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Looking upon all judgments of this class as having both Extension and Comprehension, we can obtain from any given proposition a set of what have been called by Kant Syllogisms of the Understanding, and by Hamilton Immediate Inferences, or what I call Implied or Transposed Judgments. Thus, the judgment being given, All men are responsible,' we can by Extension derive such judgments as the following:-that man is a species in the genus responsible; that some responsible beings are men; that any one man is responsible; that it is not true that no men are responsible; or that some men are not responsible; that men of genius are responsible with their genius; and that God who calls men to account is calling to account responsible beings. Again, by Comprehension we can say, that responsibility should always accompany our notion of man; that responsibility exists, being found in man who really exists; that no man is irresponsible; that irresponsible beings cannot be men; and since responsibility is to God, man being responsible is responsible to God. These implied judgments bring us to the very verge of mediate reasoning. By subalternation we declare that all men being responsible, some men are responsible: there is but a step between this and mediate reasoning, in which we argue that all men being responsible, the New Zealanders who are men, that is, some men, are responsible. These Transposed Judgments appeared in the old Logic under the heads of Opposition and Conversion; and in the New Analytic they have been drawn out fully in Archbishop Thomson's

Laws of Thought (p. iii., where, however, they are not drawn by Extension and Comprehension). It is a defect in Mr. Mill's work, professedly A System of Logic, Ratiocinative and Inductive, that it does not discuss. such topics.

CHAPTER XVI.

REASONING.

In order that they may reason, and reason validly, it is not necessary that persons be logicians. Man reasons spontaneously. The logician reflects upon the natural operation, and seeks to unfold its nature and its laws; and he strives also to lay down rules fitted to guide and guard us as we reason. The grand question to be determined in scientific logic is, what is the regulating principle of spontaneous ratiocination? On this subject there is a general agreement, and yet considerable diversity of opinion, among logicians. Almost all admit that the principle (when the conclusion is affirmative) may be expressed, 'Things which agree with one and the same agree with one another.' But this form is too vague, for it does not specify the nature of the agreement. And so logicians have endeavoured to make the statement more definite. According to the Dictum of Aristotle, the things must agree in being both under some higher class or genus. The form has sometimes been put, 'Things are the same which are the same with a third.' Mr. Mill expresses it, 'Things which

co-exist with the same co-exist with one another.'. The distinctions which have been drawn in the two last chapters in regard to the Notion and Judgment will be found, if followed out, to throw light on some of these points.

First, There are simple cases of reasoning in which the terms are Singular or Abstract :

Thomas à Kempis was the author of the 'Imitation of Christ;' Gerson was not Thomas à Kempis;

.. Gerson was not the author of the Imitation of Christ.'

Or the unfigured syllogism of Hamilton:--

Sulphate of iron is copperas ;

Sulphate of iron is not sulphate of copper;

... Sulphate of copper is not copperas.

In the same class may be placed all reasoning in which the propositions are definitions or substitutive : as, Logic is the science of the laws of thought; Ethics is the science of the laws of our moral nature; therefore Logic is not Ethics.' Under this head I put all quantitative reasoning; as, 'A=B; BC; therefore A = C.' In such examples none of the notions is properly a class-notion or attributive. As none of them has quantity or extension, so we cannot speak of a minor or major term, or of a minor or major premiss. The division into figures has no place; for, as any one will at once see on trial, the middle term may be made, as we please, the subject or the predicate of either premiss. The regulating principle in all such cases is either, 'Things are the same which are the same with a third,' or 'things which are equal to the

same are equal to one another.' Much confusion is avoided by allotting reasoning of this description to a separate head. As there is no class-notion the Dictum cannot be the regulating principle.

Second, There is more complex reasoning in which there is an attributive predicate or a class-notion. In this the old Aristotelian Dictum remains, after all discussion, the fundamental regulating principle: 'Whatever is predicated of a class may be predicated of all the members of the class.' No other proposed Dictum has lived beyond the age of its inventor. I am convinced that the same fate awaits that propounded by our author (Logic, II. I-IV.).

The "really fundamental axiom of ratiocination,” as announced by him is, "Things which co-exist with the same thing, co-exist with one another;" and "a thing " which co-exists with another thing, with which other "a third thing does not co-exist, is not co-existent "with that third thing." But the phrase 'co-exist,' if limited to co-existence in respect of time or space, does not include most important cases of reasoning; and if widened beyond this it becomes meaningless. When we argue that the man having committed murder deserves punishment, the premisses and the conclusion have reference, not to space or time, but to far different relations. When we infer from A being equal to B, and B to C, that A is equal to C, we are not making affirmations about co-existence. In explanation, he tells us (p. 202, footnote, 6th ed.), "the co-existence meant is that of being jointly attributes of the same subject."

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