G. H. Hardy, "A Mathematician's Apology":

Some hold that it is 'mental' and that in some sense we construct it, others that it is outside and independent of us. A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.

In a first clause there is 'could', in a second 'would have'. Kind of a mixing, it should be either 'could have' in a first, or just 'would' in a second.

The only way I see it is that in would [have solved] the whole have solved stands for the verb (with a taste of the perfect aspect). But I have never read about it. It would mean that have belongs to either would or the verb: would have [solved], would [have solved].


This is not so much a matter of grammar as it is a matter of the hypothetical reality the grammar reflects.

In Hardy's view, a “convincing account of mathematical reality” cannot be given unless one has already solved certain difficult metaphysical problems, and an account of both mathematical and physical reality cannot be given unless one has solved all the difficult metaphysical problems.

Consequently, if I could provide you such an account, it would be convincing evidence that I have solved those problems.

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  • 1. So both of them are mixed conditionals here, right? 2. But I have another interpretation of the original sentence (but in a different context): If he did be able to include physical reality in his account, then it was certain that he had solved them all.(past, real) Right? @StoneyB – Kinzle B Jun 17 '14 at 10:39
  • @ZhanlongZheng 1.I don't use the "nth-conditional" terminology, so you'll have to address that to somebody else. 2. Yes - except we don't use DO with BE: you have to say "if he was able". – StoneyB on hiatus Jun 17 '14 at 11:08
  • Come to think of it, is the bold have solved a sham perfect or a true perfect in the quoted example? – Kinzle B Jun 10 '16 at 16:26
  • 1
    @KinzleB It's a true perfect, by itself in a clause subordinate to the clause in which the would appears. – StoneyB on hiatus Jun 10 '16 at 16:30

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