Full Idea
One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed.
Gist of Idea
'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed
Source
George Boolos (On Second-Order Logic [1975], p.46)
Book Reference
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.519
A Reaction
This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain.