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 Reference
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.