Surely it is more interesting to argue about what the truth is, than about what some particular thinker, however great, did or did not think. - David Deutsch

Any theory about improvement raises the question: how is the knowledge of how to make that improvement created? Was it already present at the outset? The theory that it was is creationism. Did it ‘just happen’? The theory that it did is spontaneous generation.

That progress is both possible and desirable is perhaps the quintessential idea of the Enlightenment. It motivates all traditions of criticism, as well as the principle of seeking good explanations. But it can be interpreted in two almost opposite ways, both of which, confusingly, are known as ‘perfectibility’. One is that humans, or human societies, are capable of attaining a state of supposed perfection – such as the Buddhist or Hindu ‘nirvana’, or various political utopias. The other is that every attainable state can be indefinitely improved. Fallibilism rules out that first position in favour of the second.

Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.