Since there is no official antonym of anything, it is reasonable to think of 'nothing.'
It certainly isn't 'everything,' since both anything and everything(in this case) both mean all things. As in “He who does not believe in God will believe in all things.”
“He who does not believe in God will believe in anything.”
“He who does not believe in God will believe in everything.”
or in logical reverse, one is left with something rather compromising:
He who does believe in God will believe in nothing.
What do you think? (of the grammar....)
The quote is attributed to him but he said in a number of ways. Check out this link: http://www.chesterton.org/ceases-to-worship/