CHAPTER IV. DEDUCTIVE REASONING.

Hence

It is almost needless to point out that the form of these arguments does not suffer any real modification if some of the terms happen to be negative; indeed in the last example “incapable of decomposition” may be treated as a negative term. Taking

the propositions are of the forms

whence, by substitution,

Inference of a Partial from Two Partial Identities.

However common be the cases of inference already noticed, there is a form occurring almost more frequently, and which deserves much attention, because it occupied a prominent place in the ancient syllogistic system. That system strangely overlooked all the kinds of argument we have as yet considered, and selected, as the type of all reasoning, one which employs two partial identities as premises. Thus from the propositions

we may conclude that

Taking A, B, C to represent the three terms respectively, the premises are of the forms

Now for B in (1) we can substitute its expression as given in (2), obtaining

or, in words, from

we infer

which, in the elliptical language of common life, becomes

The above is a syllogism in the mood called Barbara‍⁶ in the truly barbarous language of ancient logicians; and the first figure of the syllogism contained Barbara and three other moods which were esteemed distinct forms of argument. But it is worthy of notice that, without any real change in our form of inference, we readily include these three other moods under Barbara. The negative mood Celarent will be represented by the example