  For many of our sentences, this strong statement of holism holds only in principle. In practice, we may have a good idea what experiences would lead us to change our minds about a given sentence, and what further changes in theory would follow. Elementary arithmetic (to take that as an example) is different because it is involved in almost every part of systematic knowledge. (In Quine’s well-known metaphor, it stands near the centre of the ‘web of belief’.) Abandoning it would mean abandoning our whole system of knowledge, and replacing it with an alternative which we have not even begun to envisage. Nothing in principle rules out the possibility that the course of experience will be such that our present system of knowledge becomes wholly useless, and that in constructing a new one we find that arithmetic is of no use. But this is a purely abstract possibility, certainly not something we can imagine in any detail. So the idea that we might reject arithmetic is likewise unimaginable; hence the truths of arithmetic appear to be necessary.