Is there something such that its existence is necessary, through pure logic alone? I know that Anselm famously suggested God as such a being, but his argument is widely thought to be fallacious. But perhaps there is something else, like maybe the Universe, that exists by pure logic?
Is there something such that its existence is necessary, through pure logic alone?
Things exist or they don't and there would be no difference between something whose existence is necessary and something whose existence is not. The notion of necessity is redundant to existence.
The only cogent notion of necessity is logical necessity: A conclusion is necessarily true if the premises are true and the argument is logically valid.
The conclusion is not necessary in itself. It is also not the fact described or referred to by the conclusion which is necessary. It is only the truth of the conclusion given the truth of the premises** and given the validity of the inference from premises to conclusion.
Thus, the truth of the conclusion, though said to be necessary, is not necessary in itself. It is dependent on the validity of the inference and on the truth of the premises.
Even logical necessity is not achieved by logic alone. You always need the premises to be true for the conclusion to be necessarily true, and the premises are true as a matter of fact or as a matter of logical consequence of some other premises themselves true as a matter of fact. Logic alone is never sufficient.
Nothing that we could tell is necessary in itself.