Chapter III.
Of The Functions And Logical Value Of The Syllogism.
§ 1. We have shown what is the real nature of the truths with which the
Syllogism is conversant, in contradistinction to the more superficial
manner in which their import is conceived in the common theory; and what
are the fundamental axioms on which its probative force or conclusiveness
depends. We have now to inquire, whether the syllogistic process, that of
reasoning from generals to particulars, is, or is not, a process of
inference; a progress from the known to the unknown: a means of coming to
a knowledge of something which we did not know before.
Logicians have been remarkably unanimous in their mode of answering this question. It is universally allowed that a syllogism is vicious if there be any thing more in the conclusion than was assumed in the premises. But this is, in fact, to say, that nothing ever was, or can be, proved by syllogism, which was not known, or assumed to be known, before. Is ratiocination, then, not a process of inference? And is the syllogism, to which the word reasoning has so often been represented to be exclusively appropriate, not really entitled to be called reasoning at all? This seems an inevitable consequence of the doctrine, admitted by all writers on the subject, that a syllogism can prove no more than is involved in the premises. Yet the acknowledgment so explicitly made, has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths, whether of science or of daily life, which we believe; while those who have avoided this inconsistency, and followed out the general theorem respecting the logical value of the syllogism to its legitimate corollary, have been led to impute uselessness and frivolity to the syllogistic theory itself, on the ground of the petitio principii which they allege to be inherent in every syllogism. As I believe both these opinions to be fundamentally erroneous, I must request the attention of the reader to certain considerations, without which any just appreciation of the true character of the syllogism, and the functions it performs in philosophy, appears to me impossible; but which seem to have been either overlooked, or insufficiently adverted to, both by the defenders of the syllogistic theory and by its assailants.
§ 2. It must be granted that in every syllogism, considered as an
