David Hume accepts the principle that conceivability entails possibility. For example, in the second section of the second part of the first book of A Treatise of Human Nature Hume states: “It is an established maxim in metaphysics, that whatever the mind clearly conceives, includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible. We can form the idea of a golden mountain, and from thence conclude that such a mountain may actually exist”. Hume also adopts a second principle involving the notion of conceivability. For, in the ninth part of his Dialogues Concerning Natural Religion he writes: “Whatever we conceive as existent, we can also conceive as non-existent” and “It [is] possible for us, at any time, to conceive the non-existence of what we formerly conceived to exist”.
Hume’s first principle, viz., whatever is conceivable is possible, seems prima facie plausible. If we can coherently conceptualize something, then, in the absense of defeaters, what is thus conceptualized is reasonably taken to be not impossible. But what does Hume's second principle amount to? Does he hold that everything that exists can be conceived of as not existing? If so, this principle is untenable. For, something that exists can only be conceived of as not existing if we are able to conceive of the very thing itself. After all, without having a proper conception of the thing in question, we cannot establish that we conceive of that thing as not existing. Moreover, without an adequate conceptualization of the thing in question we cannot even establish that we are conceiving of that thing as not existing. Hence, Hume’s second principle, in order to be tenable, should be interpreted as the maxim that everything that exists and is conceivable can be conceived of as not existing.
But then Hume’s two principles can be employed to infer that God must be inconceivable. For indeed, if God would be conceivable, then, according to Hume's second principle, the non-existence of God would be conceivable as well. And from this it would follow, according to Hume's first principle, that the non-existence of God would be possible, which contradicts God's essence if God is understood as a necessarily existing being.
Therefore, if God exists, Hume’s principles actually entail the tenet of negative theology, namely that God exists inconceivably, so that no human being will ever be able to grasp God’s nature. Now, this is a quite different conclusion from the conclusion Hume himself draws, namely that necessarily existing beings are impossible, so that God, understood as such a being, cannot exist. Indeed, Hume's conclusion only follows from both principles if we presume the first interpretation of his second principle, to wit, everything that exists can be conceived of as not existing. But, as explained above, this interpretation of Hume's second principle renders that principle untenable.