Aristotle claims that all necessary arguments are syllogisms, or reduce to them. One objection to this- which has bothered me for years- was the “horse’s head” objection, namely:
A horse is an animal.
therefore the head of a horse is the head of an animal
From a single premise, one draws an absolutely necessary inference from relations that belong to both terms in the premise.
I stumbled on the response to the objection yesterday in an introduction written by Richard Berquist to the Commentary on the Posterior Analytics. His claim, which I find convincing, is that though the horse’s head argument is a necessary inference, it’s not a proof or even an argument, for it provides no evidence or reason for the conclusion. If someone were in doubt about whether the head of a horse were the head of an animal, then to tell them that a horse was an animal would neither convince them of anything, nor provide any evidence. This becomes more clear if we appeal to a disputed case: someone who is in doubt about whether the stem cells of a blastocyst are the stem cells of a person, for example, receives no evidence or even argument from one who says “every blastocyst is a person”.