Note 316 — Chapter I

If, for example, for our rule of distribution we select the rule relating to the distribution of the middle term, then the invalid syllogism,

All M is P,

No S is M,

therefore, No S is P,

does not directly involve a breach of either of our two independent rules. But if this syllogism is valid, then must also the following syllogism be valid:

All M is P (original major),

Some S is P (contradictory of original conclusion),

thereforeSome S is M (contradictory of original minor);

and here we have undistributed middle. Hence the rule relating to the distribution of the middle term establishes indirectly the invalidity of the syllogism in question. The principle involved is the same as that on which we shall find the process of indirect reduction to be based.

Take, again, the syllogism: PaM, SeM, ∴ SaP. This does not directly offend against the rules given above; but the reader will find that its validity involves the validity of another syllogism in which a direct transgression of these rules occurs.