[Footnote 1:] Ὅταν οὒν ὅροι τρεῖς αὔτως ἔχωσι πρὸς ἀλλήλους ὥστε τὸν ἔσχατον ἐν ὅλῳ εἶναι τῷ μέσῳ, καὶ τὸν μέσον ἐν ὅλῳ τῷ κρώτῳ ἢ εἶναι ἢ μὴ εἶναι, ἀνάγκη τῶν ἀκρων εἶναι συλλογισμὸν τέλειον (Anal. Prior., i. 4.)
Chapter III.
THE DEMONSTRATION OF THE SYLLOGISTIC MOODS. —THE CANONS OF THE SYLLOGISM.
How do we know that the nineteen moods are the only possible forms of valid syllogism?
Aristotle treated this as being self-evident upon trial and simple inspection of all possible forms in each of his three Figures.
Granted the parity between predication and position in or out of a limited enclosure (term, ὄρος), it is a matter of the simplest possible reasoning. You have three such terms or enclosures, S, P and M; and you are given the relative positions of two of them to the third as a clue to their relative positions to one another. Is S in or out of P, and is it wholly in or wholly out or partly in or partly out? You know how each of them lies toward the third: when can you tell from this how S lies towards P?
We have seen that when M is wholly in or out of P, and S wholly or partly in M, S is wholly or partly in or out of P.
Try any other given positions in the First Figure, and you find that you cannot tell from them how S lies relatively to P. Unless the Major Premiss is Universal, that is, unless M lies wholly in or out of P, you can draw no conclusion, whatever the Minor Premiss may give. Given, e.g., All S is in M, it may be that All S is in P, or that No S is in P, or that Some S is in P, or that Some S is not in P.
