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On What There Must Be: Existence in Logic and Some Related Riddles

It is part of an old folklore that logic should not have existential theorems or existential validities. One should not prove in pure logic the existence of anything whatsoever; nothing could be proved by means of logic alone to necessarily exist. Whatever exists might not exist. This standpoint has been expressed by several philosophers from different traditions, such as Hume, Kant, Orenstein and Quine.1 We now set the stage by examining some issues. Our main question is: “Do we actually have existential theorems in logic?” Two possible attitudes towards this question are as follows.