A counterfactual, as generally understood, is a subjunctive mood sentence where the condition is one which contradicts the actual state of affairs. For example, the subjunctive statement 'If I win the lottery, I will visit America' is not counterfactual, because I may yet win the lottery. But the statement 'If I had won the lottery, I would have been at the New York New Year Party' is, since I didn't win, and consequently wasn't there. Douglas Hofstadter writes very entertainingly about counterfactuals in Gödel, Escher, Bach: An Eternal Golden Braid (in Chapter 19, and the preceding dialogue, 'Contrafactus'), where he speculates about the abiltiies of Artificial Intelligences to analyse or come up with such statements.
At The Bristol International Noder Meet, arieh and I discussed a related topic of relevance to e2: factual nodes that are in fact not factual. Examples include attempts to prove that 1=2 (which it doesn't), or that The Vatican is a front for the International Jewish Conspiracy (because there isn't one), that Jesus was married (which he may have been, but it isn't demonstrable), and so on. We dubbed these write-ups 'counterfactuals', as they are factual in appearance, but would only be factuals in practice if their false premises were true.
And I leave you with news reported in The Skeptic this week that Jesus's resurrection can be explained in terms of an overdose of epilepsy medication. Film at 11.