Full Idea
The notion of 'object', as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege.
Gist of Idea
There is a modern philosophical notion of 'object', first introduced by Frege
Source
Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
Book Reference
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.471
A Reaction
If we say 'objects exist', I think it is crucial that if we are going to introduce 'object' as a term of art, then 'exist' had better stick to normal usage. If that drifts into a term of art as well (incorporating 'subsist', or some such) we have no hope!