MEDIATE INFERENCE-REASONING-ITS NATURE AND LAWSTHE 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 C; then I might reason thus :—

man,

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

particulars, particulars to generals, particulars to particulars. last is the foundation of both the others.

This

(b) Mill, as might be looked for, rejects immediate inference, on the ground that there is no real progression from one truth to another,the logical consequent being a mere repetition of the logical antecedent. This is not the case, as is clear from the illustrations given; and it is as incorrect to hold that there is only a change of expression in immediate inference; there is a distinction in judgment.

(c) Kant regards immediate inference as inference of the Understanding, mediate as that of the Reason.-(K. d. r. V., p. 360; Log., $ 41.)

§ 470. Mediate Inference is of two kinds-viz., Syllogism and Induction. Syllogism proceeds (a) from the general to the particular, or (b) from the equal to the equal. Induction proceeds from the individual or from the particular to the general. Syllogism, in so far as it proceeds in the first line, is a reasoning from the higher or wider to the lower or narrower; Induction is a reasoning from the lower or parts to the whole or totality which is thus constituted.

(a) We believe all either through Syllogism (σvλλoyoμoû) or through Induction (éraywyns).—(An. Pr., ii. 23.)

We learn either from induction or from demonstration (àrodeíĝet); demonstration is from universals, induction is from parts (particulars). An. Post., i. 18.)

As the proposition in demonstration is a necessary one, and of immediate certainty, these statements of Aristotle are not to be construed as implying an empirical theory of knowledge.

§ 471. In this case we have Mediate Inference or Reasoning, because we have not merely two propositions, but because we have introduced into each of the two propositions or premisses a term common to both, called the Middle Term. And let it be observed that these two propositions are not merely arbitrarily or voluntarily connected. They are connected in virtue of the law of whole and part in thought. Thus, I may find or know from observation that the crocus is a plant, and I may find, further, that plant belongs to the class organised. Each of these propositions, taken by itself, would not lead me far. I might be able from it to state the proposition in another form, but that is not much. But if I put the two propositions together, -and I am led to do this because the term or concept plant belongs to or is common to both,-I shall find that a

proposition, distinct from either, necessarily emerges. I say, first of all, every plant is organised; then, the crocus is a plant; and thus I get the new proposition, that the crocus is organised, or, in virtue of its being a plant, belongs to the class organised. Now this, whatever view we may take of its nature, is the fundamental form and type of all human reasoning, that to which valid reasoning may be reduced, and by which it may be tested. And if we seek to analyse the principle or law which regulates and necessitates this evolution, we shall find that it is analogous to that of whole and part, that it is, in fact, that of genus and species. Thus, crocus is found to be a part of plant; plant is found to be a part of organised, therefore the whole organised, inasmuch as it includes the part or species, plant, includes also the part or species of plant-viz., crocus. There you have the groundprinciple of direct or categorical reasoning, that form of thought into which the working of the mind naturally and chiefly flows. This reasoning is called mediate, because we connect crocus and organised through their participation in a common notion or term-viz., plant.

(a) Reasoning, says Wolff, is an operation of the mind, in which, from two propositions having a common term, there is formed a third, by combining the diverse terms in both. Syllogism is an expression in which the reasoning (argument, ratiocinium) or discourse (discursus) is expressly set forth.-(Logica, § 50, 332.)

(b) What is a Reasoning? Hamilton, following Esser, in the Logic Lectures, brings out its nature and scope in this manner. We have before us two notions, which are opposed to each other, -repugnant or contradictory. We wish to know which is to be affirmed of a given subject. But we are unable from an examination of the notions themselves to determine this point. We are thus in doubt, and we must remain in this state of indecision, until we get further knowledge. The knowledge, moreover, must be a general rule which will extinguish the doubt. It must be a rule with an application to the present case.

For example, we have before us the two contradictory predicates free-agent and necessary agent. We ask the question-Which of these applies to man? Is man a free-agent or is he a necessary agent? How is this question to be decided, and the doubt solved? Not certainly by a mere inspection of the two contradictory predicates. But suppose I take one-say free-agent-and find by a competent process that a freeagent is one morally responsible, or that every morally responsible agent is free, I have thus advanced a step in the line of solution. Suppose I further find that man is morally responsible,-I have thus got two related propositions, or one notion related to the two notions, freedom and moral responsibility. Now the question or problem with which I

started may be solved, and I can with necessity or absolute certainty infer that man is a free-agent. Thus

Every morally responsible agent is a free-agent;

Man is a morally responsible agent ;

Therefore, man is a free-agent.

It is obvious that the cogency of the reasoning depends on the ascertained relations of the middle term, morally responsible agent, at once to man and to free-agent.

(c) To Mill it appears that we can never discover that two notions stand in the relation of whole and part, by comparing each of them with a third. E.g., we should say this: A is a part of B, B is a part of C. By putting these together, we find that A is a part of C. Thus :

:

(All) A is a part of B (some B); (All) B is a part of C (some C'); .. (All) A is a part of C (some C).

C

B

But Mill does not admit this. A, according to him, is perceived to be A and something more. We thus perceive A and something more to be a part of C, without perceiving that A is a part of C. In other words, we perceive that (all) A is a part of B, and that (all) B is a part of C. We must, therefore, have perceived from the very first, or before putting these two propositions together, that A was a part of C. Why? we ask in wonder. Because otherwise you would have the absurdity of supposing that you perceived A and something more to be a part of C, without perceiving that A is a part of C! Suppose we perceive in this way, according to the terms :—

B

(a) All A is B.

(b) All B is C.

Is the second proposition here an advance on the first or not? Is the one necessarily involved in the other? May I not know that all