Full Idea
To say that an abstract object cannot be the cause of change seems plausible enough, but the thesis that it cannot be the subject of change is problematic. The shape of an object can change, or the number of sheep on a hill.
Gist of Idea
Abstract objects may not cause changes, but they can be the subject of change
Source
Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
Book Reference
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.491
A Reaction
This seems a pretty crucial difficulty for the standard notion of abstracta as non-causal. I would say that it is an acid which could eat away the whole edifice if you thought about it for long enough. He shifts shape-change to the physical object.