"I shall begin with observing, that there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable."
Hume's argument against attempts to demonstrate the existence of God through reason from Dialogues Concerning Natural Religion.
The only thing one cannot conceive of as not existing and be in contradiction is existence itself, but everything else can be conceived not to exist without contradiction if there is no matter of fact to its existence.
Something either exists or it doesn't. Any notion we have of something is derived from sense experience or is an idea culled from sense experience, and so to infer the existence of something from our ideas will only give us another idea of something which can either be detected in the sensual world or it can't. Just because one conceives of a being doesn't mean it exists, just that an idea exists which is a synthesis of ideas from sense experience.
When it comes to existence, one either experiences something or not, but anything more cannot be inferred with necessity. That something exists rather than nothing at all is the only necessity in the universe. The universe exists and it couldn't be otherwise, but the existence of anything else is contingent on facts.
Notice Hume says distinctly conceivable, which implies some self-fabrication or some particular contingent thing.
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