Chapter XXIX: Concerning many Demonstrations of the same thingEdit
- Several demonstrations of the same conclusion may be given, and their middle terms may be taken from different series as well as from the same series. Such middle terms must however be reciprocally predicable.
It is possible to give several demonstrations of the same things, not only by taking a middle term from the same series of terms, and that too a middle term which is not logically proximate (as for instance by taking as middles between A and B not only the proximate term C, but also D and E) but by taking one from a different series of terms. As an instance of this last let A represent Changing, B Rejoicing, D Moving, and again H represent Being calm. Now D may be correctly predicated of B, and also A of D, for one who rejoices experiences movement, and that which moves undergoes a change. Again A may also be predicated of H, and H of B, for everyone who rejoices feels a calm, and one who feels a calm undergoes a change. Hence the syllogism is established by different middle terms not derived from the same series. It is not however allowable that neither of these middle terms should be predicable of the other, for both are necessarily predicable of a common third term. The other figures of the syllogism may also be examined in order to see in how many ways a syllogism with the same conclusion may be constructed.