Full Idea
The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted.
Gist of Idea
Infinite natural numbers is as obvious as infinite sentences in English
Source
George Boolos (Must We Believe in Set Theory? [1997], p.129)
Book Reference
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.129
A Reaction
If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless.