract objects can never be confronted, and need verbal phrases for reference [Dummett]
10531 There is a modern philosophical notion of 'object', first introduced by Frege [Dummett]
17621 What matters in mathematics is its objectivity, not the existence of the objects [Dummett]
10537 The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
10542 To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]
10554 Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett]
10540 We can't say that light is concrete but radio waves abstract [Dummett]
10552 Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett]
10515 Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale]
10544 The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett]
10546 We don't need a sharp concrete/abstract distinction [Dummett]
10548 The context principle for names rules out a special philosophical sense for 'existence' [Dummett]
10281 The objects we recognise the world as containing depends on the structure of our language [Dummett]
10532 We can understand universals by studying predication [Dummett]
10534 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett]
10545 Abstract objects may not cause changes, but they can be the subject of change [Dummett]
10541 Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett]
10555 If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett]
10543 Abstract objects must have names that fall within the range of some functional expression [Dummett]