It is doubtless one of the consequences of the neglect of this principle, that the older grammarians have made it a part of the definition of a conjunction, that it is a word "devoid of signification" (φὼνη ἄσημος). See references in Harris, p. 240. Were the philosophy of grammar founded, as alone it truly can be, upon the laws of thought, I venture to think that such statements would no longer be accepted.
If the views which I have expressed needed confirmation, they would to my own mind derive it from the circumstance, that on applying to the original proposition that "mathematical analysis of logic" to which H. C. K. refers (not, I think, without a shade of scorn), it is resolved into the elementary propositions, "trees exist," "flowers exist," unconnected by any sign.
Let us take, as a second example, the proposition, "All trees are endogens or exogens." If the subject, "all trees," is to be retained, there is, I conceive, but one way in which the above proposition can mentally be formed. We form the conception of that collection of things which comprises endogens and exogens together, and we refer, by an act of judgment, "all trees" to that collection. And thus the subject "all trees," remaining unchanged, the conjunction "or" connects the terms of the predicate, as the conjunction "and" in the previous example connected those of the subject. I am prepared to show that this is the only view of the proposition consistent with its strictly logical use. If H. C. K. insist upon the resolution "any tree is an endogen, or it is an exogen," I would ask him to define the word "it." He cannot interpret it as "any tree," for the resolution would then be invalid. It must be applied to a particular tree, and then the proposition resolved is really a "singular" one, and not the proposition whose subject is "all trees."
Not only do conjunctions in certain cases couple words, but in so doing they manifest the dominion of mental laws and the operation of mental processes, which, though never yet recognised by grammarians and logicians, form an indispensable part of the only basis upon which logic as a science can rest. And however strange the assertion may appear, I do not hesitate to affirm that the science thus established is a mathematical one. I do not by this mean that its subject is the same as that of arithmetic or geometry. It is not the quantitative element to which the term is intended to refer. But I hold, with, I believe, an increasing school of mathematicians, that the processes of mathematics, as such, do not depend upon the nature of the subjects to which they are applied, but upon the nature of the laws to which those subjects, when they pass under the dominion of human thought, become obedient. Now the ultimate laws of the processes which are subsidiary to general reasoning, such as attention, conception, abstraction, as well as of those processes which are more immediately involved in inference, are such as to admit of perfect and connected development in a mathematical form alone. We may indeed, without any systematic investigation of those laws, collect together a system of rules and canons, and investigate their common principle. This the genius of Aristotle has done. But we cannot thus establish general methods. Above all,
we cannot thus establish such methods as may really guide us where the unassisted intellect would be lost amid the complexity or subtlety of the combinations involved. How small, for instance, is the aid which we derive from the ordinary doctrines of the logicians in questions in which we have to consider the operation of mixed causes and in various departments of statistical and social inquiry, in which the intellectual difficulty is almost wholly a logical one.
For the ground upon which some of these statements are made, I must refer to my recently-published work on the Laws of Thought. I trust to your courtesy to insert these remarks, and apologise for the undesigned length to which they have extended.
G. Boole.
Queens College, Cork.