Front Page Titles (by Subject) CHAPTER XIX: Of Reasoning - The Collected Works of John Stuart Mill, Volume IX - An Examination of William Hamilton's Philosophy
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CHAPTER XIX: Of Reasoning - John Stuart Mill, The Collected Works of John Stuart Mill, Volume IX - An Examination of William Hamilton’s Philosophy 
The Collected Works of John Stuart Mill, Volume IX - An Examination of William Hamilton’s Philosophy and of The Principal Philosophical Questions Discussed in his Writings, ed. John M. Robson, Introduction by Alan Ryan (Toronto: University of Toronto Press, London: Routledge and Kegan Paul, 1979).
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in common with the majority of modern writers on Logic, whose language is generally that of the Conceptualist school, Sir W. Hamilton considers Reasoning, as he considers Judgment, to consist in a comparison of Notions: either of Concepts with one another, or of Concepts with the mental representations of individual objects. Only, in simple Judgment, two notions are compared immediately; in Reasoning, mediately. Reasoning is the comparison of two notions by means of a third. As thus: “Reasoning is an act of mediate Comparison or Judgment; for to reason is to recognise that two notions stand to each other in the relation of a whole and its parts, through a recognition that these notions severally stand in the same relation to a third.”* The foundation, therefore, of all Reasoning is “the self-evident principle that a part of the part is a part of the whole.”† “Without reasoning we should have been limited to a knowledge of what is given by immediate intuition; we should have been unable to draw any inference from this knowledge, and have been shut out from the discovery of that countless multitude of truths, which, though of high, of paramount importance, are not self-evident.”‡ This recognition that we discover a “countless multitude of truths,” composing a vast proportion of all our real knowledge, by mere reasoning, will be found to jar considerably with our author’s theory of the reasoning process, and with his whole view of the nature and functions of Logic, the science of Reasoning: but this inconsistency is common to him with nearly all the writers on Logic, because, like him, they teach a theory of the science too small and narrow to contain their own facts.
Notwithstanding the great number of philosophers who have considered the definition cited above to be a correct account of Reasoning, the objections to it are so manifest, that until after much meditation on the subject, one can scarcely prevail on oneself to utter them: so impossible does it seem that difficulties so obvious should always be passed over unnoticed, unless they admitted of an easy answer. Reasoning, we are told, is a mode of ascertaining that one notion is a part of another; and the use of reasoning is to enable us to discover truths which are not self-evident. But how is it possible that a truth, which consists in one notion being part of another, should not be self-evident? The notions, by supposition, are both of them in our mind. To perceive what parts they are composed of, nothing surely can be necessary but to fix our attention on them. We cannot surely concentrate our consciousness on two ideas in our own mind, without knowing with certainty whether one of them as a whole includes the other as a part. If we have the notion biped and the notion man, and know what they are, we must know whether the notion of a biped is part of the notion we form to ourselves of a man. In this case the simply Introspective method is in its place. We cannot need to go beyond our consciousness of the notions themselves.
Moreover, if it were really the case that we can compare two notions and fail to discover whether one of them is a part of the other, it is impossible to understand how we could be enabled to accomplish this by comparing each of them with a third. A, B, and C, are three concepts, of which we are supposed to know that A is a part of B, and B of C, but until we put these two propositions together we do not know that A is a part of C. We have perceived B in C intuitively, by direct comparison: but what is B? By supposition it is, and is perceived to be, A and something more. We have therefore, by direct intuition, perceived that A and something more is a part of C, without perceiving that A is a part of C. Surely there is here a great psychological difficulty to be got over, to which logicians of the Conceptualist school have been surprisingly blind.
Endeavouring, not to understand what they say, for they never face the question, but to imagine what they might say, to relieve this apparent absurdity, two things occur to athe minda . It may be said, that when a notion is in our consciousness, but we do not know whether something is or is not a part of it, the reason is that we have forgotten some of its parts. We possess the notion, but are only conscious of part of it, and it does its work in our trains of thought only symbolically. Or, again, it may be said that all the parts of the notion are in our consciousness, but are in our consciousness indistinctly. The meaning of having a distinct notion, according to Sir W. Hamilton, is that we can discriminate the characters or attributes of which it is composed. The admitted fact, therefore, that we can have indistinct notions, may be adduced as proof that we can possess a notion, and not be able to say positively what is included in it. These are the best, or rather the only presentable arguments I am able to invent, in support of the paradox involved in the Conceptualist theory of Reasoning.
It is a great deal easier to refute these arguments than it was to discover them. The refutation, like the original difficulty, is two deep. To begin; a notion, part of which has been forgotten, is to that extent a lost notion, and is as if we had never had it. The parts which we can no longer discern in it are not in it, and cannot therefore be proved to be in it, by reasoning, any more than by intuition. We may be able to discover by reasoning that they ought to be there, and may, in consequence, put them there; but that is not recognising them to be there already. As a notion in part forgotten is a partially lost notion, so an indistinct notion is a notion not yet formed, but in process of formation. We have an indistinct notion of a class when we perceive in a general way that certain objects differ from others, but do not as yet perceive in what; or perceive some of the points of difference, but have not yet perceived, or have not yet generalized, the others. In this case our notion is not yet a completed notion, and the parts which we cannot discern in it, are undiscernible because they are not yet there. As in the former case, the result of reasoning may be to put them there; but it certainly does not effect this by proving them to be there already.
But even if these explanations had solved the mystery of our being conscious of a whole and unable to be directly conscious of its part, they would yet fail to make intelligible how, not having this knowledge directly, we are able to acquire it through a third notion. By hypothesis we have forgotten that A is a part of C, until we again become aware of it through the relation of each of them to B. We therefore had not forgotten that A is a part of B, nor that B is a part of C. When we conceived B, we conceived A as a part of it; when we conceived C, we conceived B as a part of it. In the mere fact, therefore, of conceiving C, we were conscious of B in it, and consciousness of A is a necessary part of that consciousness of B, and yet our consciousness of C did not enable us to find in it our consciousness of A, though it was really there, and though they both were distinctly present. If any one can believe this, no contradiction and no impossibility in any theory of Consciousness need stagger him. Let us now substitute for the hypothesis of forgetfulness, the hypothesis of indistinctness. We had a notion of C, which was so indistinct that we could not discriminate A from the other parts of the notion. But it was not too indistinct to enable us to discriminate B, otherwise the reasoning would break down as well as the intuition. The notion of B, again, indistinct as it may have been in other respects, must have been such that we could with assurance discriminate A as contained in it. Here then returns the same absurdity: A is distinctly present in B, which is distinctly present in C, therefore A, if there be any force in reasoning, is distinctly present in C; yet A cannot be discriminated or perceived in the consciousness in which it is distinctly present: so that, before our reasoning commenced, we were at once distinctly conscious of A, and entirely unconscious of it. There is no such thing as a reduction to absurdity if this is not one.
The reason why a judgment which is not intuitively evident, can be arrived at through the medium of premises, is that judgments which are not intuitively evident do not consist in recognising that one notion is part of another. When that is the case, the conclusion is as well known to us ab initio as the premises; which is really the case in analytical judgments. When reasoning really leads to the “countless multitudes of truths” not self-evident, which our author speaks of—that is, when the judgments are synthetical—we learn, not that A is part of C, because A is part of B and B of C, but that A is conjoined with C, because A is conjoined with B, and B with C. The principle of the reasoning is not, a part of the part is a part of the whole, but, a mark of the mark is a mark of the thing marked, Nota notæ est nota rei ipsius.[*] It means, that two things which constantly coexist with the same third thing, constantly coexist with one another; the things meant not being our concepts, but the facts of experience on which our concepts ought to be grounded.
This theory of reasoning is free from the objections which are fatal to the Conceptualist theory. We cannot discover that A is a part of C through its being a part of B, since if it really is so, the one truth must be as much a matter of direct consciousness as the other. But we can discover that A is conjoined with C through its being conjoined with B; since our knowledge that it is conjoined with B, may have been obtained by a series of observations in which C was not perceptible. C, we must remember, stands for an attribute, that is, not an actual presentation of sense, but a power of producing such presentations: and that a power may have been present without being apparent, is in the common course of things, implying nothing more than that the conditions necessary to determine it into act were not all present. This power or potentiality, C, may in like manner have been ascertained to be conjoined with B, by another set of observations, in which it was A’s turn to be dormant, or perhaps to be active, but not attended to. By combining the two sets of observations, we are enabled to discover what was not contained in either of them, namely, a constancy of conjunction between C and A, such that one of them comes to be a mark of the other: though, in neither of the two sets of observations, nor in any others, may C and A have been actually observed together; or, if observed, not with the frequency, or under the experimental conditions, which would warrant us in generalizing the fact. This is the process by which we do, in reality, acquire the greater part of our knowledge; all of it (as our author says) which is not “given by immediate intuition.”[*] But no part of this process is at all like the operation of recognising parts and a whole; or of recognising any relation whatever between Concepts; which have nothing to do with the matter, more than is implied in the fact, that we cannot reason about things without conceiving them, or representing them to the mind.
The theory which supposes Judgment and Reasoning to be the comparison of concepts, is obliged to make the term concept stand for, not the thinker’s or reasoner’s own notion of a thing, but a sort of normal notion, which is understood as being owned by everybody, though everybody does not always use it; and it is this tacit substitution of a concept floating in the air for the very concept I have in my own mind, which makes it possible to fancy that we can, by reasoning, find out something to be in a concept, which we are not able to discover in it by consciousness, because, in truth, that concept is not in bourb consciousness. But a concept of a thing, which is not that whereby I conceive it, is to me as much an external fact, as a presentation of the senses can be: it is another person’s concept, not mine. It may be the conventional concept of the world at large—that which it has been tacitly agreed to associate with the class; in other words, it may be the connotation of the class-name; and if so, it may very possibly contain elements which I cannot directly recognise in it, but may have to learn from external evidence: but this is because I do not know the signification of the word, the attributes which determine its application—and what I have to do is to learn them: when I have done this, I shall have no difficulty in directly recognising as a part of them, anything which really is so. But with regard to all attributes not included in the signification of the name, not only I do not find them in the concept, but they do not even become part of it after I have learnt them by experience; unless we understand by the concept, not, with philosophers in general, only the essence of the class, but with Sir W. Hamilton, all its known attributes. Even in Sir W. Hamilton’s sense, they are not found in the concept, but added to it; and not until we have already assented to them as objective facts—subsequently, therefore, to the reasoning by which they were ascertained.
Take such a case as this. Here are two properties of circles. One is, that a circle is bounded by a line, every point of which is equally distant from a certain point within the circle. This attribute is connoted by the name, and is, on both theories, a part of the concept. Another property of the circle is, that the length of its circumference is to that of its diameter in the approximate ratio of 3·14159 to 1. This attribute was discovered, and is now known, as a result of reasoning. Now, is there any sense, consistent with the meaning of the terms, in which it can be said that this recondite property formed part of the concept circle, before it had been discovered by mathematicians? Even in Sir W. Hamilton’s meaning of concept, it is in nobody’s but a mathematician’s concept even now: and if we concede that mathematicians are to determine the normal concept of a circle for mankind at large, mathematicians themselves did not find the ratio of the diameter to the circumference in the concept, but put it there; and could not have done so until the long train of difficult reasoning which culminated in the discovery was complete.
It is impossible, therefore, rationally to hold both the opinions professed simultaneously by Sir W. Hamilton—that Reasoning is the comparison of two notions through the medium of a third, and that Reasoning is a source from which we derive new truths. And the truth of the latter proposition being indisputable, it is the former which must give way. The theory of Reasoning which attempts to unite them both, has the same defect which we have shown to vitiate the corresponding theory of Judgment: it makes the process consist in eliciting something out of a concept which never was in the concept, and if it ever finds its way there, does so after the process, and as a consequence of its having taken place.
[* ]Lectures, Vol. III, p. 274.
[† ]Ibid., p. 271.
[‡ ]Ibid., p. 277.
[[*] ]This idea derives from Aristotle: see The Categories, in The Categories, On Interpretation, Prior Analytics (Greek and English), trans. Harold P. Cooke and Hugh Tredennick (London: Heinemann; Cambridge, Mass.: Harvard University Press, 1938), p. 16 (1b 9-12).
[[*] ]Lectures, Vol. III, p. 277.