§ 161. On this it may be fairly said that while Non-Contradiction cannot tell us of a new predicate,-this being due to observation, experiment, induction,-it yet negatively enacts that this alleged new predicate is not combinable with the concept we know, unless as non-contradictory of it, or of its other attributes. This is its logical application. And further, as logical thought is that of relation between concepts, or individuals and concepts, the terms of a judgment, the terms of a reasoning, it matters nothing to it whether the judgments of a reasoning are (materially) analytical or synthetical, provided only they are given or placed in the relation of the containing and the contained. Thus it matters nothing in a reasoning whether the major be a synthetical judgment or not. I may have as a major the synthetical a priori judgment that every event is caused. My reference under this major to a particular event as caused follows the same rule as if the proposition had been analytical. And the same holds true of all the generalisations of Induction. Further, in the mind of the thinker and speaker, every judgment is in a sense analytical, for it is the statement explicitly or by analysis of what he conceives of the subject, and knows of the subject, or as he enounces. So that logically, for the purposes of logical dealing and inference, there is no difference between analytical and synthetical propositions.

§ 162. While it is true, on the one hand, that Logic, as the science of the necessary relations of thinking can discover no new fact, or do anything in this way to amplify science, it can yet contribute to the progress of science. For it makes what is already acquired clearer, more distinct, more intelligible by classification and arrangement; it further helps. us to see new relations among the materials accumulated.1 Every time we reach the connection of two terms or notions of a matter of fact, through the connection of each of these with a common third which perhaps we had known before, -though we did not know the common relation of the notion to the other two,-we add a new truth to the stock of our knowledge, and we do this in virtue of the operation of logical law and the canons of logical science. Abstract these and our progress is paralysed. In the simplest instances this holds good. The unknown property or proper1 Cf. Hamilton, Logic, L. iii.

ties of any physical substance may be revealed to us by finding that the substance belongs to a class which we knew before, although we now discover for the first time that it does so belong. Because we may at the same time know of some property belonging to this class which we now are able for the first time, in virtue of logical law, to predicate or conclude of the substance with which we started. Is this particular thing this A—with which I am dealing, possessed of a particular property or not? Is it, for example, a poisonous substance or not? It belongs, I find, after the proper observational and experimental methods, to a class of things which I had not suspected-it belongs to B. All the Bs, I may already know, have poisonous qualities as part of their properties. I have now a certainty that A has those properties. I have here the knowledge of a new relation in which I can regard A. This is a new truth for me, in a sense a new fact, upon which I can act; and but for the aid of the canons of reasoning supplied by pure logic, working along with or after the methods of observation and induction, I could have no certainty of it. If a new planet is discovered, I can at once infer that it will exhibit in its movements conformity to the laws of motion, as established by Kepler and Newton, simply from a comparison of the notion of it with other planets which exhibit this conformity. In applying the general law to a new case, I widen the range of my science. And this is what logic teaches. It teaches the general or universal laws of pure inference, whatever be the matter or science in which we infer; and it helps to form the habit of the correct application of those rules. Clearly, too, it follows from this that Observation, Experiment, Induction, all the means by which we get the materials of knowledge, and the laws of facts, are prior to the strict logical process of inference, and that the analysis of this logical process is to be done independently altogether of the inductive methods. How we get our premisses is a point of wholly secondary importance in considering what these involve. It is enough for logic if they be given; it is indifferent even to it whether they be actually true or false; the science has a perfectly definite, and very wide sphere of inquiry, in tracing the laws and conditions under which these premisses are explicated, and their conclusion implicated.

138

CHAPTER XIII.

THE LAWS OF THOUGHT-HAMILTON AND MILL.

§ 163. The true nature and applications of the Laws of Thought are perhaps best brought out in confronting one view with another. In this chapter, accordingly, I shall present the antagonistic views of Hamilton and Mill, and in a subsequent one the doctrine of Hegel on the subject.

§ 164. On the nature of these laws of thought Hamilton remarks: "When I speak of laws and of their absolute necessity in relation to thought, you must not suppose that these laws and that necessity are the same in the world of mind as in the world of matter. For free intelligences, a law is an ideal necessity given in the form of a precept, which we ought to follow, but which we may also violate if we please; whereas, for the existences which constitute the universe of nature, a law is only another name for those causes which operate blindly and universally in producing certain inevitable results. By law of thought or by logical necessity, we do not, therefore, mean a physical law, such as the law of gravitation, but a general precept which we are able certainly to violate, but which if we do not obey, our whole process of thinking is suicidal or absolutely null." 1

Hamilton here very properly marks out the contrast between the operation of physical and of logical law. In the former case the law is a sequence, a necessary and inevitable sequence, at least hypothetically so, given the present constitution of things. The cause or antecedent being given, the effect or consequent must follow; there is no choice. The cause cannot select its effect, the effect cannot select 1 Logic, L. v., p. 78.

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ing of the term." It does not make the a priori necessary law, "like laws made by Parliament," alterable and contingent; it does not deprive them of the character of " necessities of the thinking act," and make them merely "instructions for right thinking," or "general precepts which we are able to violate;" for they are still the absolutely indispensable conditions of any and all thinking, apart from which it is suicidal and null. Mill's reasoning amounts simply to a very pretty fallacy: Logical laws are precepts (Hamilton). Acts of Parliament are precepts (Mill). Therefore, logical laws and Acts of Parliament are essentially the same (Mill).

§ 165. Hamilton naturally and properly illustrates, in the first instance, the law of Identity of the whole and parts in Comprehension. Seeing that, as he teaches, Comprehension implies Extension, it hardly probably occurred to him that further illustration in Extension was needed. But Mill, more suo, thence at once infers that the law in Hamilton's view does not apply to the whole in Extension. To say that it applies to the whole in Comprehension is, forsooth, to say that it does not apply to the whole in Extension,-that this application of it in Comprehension is inconsistent with its application to the whole of Extension, which is yet in Hamilton's view, and properly, implied in the Comprehension!

§ 166. Hamilton does not say, as Mill represents, that the Principle of Identity is "the peculiar groundwork of any special kind of reasoning," and he does not deny but affirms. that it is "an indispensable postulate [principle] in all thinking." All that he says is that the law of Non-Contradiction, of which the Principle of Identity is the primary phase, expressly regulates in this its first form, affirmative thought. Surely a man may be allowed to state one thing at a time without being held to deny everything else.

§ 167. Mill's own expression of the law of Identity is"Whatever is true in one form of words is true in every other form of words which conveys the same meaning; or it is “the reaffirmation in new language of what has been already asserted." 1

This properly speaking is not the principle of Identity; for this law does not regulate simply reaffirmation, and it applies to the elements of the proposition, or of what is true, in the

1 Examination, p. 482.