Worse Relation. In logic the degrees of relation between one term and
another are called worse in proportion as they recede from that of pure
identity or co-inclusion. Thus, "all men" and "mortal" stand to each
other in a worse relation than "all men" and "all rational upon earth"; or
"some men" and "wise" in a relation still worse than the
foregoing; and when we come to exclusion or negation, we come to the
worst relation of all.
This gradation gives rise to Sir W. Hamilton's canon for figured
syllogisms. "What worse relation of subject to predicate subsists
between either of two terms, and a common third term, with which one at
least is positively related; that relation subsists between the two
This whole subject belongs so exclusively to formal logic, and "worse
relation" to its technicalities as to be out of place in the present work, but
I am led to introduce it here in order to correct an error into which I
fell in my Outline of Logic. I there, under some obfuscation of memory,
represented Sir W. Hamilton as denying that the negative is a worse
relation than the positive.(1) He does no such thing, and a moment's
thought will show that, had he done so, he would have rendered his canon
inapplicable to a large class of syllogisms.
(1) Outline of Logic, 2nd ed. p. 99.
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