Note 290 — Chapter XX · (continued 3)

Dugald Stewart (Elements of Philosophy, &c. vol. ii., ch. ii., sect. 2) has treated this theory of Hobbes on reasoning, as well as that of Condillac, which seems much the same, with great scorn, as “too puerile to admit of (i.e. require) refutation.” I do not myself think the language of Hobbes either here, or as quoted by Stewart from his Latin treatise on Logic, so perspicuous as usual. But I cannot help being of opinion that he is substantially right. For surely, when we assert that A is B, we assert that all things which fall under the class B, taken collectively, comprehend A, or that B = A + X: B being here put, it is to be observed, not for the res prædicata itself, but for the concrete, de quibus prædicandum est. I mention this, because this elliptical use of the word predicate seems to have occasioned some confusion in writers on logic. The predicate strictly taken, being an attribute or quality, cannot be said to include or contain the subject. But to return, when we say B = A + X, or B - X = A, since we do not compare, in such a proposition, as is here supposed, A with X, we only mean that A = A, or that a certain part of B is the same as itself. Again, in a particular affirmative, Some A is B, we assert that part of A, or A - Y is contained in B, or that B may be expressed by [A - Y] + X. So also when we say, Some A is not B, we equally divide the class or genus B into A - Y and X, or assert that B = [A - Y] + X; but, in this case, the subject is no longer A - Y, but the remainder, or other part of A, namely, Y; and this is not found in either term of the predicate. Finally, in the universal negative, No A (neither [A - Y] nor Y) is B, the [A - Y] of the predicate vanishes or has no value, and B becomes equal to X, which is incapable of measurement with A, and consequently with either A - Y or Y, which make up A. Now if we combine this with another proposition, in order to form a syllogism, and say that C is A, we find, as before, that A = C + Z; and substituting this value of A in the former proposition, it appears that B = C + Z + X. Then, in the conclusion, we have, C is B; that is C is a part of C + Z + X. And the same in the three other cases or moods of the figure. This seems to be, in plainer terms, what Hobbes means by addition or subtraction of parcels, and what Condillac means by rather a lax expression, that equations and propositions are at bottom the same, or, as he phrases it better, “l’evidence de raison consiste uniquement dans l’identité.” If we add to this, as he probably intended, non-identity, as a condition of all negative conclusions, it seems to be no more than is necessarily involved in the fundamental principle of syllogism, the dictum de omni et nullo; which may be thus reduced to its shortest terms; “Whatever can be divided into parts, includes all those parts, add nothing else.” This is not limited to mathematical quantity, but includes everything which admits of more or less. Hobbes has a good passage in his Logic on this; Non putandum est computationi, id est, ratiocinationi in numeris tantum locum esse, tanquam homo a cæteris animantibus, quod censuisse narratur Pythagoras, sola numerandi facultate distinctus esset; nam et magnitudo magnitudini, corpus corpori, motus motui, tempus tempori, gradus qualitatis gradui, actio actioni, conceptus conceptui, proportio proportioni, oratio orationi, nomen nomini, in quibus omne philosophiæ genus continetur, adjici adimique potest.