Logic

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

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The common domain these three predicates range over is that of states of affairs consisting of objects that have certain specific properties or stand in certain specific relations.

Being conceivable is the easiest condition to meet. It excludes only states of affairs that we cannot think or imagine. We cannot imagine a stone that is green all over and also red all over, a stone that occupies the same space as a clump of metal, a bachelor who is married, a living horse that's not an animal, and so on.

While there is a narrow sense of "possible" that coincides with "conceivable," usually being possible is a more demanding condition. To be possible, a state of affairs must not merely be conceivable, but must be consistent with what we know about this world (e.g., the laws of nature). A puddle of water turning into a human being, an animal living forever, a daytrip to another galaxy -- these are conceivable, but not possible.

Being probable is more demanding still, requiring not merely that states of affairs are possible but that they are more likely than their contrasting states of affairs (in which the relevant properties or relations do not obtain). A patient dying from an appendectomy, an adult being ignorant of elementary arithmetic -- these states of affairs are possible but improbable: less likely than their opposites (assuming we look at people now alive in the US or Europe).

Thomas has given some examples of situations that are conceivable but not possible (in that they conflict with, say, laws of nature): for instance, in some sense one can imagine a puddle's turning into a human being, though such a transformation flies in the face of what we believe is physically possible.

But there are also circumstances which are physically possible of which we can form no picture. For instance, it's physically possible for there to be a chunk of quartz with a thousand facets, though I cannot imagine such a thing.

The question presupposes that we use the terms "conceivable" and "possible" in just one way, which is doubtful. For a little more, see Question 71.

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.

Here’s another famous example from Arnauld. Arnauld is responding to Descartes’ claim in the 6th Meditation that since we can conceive of the mind existing apart from the body, it is possible that the mind can exist without the body. Arnauld objects that someone uneducated in geometry might be able to conceive of a right triangle that does not obey the Pythagorean Theorem. However this doesn’t mean that it’s possible for there to be a right triangle that fails to obey the Pythagorean Theorem.

Part of the problem is that it's not altogether clear what it is for something to be "conceivable."

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