The Port-Royal logicians devised a nifty aporetic barbara syllogism:
Who calls you an animal speaks the truth
Who calls you a jackass calls you an animal.
So who calls you a jackass speaks the truth.
Once you get the hang of it, you can prove anything is anything else it shares a genus with:
Whoever says black is a color speaks the truth
Whoever says black is white says it’s a color.
Whoever says black is white speaks the truth.
You can even prove anything is anything. Whoever says being is non-being says you have a word for it, right? Barbara has exploded.
The argument shows that any conclusion is only true so far as its terms are joined per se in a middle term and no further. There are at least two important corollaries to this:
1a.) Since the presence of a middle term allows for the truth of the conclusion only so far as some term joins the truth together per se, where no middle term is given (like in any hypothetical syllogism or even in the truth tables of modern logic, for example) the conclusions drawn are not even formally true.
1b.) Following this, there is something dissatisfying about the validity-soundness definition. Something can follow necessarily from premises without being formally true. If we insist on some account of validity, the best we can do is base it, as Aristotle does, on “what follows necessarily” (see chapter 1).
2.) The middle term of truths now called scientific is the result of a contrived environment (i.e. an experiment). I suppose this is better than nothing, but formally, it’s not an account of nature at all, but of nature-cum-art, with the two fused together in such a way as to cause an in-principle impossibility of determining how much each element is in play.