Professor Boole's communication on the above question reminds me of some remarks of mine, published in an article on Sir John Stoddart's Philosophy of Language, in the North British Review for November, 1850. In reference to the opinion maintained by Sir John Stoddart and Dr. Latham, that the conjunction always connects sentences, the preposition words, it is observed:
"It does not apply to cases where the conjunction unites portions of the predicate, instead of the subject, of a proposition. If I assert that a gentleman of my acquaintance drinks brandy and water, he might not relish the imputation of imbibing separate potations of the neat spirit and the pure element. Stradling versus Stiles is a case in point: 'Out of the kind love and respect I bear to my much honoured and good friend, Mr. Matthew Stradling, Gent., I do bequeath unto the said Matthew Stradling, Gent., all my black and white horses.' The testator had six black horses, six white horses, and six pied horses. The whole point at issue turns upon the question whether the copulative and joins sentences or words. If the former, the plaintiff is entitled to the black horses, and also to the white, but not to the pied. If the latter he has a right to the pied horses but must forego his claim to the rest. And if the latter interpretation be adopted, must we say that and is a preposition, not a conjunction, or must we modify the definitions of these two parts of speech?"
The following definitions are finally proposed in place of the ordinary ones:
"A preposition is a part of speech annexed to a noun or verb in a proposition, and serving to connect it with a noun or pronoun by which it is limited, as the subject or predicate of that proposition."
"A conjunction is a part of speech serving to unite two propositions as parts of the same complex assertion, or two words as similar parts of the subject or predicate of one proposition. By similar parts it is meant that the words so united stand in similar relations to the term to which they belong. For example, 1. As attributes, both qualifying a subject, 'Sic bonus et sapiens dignis ait esse paratus.' 2. As prepositions, both introducing limiting nouns 'without money and without price.' 3. As substantives, both forming parts of a collective subject, 'two and three are five.' Whereas with the preposition, the words united are not similar, but opposed, the limiting and the limited notion."
While differing from some of Professor Boole's views on the relation of logic to mathematics, I fully agree with him that the true functions of the several parts of speech must be determined by an analysis of the laws of thought. Both grammar and logic might be considerably improved by an accurate development on psychological principles.
H. L. Mansel, B.D.
St. John's College, Oxford.
Has not your correspondent G. Boole fallen into an inaccuracy whilst contending about the accuracy of another's logic? He seems to employ the proposition, all trees are endogens or exogens, as an example of an accurate proposition.
I forget the technicalities in which the objection to such a proposition would be properly expressed; but it cannot well be denied that all comprehends the whole genus, and expresses that whole collectively. If so, the proposition affirms that the whole genus of trees must either be acknowledged to be endogens, or else to be all exogens. Does not such an affirmation require the word every to clear it from ambiguity? Will it be cleared of ambiguity by saying, "Every tree is endogen or exogen?" Or must we say "Every tree is either endogen or exogen?"
If your correspondents should happen to take down the second volume of Locke on Human Understanding, b. III. ch. iii. § 11., on "Universals," his note will supply them with another knot to unravel, of which I would gladly see their solution. For he has there said, "Three Bobaques are all true and real Bobaques, supposing the name of that species of animals belongs to them." Is this name formed in jest? For the philosopher sometimes puts on an awkward affectation of humour in his replies to Bishop Stillingfleet, to whom this note is addressed.