Validity is not the same thing as truth
A syllogism is valid if the conclusion follows necessarily from the premises — if, assuming the premises were true, the conclusion could not be false. It says nothing whatsoever about whether the premises are true. This distinction, elementary as it sounds, has caused a remarkable amount of confusion across the centuries, particularly in the hands of people who are very confident about things.
Every syllogism produced by this tool is formally valid. The argument structure is impeccable. Aristotle would have no objection. If all things found beneath a hedge were in fact profoundly melancholy, and if all bishops were in fact things found beneath a hedge, then all bishops would indeed be profoundly melancholy — you couldn’t wriggle out of it. The premises, of course, are another matter entirely. Whether they are true is left as an exercise for the empirically inclined.
The six forms used here are drawn from the classical tradition of syllogistic logic, which Aristotle developed in the Prior Analytics around 350 BC and which dominated Western logic for over two thousand years. Each form is identified by a Latin name and a three-letter mood (where A = “All S are P”, E = “No S are P”, I = “Some S are P”, O = “Some S are not P”) plus its figure (which tells you where the middle term appears).
| Name | Mood–Fig. | Structure |
|---|---|---|
| Barbara | AAA–1 | All M are P · All S are M · ∴ All S are P |
| Celarent | EAE–1 | No M are P · All S are M · ∴ No S are P |
| Darii | AII–1 | All M are P · Some S are M · ∴ Some S are P |
| Ferio | EIO–1 | No M are P · Some S are M · ∴ Some S are not P |
| Camestres | AEE–2 | All P are M · No S are M · ∴ No S are P |
| Baroco | AOO–2 | All P are M · Some S are not M · ∴ Some S are not P |
The medieval scholastics gave these forms their names as a mnemonic device: the vowels encode the proposition types, in order. Barbara contains three A propositions; Celarent has E, A, E; and so on. The consonants were used as a guide to how to reduce each form to a first-figure syllogism, but we need not go into that here. The names have a pleasant ring to them. Baroco in particular sounds like somewhere you’d go for a long lunch.
There are 256 possible combinations of four proposition types across two premises and a conclusion in four figures, but only 24 are valid, of which 15 are traditionally recognised as the core forms. These six were selected because they produce the most natural-sounding English sentences, which is to say the most entertainingly absurd conclusions.