(Vol. viii., pp. 514. 629.)
As my name appears to have been referred to by two of your correspondents,
MR. INGLEBY and H. C. K., in connexion with the above question, I request
to be permitted to state my real views upon it, together with the grounds
upon which they rest. In doing this I can only directly refer to the
observations of H. C. K., not having seen those of MR. INGLEBY to which he
makes allusion.
Admitting that there are many conjunctions which connect propositions only,
I am unable to coincide with the view of my friend Dr. Latham and other
grammarians, that the property is universal. And I agree with MR. INGLEBY,
as quoted by H. C. K., in thinking that the incorrectness of that view may
be _proved_. We possess the power of conceiving of any distinct classes of
things, as "trees," "flowers," &c. And we possess the power of connecting
such conceptions in thought, so as to form, for instance, the conception of
that collection of things which consists of "trees and flowers" together.
If we possess the power of _performing_ this mental operation, we have
clearly also the power of _expressing_ it by a sign. This sign is the
conjunction "and." It is assumed, what consciousness indeed makes evident,
that the power of forming conceptions is antecedent to that of forming
judgments expressed by propositions.
But even if we proceed to form a judgment, as "trees and flowers exist," it
may still be shown that the conjunction "and" connects the substantives
"trees," "flowers," and not propositions. For if we reduce the given
proposition to the form, "trees exist and flowers exist," the conjunction
becomes wholly superfluous. It adds nothing whatever to the meaning of the
separate propositions, "trees exist," "flowers exist." Omit, however, the
conjunction between the substantives in the original proposition, and the
sense is wholly lost. What meaning can we attach, except by a convention,
to the form of words "trees flowers exist." Now there is, I conceive, no
more obvious principle in grammar than that the doctrine of the elements of
speech should be founded upon the examination of instances in which they
have a real meaning--in which their employment is essential, not
accidental.
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" ([Greek: phônê
asêmos]). 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, {181} 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.