A synthetic statement can be verified only by checking the facts. If I say, “My neighbor weighs three hundred pounds and enjoys reading books by Richard Dawkins,” you cannot tell from the statement itself whether it is true. You have to visit my neighbor’s house and ask him. Hume argued that analytic statements are true a priori, i.e., by definition. Synthetic statements, on the other hand, are true a posteriori, i.e., by looking at the evidence. For Hume, the physical sciences provide the standard model of synthetic truths. Through the scientific method—hypothesis, experimentation, verification, and criticism— we can discover synthetic truths about the world.
On this basis Hume delivered his famous dismissal of metaphysics, which he did not consider any kind of truth at all. Consider the central religious claims that “there is life after death” or “God made the universe:’ Hume’s point is that these statements are neither true by definition, nor can they be verified by checking the facts. Consequently, he argued, these statements are not even untrue—they are meaningless. Hume wrote, “If we take in our hand any volume—of divinity or school metaphysics, for instance—let us ask, does it contain any abstract reasoning concerning quality or number? No. Does it contain any experimental reasoning concerning matters of fact or experience? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion.”
This is sometimes known as Hume’s principle of empirical verifiability. It allows only two kinds of truths: those that are true by definition and those that are true by empirical confirmation. Right away, however, we see a problem. Let us apply Hume’s criteria to Hume’s own doctrine: Is the principle of verifiability true by definition? No. Well, is there a way to confirm it empirically? Again, no. Consequently, taking Hume’s advice, we should commit his principle to the flames because it is not merely false, it is also incoherent.