conceivability capability of being conceived or imagined. Thus, golden mountains are conceivable; round squares, inconceivable. As Descartes pointed out, the sort of imaginability required is not the ability to form mental images. Chiliagons, Cartesian minds, and God are all conceivable, though none of these can be pictured ‘in the mind’s eye.’ Historical references include Anselm’s definition of God as ‘a being than which none greater can be conceived’ and Descartes’s argument for dualism from the conceivability of disembodied existence. Several of Hume’s arguments rest upon the maxim that whatever is conceivable is possible. He argued, e.g., that an event can occur without a cause, since this is conceivable, and his critique of induction relies on the inference from the conceivability of a change in the course of nature to its possibility. In response, Reid maintained that to conceive is merely to understand the meaning of a proposition. Reid argued that impossibilities are conceivable, since we must be able to understand falsehoods. Many simply equate conceivability with possibility, so that to say something is conceivable (or inconceivable) just is to say that it is possible (or impossible). Such usage is controversial, since conceivability is broadly an epistemological notion concerning what can be thought, whereas possibility is a metaphysical notion concerning how things can be.
The same controversy can arise regarding the compossible, or co-possible, where two states of affairs are compossible provided it is possible that they both obtain, and two propositions are compossible provided their conjunction is possible. Alternatively, two things are compossible if and only if there is a possible world containing both. Leibniz held that two things are compossible provided they can be ascribed to the same possible world without contradiction. ‘There are many possible universes, each collection of compossibles making one of them.’ Others have argued that non-contradiction is sufficient for neither possibility nor compossibility. The claim that something is inconceivable is usually meant to suggest more than merely an inability to conceive. It is to say that trying to conceive results in a phenomenally distinctive mental repugnance, e.g. when one attempts to conceive of an object that is red and green all over at once. On this usage the inconceivable might be equated with what one can ‘just see’ to be impossible. There are two related usages of ‘conceivable’: (1) not inconceivable in the sense just described; and (2) such that one can ‘just see’ that the thing in question is possible. Goldbach’s conjecture would seem a clear example of something conceivable in the first sense, but not the second. See also LEIBNIZ , NECESSITY, POSSIBLE WORLD. P.Ti.