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Logically what is the difference between conceivable and probable or possible?

Sometimes people use the word “possible” to mean something like, “does not entail a contradiction.” This sense of “possible” is narrower than “consistent with the laws of nature.” I gather this is what Thomas Pogge was alluding to when he said that there is a sense of “possible” that coincides with “conceivable.” Some have raised worries about whether conceivability implies possibility in this more narrow sense. Here’s an interesting example from Barry Stroud’s book on Hume (p. 50). Goldbach’s Conjecture states that every even number is the sum of two primes. At this point (as far as I know) no one has offered a proof of Goldbach’s Conjecture, and no one has disproved it either. If Goldbach’s Conjecture is false, it presumably says something that is not possible (in the narrow sense). But one might argue that I can nevertheless conceive of a state of affairs in which someone proves that Goldbach’s Conjecture is true. In that case, it seems, I would have conceived of something impossible. ...