It is the fourth premise of this argument that is crucial. This fourth premise reflects Hume's identification of possibility with conceivability. To say that God's existence is necessary is to say that his non-existence is impossible. In making this identification of the metaphysical distinction between possibility and impossibility with the introspectible psychological distinction between conceivability and inconceivability, Hume is taking to its logical conclusion a turn away from the real natures of things and toward our ideas of things that began with the philosophy of Nominalism, created in the 14th century by William of Ockham. This substitution of psychology for metaphysics also links Hume to the analytic philosophy of the early 20th century, especially the school of logical positivism or logical empiricism.
Nominalists hold that there is no such thing as natures or essences.
Since things have no real natures, there is nothing in things that can make certain conditions possible or impossible. Instead, possibility and impossibility are simply by-products of our use of language and concepts. An impossible condition is one that would correspond to an inconsistent or incoherent mental picture. In contrast, realists like Plato, Aristotle or Aquinas, hold that there are real natures in things. Our concepts are linked causally to these real natures.