§ 463. But while this criticism is inept, the ordinary theory is open to objection, and needs amendment. Some seems to have three distinct meanings, and it is only in two of these that the contradiction between 0 and A is sustained. (1.) Some, taken in its ordinary logical acceptation, means some at least, perhaps all, I don't know whether or not. If, then, I deny that some at least of men are not civilised, I do not necessarily assert that all men are, I only imply that some are civilised, though I do not know whether the whole are, whether even others are or not. This is the extreme of indefinitude, and here O does not yield A as contradictory, but only I.

(2.) If some means some only, and I deny that only some men are not civilised, I imply that all men are civilised,—that is, O implies A as its contradictory. Not some only are clearly means all are. Some only is thus seen to be tacitly and without proper acknowledgment accepted in the ordinary logical formulæ.

(3.) Some may be taken as meaning even some, or even some part. Thus, even some part of man is not without a sense of a transcendent Being. This (0) implies (A) that every part of man or all man has a sense of transcendent Being. This comes very near the definitude of any - ullus. It is denied that

some (even one) X is not Y, therefore every X is Y.

(a) Some (at least). This is all that is necessary to a Particular Proposition. To sublate Universality, some one requires to be excepted. Between some (plural, several) and none, there intervenes some one. To deny that all the apostles of Christ were faithful to their Lord—it is not necessary to assert several were unfaithful, but only one-some one.

It ought to be noted that while of contradictories one is always true and the other false, it often happens that we cannot, as a matter of fact, tell which is true or which is false. This happens especially in future contingents. Thus, it will rain to-morrow, it will not rain to-morrow; but which is true or to happen we cannot determine.1

§ 464. Contradictories, considered in reference to the subject, are of two kinds-(a) The subject in the one is a Universal, or (b) a Singular, certain, and designate,-as every man is just, not every man is just―Cato is just, Cato is not just.

1 Duncan, Instit. Log., vi. 2.

In the case of the universal subject, the contradiction requires difference both in quantity and in quality, or between A and O. These two forms are expressly recognised by Aristotle.

(a) With Aristotle contradiction is of (1.) Universals, as, all man is white, some man is not white; no man is white, some man is white. (2.) Singulars, as, Socrates is white, Socrates is not white.—(Cf. De Int., c. vi. vii.)

(b) Occam recognises a form of Contradiction which he names Inferential. Thus, no animal runs, some man runs. The latter implies the contradictory of the former, for if some man runs, some animal runs.—— (Summ. Log., i. 36.) This, however, is not contradictory to any one who has not identified some man and some animal. It thus makes no new form.

§ 465. On Hamilton's system there is no contradiction between any two propositions which contain whole and part. The only true contradiction is between Singulars and Totalities indivisible, that is, regarded as Singulars. Socrates is sick; Socrates is not sick. The whole of A is (identical with) the whole of B.1

In the doctrine of the Opposition of Propositions, the modifications introduced by Hamilton arise mainly from the semi-definite meaning of some, as some at most, some only.

Some, according to Hamilton, is always thought as semidefinite-that is, some at most or only, when the other term of the judgment is universal. Thus, some animals are (all) carnivorous, means negation of all are carnivorous—that is, not all are carnivorous or some only of animals are carnivorous. (Only) some sunsets are stormy-that is, others are not, or not

all are.

In the case of Subalterns, we infer I from A and O from E-All is some, .. some is some; all is not, .. some is not. This only holds good if we mean some at least. If we mean some only, the two propositions are inconsistent—that is, they cannot both be true.

Thus, All African is (some) black (only); .. some African is (some) black (only.)—(AfI, IfA.) All men are copper-coloured; some men only (not all) are copper-coloured—are inconsistent. Some horses (only) are not swift is opposed to no horses are swift.

§ 466. In Sub-contrary Opposition (so called) there is an inference from some only to some other. If I say all men 1 See Bowen, Logic, p. 173.

are some animals or some animals are all men, I can infer all men are not some animals, or some animals are not some men. Some animals only, implies that men are a certain some, and not any other animals, or other part of the class. This inference Hamilton calls Integration, inasmuch as it is a completing of the whole, of which a part only has been given.

"1

$467. Under Immediate Inference, Hamilton further latterly included the two forms of Hypothetical Reasoning,the Conjunctive and Disjunctive. This doctrine appears in the note to "The Essay on the New Analytic of Logical Forms" (1850). "All mediate inference is one; that incorrectly called Categorical; for the Conjunctive and Disjunctive forms of Hypothetical Reasoning are reducible to Immediate Inferences." The nature of Hypothetical Reasoning had occupied Hamilton's attention specially for some time from 1848 to 1852. Certain fragmentary results are given in the Appendix to the Lectures on Logic.2 From these we gather that he held all inference to be hypothetical, and that what have been called Hypothetical Syllogisms are not more hypothetic than others. In one of the fragmentary papers, he says that Aristotle in ignoring them as forms of reasoning was right, that they are not composite by contrast to the regular Syllogism, but more simple, that if inferences at all they are immediate, not mediate, that they are not argumentations, but preparations for augmentation, as only putting the question in preparation for the syllogistic process. Hamilton cannot be said to have reached a conclusion on this subject wholly definite, clear, or satisfactory. He inclines on the whole to the view that Conjunctive and Disjunctive Syllogisms are reducible to forms of Immediate Inference, at once resembling and different from each other.3

(a) In 1848, he gave as kinds of Immediate Inference, i. Sub-alternation; ii. Conversion; iii. Opposition, (a) of Contradiction, (b) of Contrariety, (c) of Sub-contrariety; iv. Equipollence; v. Modality; vi. Contraposition; vii. Correlation; viii. Identity.-(Logic, App. VIII, p. 373.)

iv.

1 Discussions, p. 651.

2 Appendix VIII., vol. iv. p. 369 et seq.

3 IV. p. 387.

369

CHAPTER XXIX.

MEDIATE INFERENCE-REASONING-ITS NATURE AND LAWS

THE SYLLOGISM-ORDER OF ENUNCIATION.

§ 468. Inference in every form means necessary implication. In other words, given a certain proposition or statement, another proposition or statement must also be admitted along with it or in consequence of it. That other statement is implied in it, and necessarily implied in it. This is inference, the first form of Inference,-Immediate Inference. Thus, if I say: No Christian can be cruel to the creatures whom God has made, I am entitled to say that the man who is cruel to these creatures is not a Christian. If the first proposition be granted, the second must be granted. The first proposition may, of course, be disputed; but, given that, the second follows, and necessarily follows. Thus the inference is immediate; that is, I do not need any third or other term beyond what I have in my original statement to warrant my inference.

A single proposition may thus yield an inference, apart altogether from what is called reasoning. And one of the most necessary things in our ordinary practical dialectic is simply to be able at once to catch at the immediate inference which a statement implies,-unknown, it may be, to the person who makes it. Every proposition, if we but definitely understand, and, much more, definitely state the character of our terms, must yield a direct or immediate inference.

§ 469. But there is another kind of Inference besides this, -the inference which we usually call Argument or Reasoning. Now, what is the type or form of a perfect reasoning?

It is that I have two propositions, not one merely, as in the case of Immediate Inference, and out of these two I not only get, but I am obliged to get a third. This, for example,

will stand as a type of reasoning :—

Now, the conclusiveness of this reasoning-i.e., the connection between the premisses and the conclusion—is entirely independent of the matter or subject about which we reason. It is of no consequence whatever what the terms of the reasoning are, whether they are free-intelligent, responsible, and man, or what they are. These may be quite changed, yet if we preserve the connection between the terms, our reasoning will be equally valid or conclusive. Thus, suppose I substitute for free-intelligent, A; and for responsible, B; and for man, C; then I might reason thus:—

Every A is B;

Every C is A;

.. Every C is B.

It matters thus nothing what are the notions or terms of our reasonings, the law of reasoning is the same. In technical language, the matter of our reasoning may vary; but the form remains the same. I have got here, as it were, the mould of human reasoning. I care not whether it be applied to science, to ordinary matter of fact, to history, or to philosophy. The reasoning process is all the same in these. I have got the law, or form, or type of reasoning which runs through the infinity of things about which I can think. Amid changing matter, I have got the unchanging form,—the ideal of accurate sequence in thought. This is the conception which regulates the chaos of associated impressions. This is the golden band that runs through and holds together all the materials of thought.

(a) Mill's conception of inference is that of proceeding from the known to the unknown, or from truths known to others really distinct from them. Inference with him is of three kinds-from generals to