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
| Sodium is a metal | (1) |
| Metals conduct electricity, | (2) |
we may conclude that
Sodium conducts electricity. (3)
Taking A, B, C to represent the three terms respectively, the premises are of the forms
A = AB (1)
B = BC. (2)
Now for B in (1) we can substitute its expression as given in (2), obtaining
A = ABC, (3)
or, in words, from