by "rash," never coexist in the same subject; which is also the exact meaning which would be expressed by saying, that no rash man is a great general. When we say that all quadrupeds are warm-blooded, we assert, not only that the attributes connoted by "quadruped" and those connoted by "warmblooded" sometimes coexist, but that the former never exist without the latter: now the proposition, Some warm-blooded creatures are quadrupeds, expresses the first half of this meaning, dropping the latter half and therefore has been already affirmed in the antecedent proposition, All quadrupeds are warm-blooded. But that all warm-blooded creatures are quadrupeds, or, in other words, that the attributes connoted by warmblooded" never exist without those connoted by "quadruped," has not been asserted, and cannot be inferred. In order to reassert, in an inverted form, the whole of what was affirmed in the proposition, All quadrupeds are warm-blooded, we must convert it by contraposition, thus, Nothing which is not warm-blooded is a quadruped. This proposition, and the one from which it is derived, are exactly equivalent, and either of them may be substituted for the other; for, to say that when the attributes of a quadruped are present, those of a warmblooded creature are present, is to say that when the latter are absent the former are absent. 66 asserted before, there is no more important intellectual habit, nor any the cultivation of which falls more strictly within the province of the art of logic, than that of discerning rapidly and surely the identity of an assertion when disguised under diversity of language. That important chapter in logical treatises which relates to the Opposition of Propositions, and the excellent technical language which logic provides for distinguishing the different kinds or modes of opposition, are of use chiefly for this purpose. Such considerations as these, that contrary propositions may both be false, but cannot both be true; that subcontrary propositions may both be true, but cannot both be false; that of two contradictory propositions one must be true and the other false; that of two subalternate propositions the truth of the universal proves the truth of the particular, and the falsity of the particular proves the falsity of the universal, but not vice versâ ; are apt to appear, at first sight, very technical and mysterious, but when explained, seem almost too obvious to require so formal a statement, since the same amount of explanation which is necessary to make the principles intelligible, would enable the truths which they convey to be apprehended in any particular case which can occur. In this respect, however, these axioms of logic are on a level with those of mathematics. * That things which are equal to the same thing are equal to one another, is as obvious in any particular case as it is in the general statement; and if no such general maxim had ever been laid down, the demonstrations in Euclid would never have halted for any difficulty in stepping across the subcontraries. Some A is not Bcontradictories. No A is B) Some A is B All A is B Some A is B gap which this axiom at present serves | The meaning intended by these exto bridge over. Yet no one has ever pressions is, that Induction is inferring censured writers on geometry for a proposition from propositions less placing a list of these elementary general than itself, and Ratiocination generalisations at the head of their is inferring a proposition from propositreatises, as a first exercise to the tions equally or more general. When, learner of the faculty which will be from the observation of a number of required in him at every step, that of individual instances, we ascend to a apprehending a general truth. And general proposition, or when, by com. the student of logic, in the discussion bining a number of general proposieven of such truths as we have cited tions, we conclude from them another above, acquires habits of circumspect proposition still more general, the prointerpretation of words, and of exactly cess, which is substantially the same measuring the length and breadth of in both instances, is called Induction. his assertions, which are among the When from a general proposition, not most indispensable conditions of any alone (for from a single proposition considerable mental attainment, and nothing can be concluded which is not which it is one of the primary objects involved in the terms), but by combinof logical discipline to cultivate. ing it with other propositions, we infer a proposition of the same degree of generality with itself, or a less general proposition, or a proposition merely individual, the process is Ratiocination. When, in short, the conclusion is more general than the largest of the premises, the argument is commonly called Induction; when less general, or equally general, it is Ratiocination. 83. Having noticed, in order to exclude from the province of Reasoning or Inference properly so called, the cases in which the progression from one truth to another is only apparent, the logical consequent being a mere repetition of the logical antecedent; we now pass to those which are cases of inference in the proper acceptation of the term, those in which we set out from known truths, to arrive at others really distinct from them. Reasoning, in the extended sense in which I use the term, and in which it is synonymous with Inference, is popularly said to be of two kinds : reasoning from particulars to generals, and reasoning from generals to particulars; the former being called Induction, the latter Ratiocination or Syllogism. It will presently be shown that there is a third species of reasoning, which falls under neither of these descriptions, and which, nevertheless, is not only valid, but is the foundation of both the others. It is necessary to observe, that the expressions, reasoning from particulars to generals, and reasoning from generals to particulars, are recommended by brevity rather than by precision, and do not adequately mark, without the aid of a commentary, the distinction between Induction (in the sense now adverted to) and Ratiocination. As all experience begins with individual cases, and proceeds from them to generals, it might seem most conformable to the natural order of thought that Induction should be treated of before we touch upon Ratiocination. It will, however, be advantageous, in a science which aims at tracing our acquired knowledge to its sources, that the inquirer should commence with the latter rather than with the earlier stages of the process of constructing our knowledge; and should trace derivative truths backward to the truths from which they are deduced, and on which they depend for their evidence, before attempting to point out the original spring from which both ultimately take their rise. The advantages of this order of proceeding in the present instance will manifest themselves as we advance, in a manner superseding the necessity of any further justification or explanation. Of Induction, therefore, we shall say no more at present, than that it at least is, without doubt, a process of real inference. The conclusion in an induction embraces more than is contained in the premises. The principle or law collected from particular instances, the general proposition in which we embody the result of our experience, covers a much larger extent of ground than the individual experiments which form its basis. A principle ascertained by experience is more than a mere summing up of what has been specifically observed in the individual cases which have been examined; it is a generalisation grounded on those cases, and expressive of our belief that what we there found true is true in an indefinite number of cases which we have not examined, and are never likely to examine. The nature and grounds of this inference, and the conditions necessary to make it legitimate, will be the subject of discussion in the Third Book: but that such inference really takes place is not susceptible of question. In every induction we proceed from truths which we knew to truths which we did not know; from facts certified by observation to facts which we have not observed, and even to facts not capable of being now observed; future facts, for example; but which we do not hesitate to believe on the sole evidence of the induction itself. Induction, then, is a real process of Reasoning or Inference. Whether, and in what sense, as much can be said of the Syllogism, remains to be determined by the examination into which we are about to enter. CHAPTER II. A OF RATIOCINATION, OR SYLLOGISM. § 1. THE analysis of the Syllogism has been so accurately and fully performed in the common manuals of Logic, that in the present work, which is not designed as a manual, it is sufficient to recapitulate, memorice causâ, the leading results of that analysis, as a foundation for the remarks to be afterwards made on the functions of the Syllogism, and the place which it holds in science. To a legitimate syllogism it is essential that there should be three, and no more than three, propositions, namely, the conclusion, or proposition to be proved, and two other propositions which together prove it, and which are called the premises. It is essential that there should be three, and no more than three, terms, namely, the subject and predicate of the conclusion, and another called the middle term, which must be found in both premises, since it is by means of it that the other two terms are to be connected together. The predicate of the conclusion is called the major term of the syllogism; the subject of the conclusion is called the minor term. As there can be but three terms, the major and minor terms must each be found in one, and only one of the premises, together with the middle term which is in them both. The premise which contains the middle term and the major term is called the major premise; that which contains the middle term and the minor term is called the minor premise. Syllogisms are divided by some logicians into three figures, by others into four, according to the position of the middle term, which may either be the subject in both premises, the predicate in both, or the subject in one and the predicate in the other. The most common case is that in which the middle term is the subject of the major premise and the predicate of the minor. This is reckoned as the first figure. When the middle term is the predicate in both premises, the syllogism belongs to the second figure; when it is the subject in both, to the third. In the fourth figure the middle term is the subject of the minor premise and the predicate of the major. Those writers who reckon no more than three figures include this case in the first. : Each figure is divided into moods, of all the legitimate moods, that is according to what are called the all those in which the conclusion corquantity and quality of the proposi-rectly follows from the premises. A tions, that is, according as they are is the minor term, C the major, B the universal or particular, affirmative or middle term. negative. The following are examples In these exemplars, or blank forms for making syllogisms, no place is assigned to singular propositions; not, of course, because such propositions are not used in ratiocination, but because, their predicate being affirmed or denied of the whole of the subject, they are ranked, for the purposes of the syllogism, with universal propositions. Thus, these two syllogisms-All men are mortal, All men are mortal, All kings are men, Socrates is a man, therefore therefore All kings are mortal, Socrates is mortal, are arguments precisely similar, and are both ranked in the first mood of the first figure.* * Professor Bain denies the claim of Singular Propositions to be classed, for the purposes of ratiocination, with Universal; though they come within the designation which he himself proposes as an equivalent for Universal. that of Total. He would even, to use his own expression, banish them entirely from the syllogism. takes as an example, He No C is B All B is A therefore Some A is not C No C is B Some B is A therefore Some A is not C The reasons why syllogisms in any of the above forms are legitimate, that is, why, if the premises are true, the conclusion must inevitably be so, and why this is not the case in any other possible mood, (that is, in any other combination of universal and particular, affirmative and negative propositions,) any person taking interest in these inquiries may be presumed to have either learned from the common school-books of the syllogistic logic, or to be capable of discovering for himself. The reader may, however, be referred for every needful explanation to Archbishop Whately's Elements of Logic, where he will find stated with philosophical precision, and explained with remarkable perspicuity, the whole of the common doctrine of the syllogism. All valid ratiocination, all reasoning by which, from general propositions previously admitted, other propositions equally or less general are inferred, may be exhibited in some of the above forms. The whole of Euclid, for example, inight be thrown without difficulty into a series of syllogisms, regular in mood and figure. Though a syllogism framed according to any of these formulæ is a valid argument, all correct ratiocination admits of being stated in syllogisms wise, poor, and a man, and we merely repeat the concurrence which is selected from the whole aggregate of properties making up the whole, Socrates. The case is one under the head Greater and Less Connotation' in Equivalent Propositional Forms, or Immediate Inference. "But the example in this form does not do justice to the syllogism of singulars. We must suppose both propositions to be real, the predicates being in no way involved in the subject. Thus Socrates was the master of Plato, The master of Plato fought at Delium. "It may fairly be doubted whether the transitions, in this instance, are anything more than equivalent forms. For the proposition 'Socrates was the master of Plato and fought at Delium,' compounded out of the two premises, is obviously nothing more than a grammatical abbreviation. No one can say that there is here any change of meaning, or anything beyond a verbal modification of the original form. The next step is, 'The master of Plato fought at Delium,' which is the previous statement cut down by the omission of Socrates. It contents itself with reproducing a part of the meaning, or saying less than had been previously said. The full equivalent of the affirmation is, "The master of Plato fought at Delium, and the master of Plato was Soerates:' the new form omits the last piece of information, and gives only the first. Now, we never consider that we have made a real inference, a step in advance, when we repeat less than we are entitled to say, or drop from a complex statement some portion not desired at the moment. Such an operation keeps strictly within the domain of equivalence, or Immediate Inference. In no way, therefore, can a syllogism with two singular premises be viewed as a genuine syllogistic or deductive inference" (Logic, i. 159). The first argument, as will have been of the first figure alone. The rules The pro may be reduced as follows. The second part of Mr. Bain's argument, All bees are insects, therefore Some insects are intelligent: one might use the same liberty taken by Mr. Bain, of joining together the two premises as if they were one-" All bees are insects and intelligent"-and might say that in omitting the middle term bees we make no real inference, but merely reproduce part of what had been previously said. Mr. Bain's is really an objection to the syllogism itself, or at all events to the third figure: it has no special applicability to singular propositions. Note to § 4 of the chapter on Definition, supra, p. 92. |