GRAMMAR IN RELATION TO LOGIC.
Dr. Latham (Outlines of Logic, p. 21., 1847, and English Language, p. 510., 2nd edition) defines the conjunction to be a part of speech that connects propositions, not words. His doctrine is so palpably and demonstrably false, that I am somewhat at a loss to understand how a man of his penetration can be so far deceived by a crotchet as to be blind to the host of examples which point to the direct converse of his doctrine. Let the learned Doctor try to resolve the sentence, All men are either two-legged, one-legged, or no-legged, into three constituent propositions. It cannot be done; either and or are here conjunctions which connect words and not propositions. In the example, John and James carry a basket, it is of course quite plain that the logic of the matter is that John carries one portion of the basket, and James carries the rest. But to identify these two propositions with the first mentioned, is to confound grammar with logic. The former deals with the method of expression, the latter with the method of stating (in thought) and syllogising. To take another example, Charles and Thomas stole all the apples. The fact probably was, that Charles' pockets contained some of the apples, and Thomas' pockets contained all the rest. But the business of grammar in the above sentence is to regulate the form of the expression, not to reason upon the matter expressed. A little thought will soon convince any person accustomed to these subjects that conjunctions always connect words, not propositions. The only work in which I leave seen Dr. Latham's fundamental error exposed, is in Boole's Mathematical Analysis of Logic; the learned author, though he seems unsettled on many matters of logic and metaphysics, has clearly made up his mind on the point now under discussion. He says:
"The proposition, every animal is either rational or irrational, cannot be resolved into, Either every animal is rational, or every animal is irrational. The former belong to pure categoricals, to latter to hypotheticals [Query disjunctives]. In singular propositions such conversions would seem to be allowable. This animal is either rational or irrational, is equivalent to, Either this animal is rational, or it is irrational. This peculiarity of singular propositions would almost justify our ranking them, though truly universals, in a separate class, as Ramus and his followers did."—P. 59.
This certainly seems unanswerable.
If Dr. Latham is a reader of "N. & Q.," I should be glad if he would give his reasons for adhering to his original doctrine in the face of such facts as those I have instanced.
C. Mansfield Ingleby.
Birmingham.