sary law of existence that similar logical antecedents should be accompanied by similar consequents.

In the absence of better terms, we shall style all inferences whose validity depends upon their conformity to this law of being and of belief, homological; while those inferences whose force is independent of any comparison of present with previously perceived cases of consequence we shall call orthological.

Homological inference takes place whenever one reasons from experience, or from any knowledge of some similar case or cases. If a little child but once puts its finger into the flame of a candle, it will avoid doing so thereafter. In this it is guided by a conclusion from a past experience. An adult person, who avoids touching fire on the general principle that "fire burns," likewise reasons homologically, even though he may not directly refer to a past experience; for the general principle from which he reasons is derived from the past experience of himself and others.

So also the student who, by a series of immediate judgments, has perceived that the three angles of some plane triangle are equal to two right angles, feels warranted to assume this to be true respecting any other plane triangle. Moreover, he can obtain a general principle from his immediate perception of truth, and can employ this, homologically, as a rule of inference.

Orthological reasoning takes place in the more intuitional steps of mathematical and geometrical demonstration, and in what have been called immediate inferences generally. It is such as Locke mentions in the following passage. "I ask," he says, "is it not possible for a young lad to know that his whole body is bigger than his little finger but by virtue of this maxim, that the whole is bigger than a part, nor to be assured of it till he has learned that maxim? Or cannot a country wench know, that, having received a shilling from one that owes her three, and a shilling also from another that owes her three, the remaining debts in each of their hands are equal? Cannot she know this, I say, without she fetch the certainty of it from this maxim, that, if you take equals from equals, the remainders will be equals, a maxim which possibly she never heard or thought of? I desire any one to consider . . . which is known first and clearest by most people, the particular instance or the general rule; and which it is that gives birth and life to the other.'

In these inferences described by Locke, two things are observable. In the first place, the force of the reasoning is not derived either from or through any general principle. This is the point which Locke enforces. If one were to cut an apple

into pieces, and think only of that apple and those pieces, he could immediately reason, and say respecting any one piece, that it was less than the whole apple, and this with as much certainty as if he should say,

Wherever there are whole and parts, each part is less than the whole;
In this case there is a whole with its parts; therefore

Each of these parts is less than the whole.

And no strength would be added to the reasoning of the countrywoman by saying, –

When equals are taken from equals, the remainders are equal;

In this case equals have been taken from equals; therefore
The remainders are equal.

The maxim, or general principle, in such cases may serve to test the reasoning, but is not the source of its validity,— that is, of its power to produce correct conviction.

Secondly, we must notice that orthological inference takes place not only without reference to any general principle, but also without reference to any previously perceived particular case of necessary connection. Locke did not fully apprehend this point. His zeal is directed against the doctrine "that all knowledge [or reasoning] depends on certain præcognita, or general maxims, called principles." He nowhere denies that all inference may derive its force from remembered instances of a similar nature. But it is clear that we often reason without any reference either to general principles or to any similar case of necessary connection previously perceived.

We often note a certain fact, simple or complex, and thereupon immediately infer another fact. This is the most striking peculiarity of those inferences mentioned in the above quotation from Locke. If one event precedes another, we can immediately, or without reference to any other case, affirm that the other follows it; and if a first event precedes a second, which precedes a third, we can assert, with equal directness, that the first is prior to the third as well as to the second.

There may be ground for question whether, without any presentational knowledge of things as connected in necessary ontological relations, the mind could originate the conception of unseen consequents to be inferred from perceived antecedents. We may even allow that the relational conceptions which orthological inference employs are first obtained by the mind in its immediate cognitions of fact. But there can be no question that many inferential convictions give no indication of being dependent on any knowledge of similar cases of connection.

On the contrary, that same mental power which immediately recognizes the necessary connection between two things presentationally perceived, also immediately asserts the necessary connection between two things of which one is known, and the other only conceived, to exist; and thereby directly infers the existence of the other thing.

Here the question occurs, In what way can we determine whether any particular inference be orthological or homological? To which we reply that this is to be determined by asking, On what does the force of this inference essentially depend? If it arise simply from consideration of the nature of the antecedent, and is independent of reference to any other similar fact known to be logically necessitant, the inference is orthological; if it arise in connection with such reference, it is homological.

All inference

form. All in

Hence it is clear that all reasoning from general principles is homological. A general principle has no force originally belonging to itself. It is derived from the perception of a particular case of consequence, or of a number of such cases, and has its validity according to the law that whatever is necessary in any individual instance is necessary likewise in every other instance in which there is an antecedent containing the same necessitative conditions. When we reason from a general principle, we do, in effect, reason from the similar to the similar. In all cases of inference we may be said to reason may be given in accordance with general principles. Therefore, a homological also, a homological form may be given to all reasonference based ing. But any inference which is in no way dependent on ontologi- on the general principle should not be regarded as cal relations. homological. For this reason we distinguish between that apparent and formal reasoning from principles, when mathematical, geometrical, and metaphysical axioms are employed, and that real use of principles and general theorems which takes place in the development of any form of ontological science. After we have made some progress, orthologically, through a consideration of individual constructions of figure, or of particular concatenations of fact as in various necessary relations, we generalize the truths thus obtained; and thereupon, neglecting and forgetting the methods by which such truths were reached, we use these as general rules or principles in our further reasonings. Thus, without remembering how we first came to adopt the rules, we ascertain the comparative solidity of cones by multiplying the area of their bases by one third of their altitudes, and we extract the cube root of numbers by a more complicated method. In such cases we are guided by general principles, and reason homologically.

Comparing the two modes of inference with reference to our use of them, we find that the most noticeable part of human reasoning is homological, while, at the same time, the ultimate principles of inference, with one exception, are orthological. Homological reasoning has only one ultimate principle, while orthological has many. Here, by ultimate principles, we mean such as are immediately subordinate to the universal principle of reason and consequent.

It will be noticed that orthological inference is more evidently, though not more truly, illustrative of this fundamental law than the homological. When we collect at random a number of diverse orthological inferences, we find that they can be coordinated under no one general law, except that of reason and consequent. But when we collect homological inferences, we are distracted by the duality of the principle according to which they are constructed, and by its wonderful universality of application.

Because of this latter characteristic the homologic principle has been mistaken for the fundamental principle of all reasoning. This error has been facilitated by the circumstance that in every train of inferences the successive steps, though sometimes orthological and sometimes homological, can all be given that form of expression which is properly necessary only for the explicit statement of our reasonings from general principles. All reasoning may take a homologic form, and therefore we wrongly say that all reasoning is based on the homologic principle. This has been the almost universal mistake of logicians from Aristotle down.

Again, considering both kinds of inference as setting forth things as logically connected with one another, the ontological character of both becomes apparent. By this we mean that the radical laws of connection which the mind uses in these forms of ratiocination are such as must belong to any system of things and form a basis for one's reasoning with respect to it. Collecting and analyzing orthological inferences, we find them to arise from consideration of the necessary relations of times, spaces, quantities, substances, powers, actions, changes, in short, of such relations as must pertain to things, provided they exist at all, and which could be annihilated only by the annihilation of being; while the homologic principle that similar consequents attend similar antecedents that what is necessary in any case, by reason of the nature of the case, is necessary again upon the recurrence of that case - is also ontological.

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It may be asked, Can homological inference be based on ontological necessity when it produces belief in things that are not

ontologically necessary, as, for example, when it predicts the freezing of water at a certain temperature? For we may suppose that almighty power could change the nature of water in this one respect, so that, on the sea-level, it would remain liquid, or would boil, at the temperature of 32° Fahrenheit.

We reply that not only that prediction of natural events which is characterized by the highest moral certainty, but also our merely probable expectations, and, in short, all inferences whatever, -are based on the recognition of the necessary character of ontological relations. Demonstrative reasoning assumes a perfect and complete antecedent of necessity; contingent or problematic reasoning assumes an imperfect and incomplete antecedent of necessity; but in both the force of the inference depends on a perception of the necessary, ontological, relations of entity.

The truth of this doctrine is supported by the fact that probable inference may assume a mathematical expression, as it does in the "Calculation of Chances ;" but any complete discussion of it belongs to the philosophy of Logic. At present we must content ourselves with saying that the radical principles of probable inference are as ontological as those of demonstrative inference, and would, as a matter of course, be employed, by minds like ours, in any universe, or constitution of things, whatever.

CHAPTER XLIX.

EXPERIENCE AND INTUITION.

Three com- 1. EXPERIENCE, in common language, has three mon mean- principal meanings.

ings of the term "expe

First, it is a name for all of man's psychical life, rience." all he does or suffers, so far as he is distinctly conscious of it. According to this, we say, "One's experience during such or such a period was monotonous or varied, happy or full of sorrow."

Secondly, it may denote all of those cognitions, or perceptions, of present objects and relations which take place immediately on the occasion of one's psychical life, whether the objects be included in this life or only in some way connected with it. In this sense experience" is a comprehensive term, including every form of sense-perception, concomitant perception, and

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