Hume's law or Hume's guillotine is the thesis that, if a reasoner only has access to non-moral and non-evaluative factual premises, the reasoner cannot logically infer the truth of moral statements. (Wikipedia)
I do not claim that I can infer the truth of ought statements from is statements but I claim that it would be possible to do it if a suitable set of is statements turned out to be true, hence that Hume’s law is not true in the sense in which it is usually imagined to be, as a conclusion depending only on logical argument not on factual claims.
My argument starts with intuitionism, the philosophical position that holds that just as humans have senses such as sight and hearing that imperfectly sense physical facts so we have a moral sense that imperfectly senses moral facts. For a book length exposition see Ethical Intuitionism by Michael Huemer, for a short sketch, including my response to obvious counterarguments, Chapter 61 of The Machinery of Freedom.
The argument for intuitionism, beyond the fact that it describes how most people feel about morality — that certain acts really are wicked — is consistency. We believe that our physical senses are not lying to us about physical reality because what they report usually passes all the consistency tests we can subject them to, consistency both between information reported to us by sight, hearing, smell and touch and between the observations of physical reality made by different people. It is possible that it is all an illusion — what I know about what other people perceive ultimately reaches me through my senses, which could all be lying to me — but it is the best evidence we have available. If moral perceptions are similarly consistent, if almost everyone, given a sufficiently well described situation and action, will have about the same moral response, that would be evidence that there is a moral reality out there which we are perceiving.
Whether that situation exists, whether almost everyone has about the same moral perceptions, is a fact of reality, a non-moral fact. Suppose it does. One might still reject the conclusion on the basis of an alternative explanation. Perhaps there are no moral facts, just moral beliefs, consistent because they were produced by biological evolution hard wiring into us beliefs that cause us to behave in ways that lead to reproductive success, or societal evolution producing societies that indoctrinate their population into the set of moral beliefs that that make a society more likely to survive.
This alternative explanation, however, is subject to factual tests. One could imagine evidence showing that some widely held moral belief did not contribute to reproductive success or societal survival. I do not claim to have any such evidence but it is at least logically possible. If it existed, and if we observed consistency across humans of moral judgement, that would be evidence for a moral reality that humans could perceive; their common perceptions would be evidence of moral facts just as ordinary perception is of physical facts. Hence it is logically possible to deduce ought from is.
It may be that moral nihilism is correct, that intuitionism and other forms of moral realism are wrong, that the necessary facts are not true, but they could be. Hume’s law is not a claim about what facts exist but about the logical impossibility of deducing moral facts from physical facts and I believe I have shown that it is false.
I have shown the possibility of evidence, not of proof, but that is true of all our factual beliefs. I cannot prove that the sun will rise tomorrow or that the Earth is round, I can only offer very strong evidence for those claims. I believe that the is-ought claim as commonly understood, certainly as I understood it, applies to evidence for moral facts as well as to proof of moral facts.