This preliminary inquiry3 we have prosecuted4 to a definite result. Assertion, in the first place, relates either to the meaning of words, or to some property of the things which words signify. Assertions respecting the meaning of words, among which definitions are the most important, hold a place, and an indispensable one, in philosophy; but as the meaning of words is essentially5 arbitrary, this class of assertions are not susceptible6 of truth or falsity, nor therefore of proof or disproof. Assertions respecting Things, or what may be called Real Propositions, in contradistinction to verbal ones, are of various sorts. We have analysed the import of each sort, and have ascertained7 the nature of the things they relate to, and the nature of what they severally assert respecting those things. We found that whatever be the form of the proposition, and whatever its nominal8 subject or predicate, the real subject of every proposition is some one or more facts or phenomena9 of consciousness, or some one or more of the hidden causes or powers to which we ascribe those facts; and that what is predicated or asserted, either in the affirmative or [Pg 176]negative, of those phenomena or those powers, is always either Existence, Order in Place, Order in Time, Causation, or Resemblance. This, then, is the theory of the Import of Propositions, reduced to its ultimate elements: but there is another and a less abstruse10 expression for it, which, though stopping short in an earlier stage of the analysis, is sufficiently11 scientific for many of the purposes for which such a general expression is required. This expression recognises the commonly received distinction between Subject and Attribute, and gives the following as the analysis of the meaning of propositions:—Every Proposition asserts, that some given subject does or does not possess some attribute; or that some attribute is or is not (either in all or in some portion of the subjects in which it is met with) conjoined with some other attribute.
We shall now for the present take our leave of this portion of our inquiry, and proceed to the peculiar12 problem of the Science of Logic, namely, how the assertions, of which we have analysed the import, are proved or disproved; such of them, at least, as, not being amenable13 to direct consciousness or intuition, are appropriate subjects of proof.
We say of a fact or statement, that it is proved, when we believe its truth by reason of some other fact or statement from which it is said to follow. Most of the propositions, whether affirmative or negative, universal, particular, or singular, which we believe, are not believed on their own evidence, but on the ground of something previously14 assented15 to, from which they are said to be inferred. To infer a proposition from a previous proposition or propositions; to give credence16 to it, or claim credence for it, as a conclusion from something else; is to reason, in the most extensive sense of the term. There is a narrower sense, in which the name reasoning is confined to the form of inference which is termed ratiocination17, and of which the syllogism18 is the general type. The reasons for not conforming to this restricted use of the term were stated in an earlier stage of our inquiry, and additional motives19 will be suggested by the considerations on which we are now about to enter.
[Pg 177]
§ 2. In proceeding20 to take into consideration the cases in which inferences can legitimately22 be drawn23, we shall first mention some cases in which the inference is apparent, not real; and which require notice chiefly that they may not be confounded with cases of inference properly so called. This occurs when the proposition ostensibly inferred from another, appears on analysis to be merely a repetition of the same, or part of the same, assertion, which was contained in the first. All the cases mentioned in books of Logic as examples of ?quipollency or equivalence of propositions, are of this nature. Thus, if we were to argue, No man is incapable25 of reason, for every man is rational; or, All men are mortal, for no man is exempt26 from death; it would be plain that we were not proving the proposition, but only appealing to another mode of wording it, which may or may not be more readily comprehensible by the hearer, or better adapted to suggest the real proof, but which contains in itself no shadow of proof.
Another case is where, from an universal proposition, we affect to infer another which differs from it only in being particular: as All A is B, therefore Some A is B: No A is B, therefore Some A is not B. This, too, is not to conclude one proposition from another, but to repeat a second time something which had been asserted at first; with the difference, that we do not here repeat the whole of the previous assertion, but only an indefinite part of it.
A third case is where, the antecedent having affirmed a predicate of a given subject, the consequent affirms of the same subject something already connoted by the former predicate: as, Socrates is a man, therefore Socrates is a living creature; where all that is connoted by living creature was affirmed of Socrates when he was asserted to be a man. If the propositions are negative, we must invert27 their order, thus: Socrates is not a living creature, therefore he is not a man; for if we deny the less, the greater, which includes it, is already denied by implication. These, therefore, are not really cases of inference; and yet the trivial examples by which, in manuals of Logic, the rules of the syllogism are [Pg 178]illustrated, are often of this ill-chosen kind; formal demonstrations28 of conclusions to which whoever understands the terms used in the statement of the data, has already, and consciously, assented.
The most complex case of this sort of apparent inference is what is called the Conversion29 of propositions; which consists in turning the predicate into a subject, and the subject into a predicate, and framing out of the same terms thus reversed, another proposition, which must be true if the former is true. Thus, from the particular affirmative proposition, Some A is B, we may infer that Some B is A. From the universal negative, No A is B, we may conclude that No B is A. From the universal affirmative proposition, All A is B, it cannot be inferred that all B is A; though all water is liquid, it is not implied that all liquid is water; but it is implied that some liquid is so; and hence the proposition, All A is B, is legitimately convertible30 into Some B is A. This process, which converts an universal proposition into a particular, is termed conversion per accidens. From the proposition, Some A is not B, we cannot even infer that some B is not A; though some men are not Englishmen, it does not follow that some Englishmen are not men. The only mode usually recognised of converting a particular negative proposition, is in the form, Some A is not B, therefore, something which is not B is A; and this is termed conversion by contraposition. In this case, however, the predicate and subject are not merely reversed, but one of them is changed. Instead of [A] and [B], the terms of the new proposition are [a thing which is not B], and [A]. The original proposition, Some A is not B, is first changed into a proposition ?quipollent with it, Some A is "a thing which is not B;" and the proposition, being now no longer a particular negative, but a particular affirmative, admits of conversion in the first mode, or as it is called, simple conversion.[1]
[Pg 179]
In all these cases there is not really any inference; there is in the conclusion no new truth, nothing but what was already asserted in the premises31, and obvious to whoever apprehends32 them. The fact asserted in the conclusion is either the very same fact, or part of the fact asserted in the original proposition. This follows from our previous analysis of the Import of Propositions. When we say, for example, that some lawful33 sovereigns are tyrants34, what is the meaning of the assertion? That the attributes connoted by the term "lawful sovereign," and the attributes connoted by the term "tyrant," sometimes coexist in the same individual. Now this is also precisely35 what we mean, when we say that some tyrants are lawful sovereigns; which, therefore, is not a second proposition inferred from the first, any more than the English translation of Euclid's Elements is a collection of theorems different from, and consequences of, those contained in the Greek original. Again, if we assert that no great general is a rash man, we mean that the attributes connoted by "great general," and those connoted 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 "warm-blooded" 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 "warm-blooded" never exist without those connoted by "quadruped," has not been asserted, and cannot be inferred. In order to reassert, in an inverted36 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 derived37, are exactly equivalent, and either of them may be substituted [Pg 180]for the other; for, to say that when the attributes of a quadruped are present, those of a warm-blooded creature are present, is to say that when the latter are absent the former are absent.
In a manual for young students, it would be proper to dwell at greater length on the conversion and ?quipollency of propositions. For, though that cannot be called reasoning or inference which is a mere24 reassertion in different words of what had been asserted before, there is no more important intellectual habit, nor any the cultivation38 of which falls more strictly39 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 treatises40 which relates to the Opposition41 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 contradictory42 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 vice43 versa;[2] 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 intelligible44, would enable the truths which they convey to be [Pg 181]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 maxim45 had ever been laid down, the demonstrations in Euclid would never have halted for any difficulty in stepping across the gap which this axiom at present serves to bridge over. Yet no one has ever censured46 writers on geometry, for placing a list of these elementary generalizations47 at the head of their treatises, as a first exercise to the learner of the faculty49 which will be required in him at every step, that of apprehending50 a general truth. And the student of logic, in the discussion even of such truths as we have cited above, acquires habits of circumspect51 interpretation52 of words, and of exactly measuring the length and breadth of his assertions, which are among the most indispensable conditions of any considerable mental attainment53, and which it is one of the primary objects of logical discipline to cultivate.
§ 3. 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 Induction54, 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 valid55, but is the foundation of both the others.
It is necessary to observe, that the expressions, reasoning [Pg 182]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 adverted56 to) and Ratiocination. The meaning intended by these expressions is, that Induction is inferring a proposition from propositions less general than itself, and Ratiocination is inferring a proposition from propositions equally or more general. When, from the observation of a number of individual instances, we ascend57 to a general proposition, or when, by combining a number of general propositions, we conclude from them another proposition still more general, the process, which is substantially the same in both instances, is called Induction. When from a general proposition, not alone (for from a single proposition nothing can be concluded which is not involved in the terms), but by combining 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.
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 advantageous58, 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 derivative59 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 superseding60 the necessity of any further justification61 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 embody62 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 generalization48 grounded on those cases, and expressive63 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 legitimate21, 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 certified64 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, remains65 to be determined66 by the examination into which we are about to enter.
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1
discriminate
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| v.区别，辨别，区分；有区别地对待 | |
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logic
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| n.逻辑(学)；逻辑性 | |
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inquiry
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| n.打听，询问，调查，查问 | |
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prosecuted
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| a.被起诉的 | |
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essentially
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| adv.本质上，实质上，基本上 | |
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susceptible
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| adj.过敏的，敏感的；易动感情的，易受感动的 | |
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7
ascertained
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| v.弄清，确定，查明( ascertain的过去式和过去分词 ) | |
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8
nominal
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| adj.名义上的；(金额、租金)微不足道的 | |
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phenomena
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| n.现象 | |
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abstruse
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| adj.深奥的，难解的 | |
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sufficiently
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| adv.足够地，充分地 | |
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peculiar
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| adj.古怪的，异常的；特殊的，特有的 | |
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amenable
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| adj.经得起检验的；顺从的；对负有义务的 | |
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previously
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| adv.以前，先前（地） | |
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assented
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| 同意，赞成( assent的过去式和过去分词 ) | |
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credence
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| n.信用，祭器台，供桌，凭证 | |
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ratiocination
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| n.推理；推断 | |
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syllogism
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| n.演绎法，三段论法 | |
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motives
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| n.动机，目的( motive的名词复数 ) | |
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proceeding
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| n.行动，进行，(pl.)会议录，学报 | |
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legitimate
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| adj.合法的，合理的，合乎逻辑的；v.使合法 | |
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legitimately
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| ad.合法地；正当地，合理地 | |
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drawn
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| v.拖，拉，拔出；adj.憔悴的，紧张的 | |
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mere
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| adj.纯粹的；仅仅，只不过 | |
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incapable
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| adj.无能力的，不能做某事的 | |
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exempt
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| adj.免除的；v.使免除；n.免税者，被免除义务者 | |
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invert
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| vt.使反转，使颠倒，使转化 | |
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demonstrations
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| 证明( demonstration的名词复数 )； 表明； 表达； 游行示威 | |
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conversion
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| n.转化，转换，转变 | |
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convertible
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| adj.可改变的，可交换，同意义的；n.有活动摺篷的汽车 | |
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premises
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| n.建筑物，房屋 | |
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apprehends
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| 逮捕，拘押( apprehend的第三人称单数 )； 理解 | |
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lawful
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| adj.法律许可的，守法的，合法的 | |
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tyrants
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| 专制统治者( tyrant的名词复数 )； 暴君似的人； （古希腊的）僭主； 严酷的事物 | |
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precisely
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| adv.恰好，正好，精确地，细致地 | |
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inverted
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| adj.反向的，倒转的v.使倒置，使反转( invert的过去式和过去分词 ) | |
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derived
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| vi.起源；由来；衍生；导出v.得到( derive的过去式和过去分词 )；（从…中）得到获得；源于；（从…中）提取 | |
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cultivation
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| n.耕作，培养，栽培（法），养成 | |
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strictly
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| adv.严厉地，严格地；严密地 | |
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treatises
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| n.专题著作，专题论文，专著( treatise的名词复数 ) | |
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opposition
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| n.反对，敌对 | |
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contradictory
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| adj.反驳的，反对的，抗辩的；n.正反对，矛盾对立 | |
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vice
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| n.坏事；恶习；[pl.]台钳，老虎钳；adj.副的 | |
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intelligible
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| adj.可理解的，明白易懂的，清楚的 | |
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maxim
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| n.格言，箴言 | |
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46
censured
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| v.指责，非难，谴责( censure的过去式 ) | |
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generalizations
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| 一般化( generalization的名词复数 )； 普通化； 归纳； 概论 | |
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48
generalization
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| n.普遍性，一般性，概括 | |
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49
faculty
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| n.才能；学院，系；(学院或系的)全体教学人员 | |
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50
apprehending
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| 逮捕，拘押( apprehend的现在分词 )； 理解 | |
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51
circumspect
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| adj.慎重的，谨慎的 | |
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52
interpretation
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| n.解释，说明，描述；艺术处理 | |
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53
attainment
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| n.达到，到达；［常pl.］成就，造诣 | |
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54
induction
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| n.感应，感应现象 | |
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valid
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| adj.有确实根据的；有效的；正当的，合法的 | |
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56
adverted
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| 引起注意（advert的过去式与过去分词形式） | |
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57
ascend
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| vi.渐渐上升，升高；vt.攀登，登上 | |
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58
advantageous
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| adj.有利的；有帮助的 | |
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59
derivative
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| n.派(衍)生物；adj.非独创性的，模仿他人的 | |
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superseding
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| 取代，接替( supersede的现在分词 ) | |
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justification
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| n.正当的理由；辩解的理由 | |
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embody
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| vt.具体表达，使具体化；包含，收录 | |
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expressive
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| adj.表现的，表达…的，富于表情的 | |
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certified
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| a.经证明合格的；具有证明文件的 | |
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remains
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| n.剩余物，残留物；遗体，遗迹 | |
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determined
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| adj.坚定的；有决心的 | |
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