[Footnote 1: [Greek: Hotan oun horoi treis autos echosi pros allelous oste ton eschaton en holo einai to meso, kai ton meson en holo to kroto e einai e me einai, ananke ton akron einai syllogismon teleion.] (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, [Greek: horos]), 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. [Illustration: Circles of M and P, overlapping, with 3 instances of a circle of S: 1. S in M, but not in P; 2. S in the overlap of M and P; 3. S in M, some S in P. ] Again, unless the Minor Premiss is affirmative, no matter what the Major Premiss may be, you can draw no conclusion. For if the Minor Premiss is negative, all that you know is that All S or Some S lies somewhere outside M; and however M may be situated relatively to P, that knowledge cannot help towards knowing how S lies relatively to P. All S may be P, or none of it, or part of it. Given all M is in P; the All S (or Some S) which we know to be outside of M may lie anywhere in P or out of it. [Illustration: Concentric circles of P and M, M in center, with 5 instances of circle of S: 1. S wholly outside P and M; 2. S partly overlapping both P and M, and partly outside both; 3. S overlapping P, but outside M; 4. S wholly within P, but wholly outside M; 5. S touching circle of P, but outside both circles. ] Similarly, in the Second Figure, trial and simple inspection of all possible conditions shows that there can be no conclusion unless the Major Premiss is universal, and one of the premisses negative.