The inference may be regarded as consisting of two judg ments, or propositions, connected with each other as antecedent and consequent; and it is rational inference, or reasoning, only when it involves a noticeable degree of analytic or comprehensive thought. The antecedent proposition may be either simple or compound, according to the nature of the fact or truth presented by it; but the inference can always be reduced to two propositions, and in a certain sense always consists of two only.

This may be seen, first, in the case of.those inferences which logicians call immediate. In the example, "Nine inches are part of a foot, therefore they are less than a foot," there are two simple propositions, the latter being the consequent and the former the antecedent. But should we say, "John is older than Hugh, and Hugh is older than William; therefore John is older than William," the antecedent might be said to contain two propositions, as it certainly does; yet neither of these by itself constitutes an antecedent; both must be taken together to express one compound fact, — namely, "John is older than Hugh, who is older than William." This compound proposition is the antecedent; so the argument is reduced to two propositions, though one of them is compounded and double.

In those inferences, also, which logicians call mediate, the antecedent consists of one proposition, - that is, of the statement of one fact, though it be compounded of two. When we say, "Hindoos are men, and men are mortal," there are two propositions, neither of which alone would lead to any conclusion ; but the compound proposition resulting from their union is a logical antecedent. For we may say, "Hindoos belong to the class, men, who are mortal," or " Hindoos have the nature of man, which is subject to death;" whence we infer, "Hindoos are mortal," or 66 are subject to death."

Any detailed discussion of the forms of rational thought does not lie within the limits of our present purpose. Logic is the science which sets forth the laws according to which these forms are constructed and employed.

We are convinced that the progress of philosophic analysis calls for a more natural and less dogmatic development of this science than any that has yet appeared, and confidently hope for a satisfactory logic in the near future. For a true theory of rational conviction must spring from analysis and not from assumption. Partly to support the possibility of this hope, we shall close our discussion of the discursive intellect with some remarks on the principal, or generic, modes of reasoning.

Reasoning, or

defined. Syllogism defined.

CHAPTER XLVIII.

RATIOCINATION.

1. THE name reasoning, or ratiocination, might ratiocination, be applied to every exercise of the discursive faculty, and is sometimes so employed. But, more commonly, it is. restricted to conscious and intentional inference; and we shall use the term with this meaning.

This inference may consist of one act of reasoning, or of many. In the latter case we have a course, or train, of reasoning. As the understanding of the single step renders the explanation of a succession of inferences a matter of little difficulty, the philosophy of ratiocination is chiefly concerned with the single step.

A step, or act, of reasoning, when fully stated or expressed, may be called a syllogism. Aristotle says: "A syllogism is a sentence in which, certain things being laid down, something else, different from the premises, necessarily results in consequence of their existence." Here the essential point is, that, something being laid down, or assumed, as true, something else follows, or may be inferred, as true.

Aristotle, indeed, does not speak of a thing, but of things, being laid down, as if inference were always grounded on a plural something. This is to be accounted for by the fact that he formally recognized only those inferences which proceed from two premises. Such has been the influence of Aristotle, that almost all logicians have followed his example in this respect. Of late years, however, particular attention has been given to certain " immediate inferences," in which one fact or truth is inferred from one other; and it seems best that these, as well as all other inferences, when fully stated, in thought or in language, should be called syllogisms.

A necessary

may not inessary consequent.

He

2. The principal point in Aristotle's definition apconsequence plies equally to all forms of inference whatever. says that the conclusion necessarily follows from the things laid down. This is true of every correctly formed syllogism, whether the conclusion be in itself true or not, and whether it set forth something as certainly or necessarily fact, or as being only doubtfully or probably or possibly true. In every case the conclusion follows necessarily from the premises, and must do so as long as the nature of things and the nature of mind remain what they are.

In order to justify this statement, and to free the doctrine of

inference from confusion, a distinction is necessary between what may be termed a convictional and an objectual necessity of consequence. In every correct inference, whether of something necessary, of something contingent, or of something probable, there is a convictional necessity of consequence. The antecedent, or premise being certainly or possibly or probably true, the consequent, or conclusion, must be true also in a corresponding sense. But an inference may be correct without any objectual necessity of consequence. This belongs only to that demonstrative inference which arises from the known or assumed existence of some antecedent of necessity. It does not belong to the inference of the contingent and the probable.

The distinction now made may be stated somewhat inadequately by saying that a necessary consequence does not always involve a necessary consequent. The former of these things belongs to the essential character of every syllogism; the latter to demonstrative reasoning only. Should we say, in contingency, Every middle-aged woman may be a married woman; This woman is middle-aged; therefore

She may be married,

the conclusion would necessarily follow, though it would not be objectually necessary. But should we say,

Every widow has been married;

This woman is a widow;

stating these things for certain, there would not only be a necessary consequence, but also a necessary consequent,

False or in

This woman has been married.

In entire consistency with the doctrine that the correct syllo- conclusion of every syllogism necessarily follows gisms. from the premises, we sometimes speak of false or incorrect syllogisms. In this, by a secondary use of language, that is called a syllogism which has some appearance of being one, while it really is not. Our language is like that of those who call a mere military display a battle- that is, a sham battle because of its outward resemblance to a fight, although the essential elements of a conflict are wanting. In false syllogisms, or inferences, the conclusion does not necessarily follow from the premises.

A threefold

inferences:

3. We shall commence our discussion of ratiocinadivision of tion by making a division of inferences with reference demonstra to the mode of logical connection between antecedent and consequent. A thing is necessarily existent when a logical necessitant of it exists and is included in an

tive, contingent, prob

able.

antecedent; it is a thing contingent or possible when some or many of the elements of that necessitant exist, while none are known to be non-existent; and it is probable when a definite proportion of the chances, or individual possibilities, attending an antecedent of contingency, are seen to include the existence of the consequent.

Inferences, therefore, are those of necessity, of contingency, and of probability; and in each of these modes they may be syllogistically, or formally, expressed. We may say,

Triangle A is equal to triangle B; and

Triangle B is equal to triangle C; therefore
Triangle A is equal to triangle C.

This would be reasoning in necessity. Or we might say,

This figure is a triangle, therefore

It may be equiangular.

This would be reasoning in contingency. Or we might say,

This is one of three individual triangles, of which one is scalene,
one isosceles, and one equilateral; therefore,

with the probability of one in three,

This triangle is equilateral.

The style of reasoning exhibited in inferences of necessity is commonly called demonstrative, or apodeictic; while the other two modes have been classed together as contingent, or probable, reasoning. Of these last two terms, the former is the more ancient designation, and the latter the more modern, for all inference arising from the conception of possibilities.

With Aristotle the contingent syllogism is what logicians now call the probable. Neither he nor they distinguish from each other the modes of reasoning which we have designated by these terms. The conception of contingencies, being a constant and prominent element of probable inference, was thought of only as included in the latter; and the more easily so because the conjecture of contingency seldom takes place without being developed into the conjecture of probability. It is not to be wondered at that one of these inferences was subordinated to the other, and that both were included under one generic name. At the same time the philosophy of thought requires that the contingent and the probable inference should sometimes be distinguished from each other specifically; and should some generic designation be then desired which should leave each of these names to its own proper application, both contingent and probable inference might be included under the title problematic, or conjectural.

In every case of problematic inference a part of an antece

dent of necessity is employed, not of choice, but because the case does not yield a whole antecedent. Therefore, in a certain sense, contingent and probable reasoning may be regarded as imperfect modes of inference, and demonstrative as the perfect mode. But as the incomplete or imperfect is more easily understood after we have obtained a correct conception of the perfect, our attention, in the first instance, must be principally directed to demonstrative reasoning.

Nevertheless, all these modes of inference can, to some extent, be studied together. Since it is the nature of all syllogisms whatever to present an antecedent with which, in some way, the existence of a supposed consequent is naturally connected, we may expect some common relations to pertain to things which are thus generically one. The most important of these relations may be brought to view if we now consider two distinctions which are of an absolutely universal application. 4. The first of these pertains to the subjective categorical, aspect of syllogisms, and sets forth two modes of and suppositive, infer- belief, or forms of assertion, either of which every inference may assume without any change in the thoughts composing it. Using this distinction, we divide syllogisms into the ostensive and the suppositive. The former have truth, or what is taken for truth, as their ground of inference; the latter are expressly based on hypothesis.

Ostensive, or

ence.

This division may be traced to Aristotle, or, at least, may be supported from his writings. He teaches that " every demonstration and every syllogism must show something to be inherent or non-inherent, and this . . . either ostensively or by hypothesis." He describes the ostensive syllogism as one "which commences from confessed theses," and "in which the premises are laid down according to truth;" and he says, "Let us first speak of the ostensive syllogisms; and when these are explained the truth will be clear also in reference to those leading to the impossible, and concerning those by hypothesis generally."

He also shows that the "syllogism ad impossibile," or the reductio ad absurdum, though suppositive, has essentially the same form, or thought-structure, with the ostensive syllogism.

66

It is to be regretted that the writings of Aristotle nowhere fulfil his promise to show hereafter what are the distinctive marks of the hypothetical syllogism, and in how many ways it is produced." We cannot tell whether he included all syllogisms founded on an hypothesis among the hypothetical, or whether he characterized as hypothetical those only which have something additional to their suppositive character. Certainly the