Logicians have been remarkably7 unanimous in their mode of answering this question. It is universally allowed that a syllogism is vicious if there be anything more in the conclusion than was assumed in the premises9. But this is, in fact, to say, that nothing ever was, or can be, proved by syllogism, which was not known, or assumed to be known, before. Is ratiocination10, then, not a process of inference? And is the syllogism, to which the word reasoning has so often been represented to be exclusively appropriate, not really entitled to be called reasoning at all? This seems an inevitable11 consequence of the doctrine12, admitted by all writers on the subject, that a syllogism can prove no more than is involved in the premises. Yet the acknowledgment so explicitly13 made, has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths, whether of science or of daily life, which we believe; while those who have avoided this inconsistency, and followed out the general theorem respecting the logical value [Pg 203]of the syllogism to its legitimate16 corollary, have been led to impute17 uselessness and frivolity18 to the syllogistic theory itself, on the ground of the petitio principii which they allege19 to be inherent in every syllogism. As I believe both these opinions to be fundamentally erroneous, I must request the attention of the reader to certain considerations, without which any just appreciation20 of the true character of the syllogism, and the functions it performs in philosophy, appears to me impossible; but which seem to have been either overlooked, or insufficiently22 adverted24 to, both by the defenders25 of the syllogistic theory and by its assailants.
§ 2. It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say,
All men are mortal,
Socrates is a man,
therefore
Socrates is mortal;
it is unanswerably urged by the adversaries26 of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general assumption, All men are mortal: that we cannot be assured of the mortality of all men, unless we are already certain of the mortality of every individual man: that if it be still doubtful whether Socrates, or any other individual we choose to name, be mortal or not, the same degree of uncertainty27 must hang over the assertion, All men are mortal: that the general principle, instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it, is dispelled28 by evidence aliundè; and then what remains29 for the syllogism to prove? That, in short, no reasoning from generals to particulars can, as such, prove anything: since from a general principle we cannot infer any particulars, but those which the principle itself assumes as known.
This doctrine appears to me irrefragable; and if logicians, [Pg 204]though unable to dispute it, have usually exhibited a strong disposition30 to explain it away, this was not because they could discover any flaw in the argument itself, but because the contrary opinion seemed to rest on arguments equally indisputable. In the syllogism last referred to, for example, or in any of those which we previously31 constructed, is it not evident that the conclusion may, to the person to whom the syllogism is presented, be actually and bona fide a new truth? Is it not matter of daily experience that truths previously unthought of, facts which have not been, and cannot be, directly observed, are arrived at by way of general reasoning? We believe that the Duke of Wellington is mortal. We do not know this by direct observation, so long as he is not yet dead. If we were asked how, this being the case, we know the duke to be mortal, we should probably answer, Because all men are so. Here, therefore, we arrive at the knowledge of a truth not (as yet) susceptible32 of observation, by a reasoning which admits of being exhibited in the following syllogism:—
All men are mortal,
The Duke of Wellington is a man,
therefore
The Duke of Wellington is mortal.
And since a large portion of our knowledge is thus acquired, logicians have persisted in representing the syllogism as a process of inference or proof; though none of them has cleared up the difficulty which arises from the inconsistency between that assertion, and the principle, that if there be anything in the conclusion which was not already asserted in the premises, the argument is vicious. For it is impossible to attach any serious scientific value to such a mere33 salvo, as the distinction drawn34 between being involved by implication in the premises, and being directly asserted in them. When Archbishop Whately says[7] that the object of reasoning is "merely to expand and unfold the assertions wrapt up, as it were, and implied in those with which we set out, and to bring a person [Pg 205]to perceive and acknowledge the full force of that which he has admitted," he does not, I think, meet the real difficulty requiring to be explained, namely, how it happens that a science, like geometry, can be all "wrapt up" in a few definitions and axioms. Nor does this defence of the syllogism differ much from what its assailants urge against it as an accusation35, when they charge it with being of no use except to those who seek to press the consequences of an admission into which a person has been entrapped36 without having considered and understood its full force. When you admitted the major premise8, you asserted the conclusion; but, says Archbishop Whately, you asserted it by implication merely: this, however, can here only mean that you asserted it unconsciously; that you did not know you were asserting it; but, if so, the difficulty revives in this shape—Ought you not to have known? Were you warranted in asserting the general proposition without having satisfied yourself of the truth of everything which it fairly includes? And if not, is not the syllogistic art prima facie what its assailants affirm it to be, a contrivance for catching37 you in a trap, and holding you fast in it?[8]
§ 3. From this difficulty there appears to be but one issue. The proposition that the Duke of Wellington is mortal, is evidently an inference; it is got at as a conclusion [Pg 206]from something else; but do we, in reality, conclude it from the proposition, All men are mortal? I answer, no.
The error committed is, I conceive, that of overlooking the distinction between two parts of the process of philosophizing, the inferring part, and the registering part; and ascribing to the latter the functions of the former. The mistake is that of referring a person to his own notes for the origin of his knowledge. If a person is asked a question, and is at the moment unable to answer it, he may refresh his memory by turning to a memorandum38 which he carries about with him. But if he were asked, how the fact came to his knowledge, he would scarcely answer, because it was set down in his note-book: unless the book was written, like the Koran, with a quill39 from the wing of the angel Gabriel.
Assuming that the proposition, The Duke of Wellington is mortal, is immediately an inference from the proposition, All men are mortal; whence do we derive40 our knowledge of that general truth? Of course from observation. Now, all which man can observe are individual cases. From these all general truths must be drawn, and into these they may be again resolved; for a general truth is but an aggregate41 of particular truths; a comprehensive expression, by which an indefinite number of individual facts are affirmed or denied at once. But a general proposition is not merely a compendious42 form for recording43 and preserving in the memory a number of particular facts, all of which have been observed. Generalization44 is not a process of mere naming, it is also a process of inference. From instances which we have observed, we feel warranted in concluding, that what we found true in those instances, holds in all similar ones, past, present, and future, however numerous they may be. We then, by that valuable contrivance of language which enables us to speak of many as if they were one, record all that we have observed, together with all that we infer from our observations, in one concise45 expression; and have thus only one proposition, instead of an endless number, to remember or to communicate. The results of many observations and [Pg 207]inferences, and instructions for making innumerable inferences in unforeseen cases, are compressed into one short sentence.
When, therefore, we conclude from the death of John and Thomas, and every other person we ever heard of in whose case the experiment had been fairly tried, that the Duke of Wellington is mortal like the rest; we may, indeed, pass through the generalization, All men are mortal, as an intermediate stage; but it is not in the latter half of the process, the descent from all men to the Duke of Wellington, that the inference resides. The inference is finished when we have asserted that all men are mortal. What remains to be performed afterwards is merely decyphering our own notes.
Archbishop Whately has contended that syllogizing, or reasoning from generals to particulars, is not, agreeably to the vulgar idea, a peculiar46 mode of reasoning, but the philosophical47 analysis of the mode in which all men reason, and must do so if they reason at all. With the deference48 due to so high an authority, I cannot help thinking that the vulgar notion is, in this case, the more correct. If, from our experience of John, Thomas, &c., who once were living, but are now dead, we are entitled to conclude that all human beings are mortal, we might surely without any logical inconsequence have concluded at once from those instances, that the Duke of Wellington is mortal. The mortality of John, Thomas, and company is, after all, the whole evidence we have for the mortality of the Duke of Wellington. Not one iota49 is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical form into which we choose to throw it can make greater than it is; and since that evidence is either sufficient in itself, or, if insufficient21 for the one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the shortest cut from these sufficient premises to the conclusion, and constrained50 to travel the "high priori road," by the arbitrary fiat51 of logicians. I cannot perceive why it should be impossible [Pg 208]to journey from one place to another unless we "march up a hill, and then march down again." It may be the safest road, and there may be a resting-place at the top of the hill, affording a commanding view of the surrounding country; but for the mere purpose of arriving at our journey's end, our taking that road is perfectly52 optional; it is a question of time, trouble, and danger.
Not only may we reason from particulars to particulars without passing through generals, but we perpetually do so reason. All our earliest inferences are of this nature. From the first dawn of intelligence we draw inferences, but years elapse before we learn the use of general language. The child, who, having burnt his fingers, avoids to thrust them again into the fire, has reasoned or inferred, though he has never thought of the general maxim53, Fire burns. He knows from memory that he has been burnt, and on this evidence believes, when he sees a candle, that if he puts his finger into the flame of it, he will be burnt again. He believes this in every case which happens to arise; but without looking, in each instance, beyond the present case. He is not generalizing; he is inferring a particular from particulars. In the same way, also, brutes55 reason. There is no ground for attributing to any of the lower animals the use of signs, of such a nature as to render general propositions possible. But those animals profit by experience, and avoid what they have found to cause them pain, in the same manner, though not always with the same skill, as a human creature. Not only the burnt child, but the burnt dog, dreads56 the fire.
I believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims57 handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition. We are constantly reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to erect58 our observations into general maxims of human or external nature. When we conclude that some person will, on some given occasion, feel or act so and so, we sometimes [Pg 209]judge from an enlarged consideration of the manner in which human beings in general, or persons of some particular character, are accustomed to feel and act: but much oftener from merely recollecting59 the feelings and conduct of the same person in some previous instance, or from considering how we should feel or act ourselves. It is not only the village matron, who, when called to a consultation60 upon the case of a neighbour's child, pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her Lucy. We all, where we have no definite maxims to steer61 by, guide ourselves in the same way: and if we have an extensive experience, and retain its impressions strongly, we may acquire in this manner a very considerable power of accurate judgment62, which we may be utterly63 incapable64 of justifying65 or of communicating to others. Among the higher order of practical intellects there have been many of whom it was remarked how admirably they suited their means to their ends, without being able to give any sufficient reasons for what they did; and applied66, or seemed to apply, recondite67 principles which they were wholly unable to state. This is a natural consequence of having a mind stored with appropriate particulars, and having been long accustomed to reason at once from these to fresh particulars, without practising the habit of stating to oneself or to others the corresponding general propositions. An old warrior68, on a rapid glance at the outlines of the ground, is able at once to give the necessary orders for a skilful69 arrangement of his troops; though if he has received little theoretical instruction, and has seldom been called upon to answer to other people for his conduct, he may never have had in his mind a single general theorem respecting the relation between ground and array. But his experience of encampments, in circumstances more or less similar, has left a number of vivid, unexpressed, ungeneralized analogies in his mind, the most appropriate of which, instantly suggesting itself, determines him to a judicious70 arrangement.
The skill of an uneducated person in the use of weapons, [Pg 210]or of tools, is of a precisely71 similar nature. The savage72 who executes unerringly the exact throw which brings down his game, or his enemy, in the manner most suited to his purpose, under the operation of all the conditions necessarily involved, the weight and form of the weapon, the direction and distance of the object, the action of the wind, &c., owes this power to a long series of previous experiments, the results of which he certainly never framed into any verbal theorems or rules. The same thing may generally be said of any other extraordinary manual dexterity73. Not long ago a Scotch74 manufacturer procured75 from England, at a high rate of wages, a working dyer, famous for producing very fine colours, with the view of teaching to his other workmen the same skill. The workman came; but his mode of proportioning the ingredients, in which lay the secret of the effects he produced, was by taking them up in handfuls, while the common method was to weigh them. The manufacturer sought to make him turn his handling system into an equivalent weighing system, that the general principle of his peculiar mode of proceeding76 might be ascertained77. This, however, the man found himself quite unable to do, and therefore could impart his skill to nobody. He had, from the individual cases of his own experience, established a connexion in his mind between fine effects of colour, and tactual perceptions in handling his dyeing materials; and from these perceptions he could, in any particular case, infer the means to be employed, and the effects which would be produced, but could not put others in possession of the grounds on which he proceeded, from having never generalized them in his own mind, or expressed them in language.
Almost every one knows Lord Mansfield's advice to a man of practical good sense, who, being appointed governor of a colony, had to preside in its court of justice, without previous judicial79 practice or legal education. The advice was to give his decision boldly, for it would probably be right; but never to venture on assigning reasons, for they would almost infallibly be wrong. In cases like this, which are of no uncommon80 occurrence, it would be absurd to suppose [Pg 211]that the bad reason was the source of the good decision. Lord Mansfield knew that if any reason were assigned it would be necessarily an afterthought, the judge being in fact guided by impressions from past experience, without the circuitous81 process of framing general principles from them, and that if he attempted to frame any such he would assuredly fail. Lord Mansfield, however, would not have doubted that a man of equal experience who had also a mind stored with general propositions derived82 by legitimate induction83 from that experience, would have been greatly preferable as a judge, to one, however sagacious, who could not be trusted with the explanation and justification84 of his own judgments85. The cases of men of talent performing wonderful things they know not how, are examples of the rudest and most spontaneous form of the operations of superior minds. It is a defect in them, and often a source of errors, not to have generalized as they went on; but generalization, though a help, the most important indeed of all helps, is not an essential.
Even the scientifically instructed, who possess, in the form of general propositions, a systematic86 record of the results of the experience of mankind, need not always revert87 to those general propositions in order to apply that experience to a new case. It is justly remarked by Dugald Stewart, that though the reasonings in mathematics depend entirely88 on the axioms, it is by no means necessary to our seeing the conclusiveness of the proof, that the axioms should be expressly adverted to. When it is inferred that AB is equal to CD because each of them is equal to EF, the most uncultivated understanding, as soon as the propositions were understood, would assent89 to the inference, without having ever heard of the general truth that "things which are equal to the same thing are equal to one another." This remark of Stewart, consistently followed out, goes to the root, as I conceive, of the philosophy of ratiocination; and it is to be regretted that he himself stopt short at a much more limited application of it. He saw that the general propositions on which a reasoning is said to depend, may, in certain cases, be altogether omitted, without impairing90 [Pg 212]its probative force. But he imagined this to be a peculiarity91 belonging to axioms; and argued from it, that axioms are not the foundations or first principles of geometry, from which all the other truths of the science are synthetically92 deduced (as the laws of motion and of the composition of forces in dynamics93, the equal mobility94 of fluids in hydrostatics, the laws of reflection and refraction in optics, are the first principles of those sciences); but are merely necessary assumptions, self-evident indeed, and the denial of which would annihilate95 all demonstration96, but from which, as premises, nothing can be demonstrated. In the present, as in many other instances, this thoughtful and elegant writer has perceived an important truth, but only by halves. Finding, in the case of geometrical axioms, that general names have not any talismanic97 virtue98 for conjuring99 new truths out of the well where they lie hid, and not seeing that this is equally true in every other case of generalization, he contended that axioms are in their nature barren of consequences, and that the really fruitful truths, the real first principles of geometry, are the definitions; that the definition, for example, of the circle is to the properties of the circle, what the laws of equilibrium100 and of the pressure of the atmosphere are to the rise of the mercury in the Torricellian tube. Yet all that he had asserted respecting the function to which the axioms are confined in the demonstrations101 of geometry, holds equally true of the definitions. Every demonstration in Euclid might be carried on without them. This is apparent from the ordinary process of proving a proposition of geometry by means of a diagram. What assumption, in fact, do we set out from, to demonstrate by a diagram any of the properties of the circle? Not that in all circles the radii102 are equal, but only that they are so in the circle ABC. As our warrant for assuming this, we appeal, it is true, to the definition of a circle in general; but it is only necessary that the assumption be granted in the case of the particular circle supposed. From this, which is not a general but a singular proposition, combined with other propositions of a similar kind, some of which when generalized are called definitions, and others axioms, we prove that a certain conclusion is true, not of all circles, but [Pg 213]of the particular circle ABC; or at least would be so, if the facts precisely accorded with our assumptions. The enunciation103, as it is called, that is, the general theorem which stands at the head of the demonstration, is not the proposition actually demonstrated. One instance only is demonstrated: but the process by which this is done, is a process which, when we consider its nature, we perceive might be exactly copied in an indefinite number of other instances; in every instance which conforms to certain conditions. The contrivance of general language furnishing us with terms which connote these conditions, we are able to assert this indefinite multitude of truths in a single expression, and this expression is the general theorem. By dropping the use of diagrams, and substituting, in the demonstrations, general phrases for the letters of the alphabet, we might prove the general theorem directly, that is, we might demonstrate all the cases at once; and to do this we must, of course, employ as our premises, the axioms and definitions in their general form. But this only means, that if we can prove an individual conclusion by assuming an individual fact, then in whatever case we are warranted in making an exactly similar assumption, we may draw an exactly similar conclusion. The definition is a sort of notice to ourselves and others, what assumptions we think ourselves entitled to make. And so in all cases, the general propositions, whether called definitions, axioms, or laws of nature, which we lay down at the beginning of our reasonings, are merely abridged104 statements, in a kind of short-hand, of the particular facts, which, as occasion arises, we either think we may proceed on as proved, or intend to assume. In any one demonstration it is enough if we assume for a particular case suitably selected, what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise. The definition of the circle, therefore, is to one of Euclid's demonstrations, exactly what, according to Stewart, the axioms are; that is, the demonstration does not depend on it, but yet if we deny it the demonstration fails. The proof does not rest on the general assumption, but on a similar assumption confined to the particular case: that case, however, [Pg 214]being chosen as a specimen105 or paradigm106 of the whole class of cases included in the theorem, there can be no ground for making the assumption in that case which does not exist in every other; and to deny the assumption as a general truth, is to deny the right of making it in the particular instance.
There are, undoubtedly107, the most ample reasons for stating both the principles and the theorems in their general form, and these will be explained presently, so far as explanation is requisite108. But, that unpractised learners, even in making use of one theorem to demonstrate another, reason rather from particular to particular than from the general proposition, is manifest from the difficulty they find in applying a theorem to a case in which the configuration109 of the diagram is extremely unlike that of the diagram by which the original theorem was demonstrated. A difficulty which, except in cases of unusual mental power, long practice can alone remove, and removes chiefly by rendering110 us familiar with all the configurations111 consistent with the general conditions of the theorem.
§ 4. From the considerations now adduced, the following conclusions seem to be established. All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formul? for making more: The major premise of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or premise, being the particular facts from which the general proposition was collected by induction. Those facts, and the individual instances which supplied them, may have been forgotten: but a record remains, not indeed descriptive of the facts themselves, but showing how those cases may be distinguished112, respecting which the facts, when known, were considered to warrant a given inference. According to the indications of this record we draw our conclusion; which is, to all intents and purposes, a conclusion from the forgotten facts. [Pg 215]For this it is essential that we should read the record correctly: and the rules of the syllogism are a set of precautions to ensure our doing so.
This view of the functions of the syllogism is confirmed by the consideration of precisely those cases which might be expected to be least favourable113 to it, namely, those in which ratiocination is independent of any previous induction. We have already observed that the syllogism, in the ordinary course of our reasoning, is only the latter half of the process of travelling from premises to a conclusion. There are, however, some peculiar cases in which it is the whole process. Particulars alone are capable of being subjected to observation; and all knowledge which is derived from observation, begins, therefore, of necessity, in particulars; but our knowledge may, in cases of certain descriptions, be conceived as coming to us from other sources than observation. It may present itself as coming from testimony114, which, on the occasion and for the purpose in hand, is accepted as of an authoritative115 character: and the information thus communicated, may be conceived to comprise not only particular facts but general propositions, as when a scientific doctrine is accepted without examination on the authority of writers, or a theological doctrine on that of Scripture116. Or the generalization may not be, in the ordinary sense, an assertion at all, but a command; a law, not in the philosophical, but in the moral and political sense of the term: an expression of the desire of a superior, that we, or any number of other persons, shall conform our conduct to certain general instructions. So far as this asserts a fact, namely, a volition117 of the legislator, that fact is an individual fact, and the proposition, therefore, is not a general proposition. But the description therein contained of the conduct which it is the will of the legislator that his subjects should observe, is general. The proposition asserts, not that all men are anything, but that all men shall do something.
In both these cases the generalities are the original data, and the particulars are elicited118 from them by a process which correctly resolves itself into a series of syllogisms. The real nature, however, of the supposed deductive process, is evident [Pg 216]enough. The only point to be determined119 is, whether the authority which declared the general proposition, intended to include this case in it; and whether the legislator intended his command to apply to the present case among others, or not. This is ascertained by examining whether the case possesses the marks by which, as those authorities have signified, the cases which they meant to certify120 or to influence may be known. The object of the inquiry121 is to make out the witness's or the legislator's intention, through the indication given by their words. This is a question, as the Germans express it, of hermeneutics. The operation is not a process of inference, but a process of interpretation122.
In this last phrase we have obtained an expression which appears to me to characterize, more aptly than any other, the functions of the syllogism in all cases. When the premises are given by authority, the function of Reasoning is to ascertain78 the testimony of a witness, or the will of a legislator, by interpreting the signs in which the one has intimated his assertion and the other his command. In like manner, when the premises are derived from observation, the function of Reasoning is to ascertain what we (or our predecessors) formerly123 thought might be inferred from the observed facts, and to do this by interpreting a memorandum of ours, or of theirs. The memorandum reminds us, that from evidence, more or less carefully weighed, it formerly appeared that a certain attribute might be inferred wherever we perceive a certain mark. The proposition, All men are mortal (for instance) shows that we have had experience from which we thought it followed that the attributes connoted by the term man, are a mark of mortality. But when we conclude that the Duke of Wellington is mortal, we do not infer this from the memorandum, but from the former experience. All that we infer from the memorandum is our own previous belief, (or that of those who transmitted to us the proposition), concerning the inferences which that former experience would warrant.
This view of the nature of the syllogism renders consistent and intelligible125 what otherwise remains obscure and [Pg 217]confused in the theory of Archbishop Whately and other enlightened defenders of the syllogistic doctrine, respecting the limits to which its functions are confined. They affirm in as explicit14 terms as can be used, that the sole office of general reasoning is to prevent inconsistency in our opinions; to prevent us from assenting126 to anything, the truth of which would contradict something to which we had previously on good grounds given our assent. And they tell us, that the sole ground which a syllogism affords for assenting to the conclusion, is that the supposition of its being false, combined with the supposition that the premises are true, would lead to a contradiction in terms. Now this would be but a lame54 account of the real grounds which we have for believing the facts which we learn from reasoning, in contradistinction to observation. The true reason why we believe that the Duke of Wellington will die, is that his fathers, and our fathers, and all other persons who were cotemporary with them, have died. Those facts are the real premises of the reasoning. But we are not led to infer the conclusion from those premises, by the necessity of avoiding any verbal inconsistency. There is no contradiction in supposing that all those persons have died, and that the Duke of Wellington may, notwithstanding, live for ever. But there would be a contradiction if we first, on the ground of those same premises, made a general assertion including and covering the case of the Duke of Wellington, and then refused to stand to it in the individual case. There is an inconsistency to be avoided between the memorandum we make of the inferences which may be justly drawn in future cases, and the inferences we actually draw in those cases when they arise. With this view we interpret our own formula, precisely as a judge interprets a law: in order that we may avoid drawing any inferences not conformable to our former intention, as a judge avoids giving any decision not conformable to the legislator's intention. The rules for this interpretation are the rules of the syllogism: and its sole purpose is to maintain consistency15 between the conclusions we draw in every particular case, and the previous general directions for drawing them; whether those general [Pg 218]directions were framed by ourselves as the result of induction, or were received by us from an authority competent to give them.
§ 5. In the above observations it has, I think, been shown, that, though there is always a process of reasoning or inference where a syllogism is used, the syllogism is not a correct analysis of that process of reasoning or inference; which is, on the contrary, (when not a mere inference from testimony) an inference from particulars to particulars; authorized127 by a previous inference from particulars to generals, and substantially the same with it; of the nature, therefore, of Induction. But while these conclusions appear to me undeniable, I must yet enter a protest, as strong as that of Archbishop Whately himself, against the doctrine that the syllogistic art is useless for the purposes of reasoning. The reasoning lies in the act of generalization, not in interpreting the record of that act; but the syllogistic form is an indispensable collateral129 security for the correctness of the generalization itself.
It has already been seen, that if we have a collection of particulars sufficient for grounding an induction, we need not frame a general proposition; we may reason at once from those particulars to other particulars. But it is to be remarked withal, that whenever, from a set of particular cases, we can legitimately130 draw any inference, we may legitimately make our inference a general one. If, from observation and experiment, we can conclude to one new case, so may we to an indefinite number. If that which has held true in our past experience will therefore hold in time to come, it will hold not merely in some individual case, but in all cases of some given description. Every induction, therefore, which suffices to prove one fact, proves an indefinite multitude of facts: the experience which justifies131 a single prediction must be such as will suffice to bear out a general theorem. This theorem it is extremely important to ascertain and declare, in its broadest form of generality; and thus to place before our minds, in its [Pg 219]full extent, the whole of what our evidence must prove if it proves anything.
This throwing of the whole body of possible inferences from a given set of particulars, into one general expression, operates as a security for their being just inferences, in more ways than one. First, the general principle presents a larger object to the imagination than any of the singular propositions which it contains. A process of thought which leads to a comprehensive generality, is felt as of greater importance than one which terminates in an insulated fact; and the mind is, even unconsciously, led to bestow132 greater attention upon the process, and to weigh more carefully the sufficiency of the experience appealed to, for supporting the inference grounded upon it. There is another, and a more important, advantage. In reasoning from a course of individual observations to some new and unobserved case, which we are but imperfectly acquainted with (or we should not be inquiring into it), and in which, since we are inquiring into it, we probably feel a peculiar interest; there is very little to prevent us from giving way to negligence133, or to any bias134 which may affect our wishes or our imagination, and, under that influence, accepting insufficient evidence as sufficient. But if, instead of concluding straight to the particular case, we place before ourselves an entire class of facts—the whole contents of a general proposition, every tittle of which is legitimately inferrible from our premises, if that one particular conclusion is so; there is then a considerable likelihood that if the premises are insufficient, and the general inference, therefore, groundless, it will comprise within it some fact or facts the reverse of which we already know to be true; and we shall thus discover the error in our generalization by a reductio ad impossibile.
Thus if, during the reign135 of Marcus Aurelius, a subject of the Roman empire, under the bias naturally given to the imagination and expectations by the lives and characters of the Antonines, had been disposed to expect that Commodus would be a just ruler; supposing him to stop there, he might only have been undeceived by sad experience. But if he [Pg 220]reflected that this expectation could not be justifiable136 unless from the same evidence he was warranted in concluding some general proposition, as, for instance, that all Roman emperors are just rulers; he would immediately have thought of Nero, Domitian, and other instances, which, showing the falsity of the general conclusion, and therefore the insufficiency of the premises, would have warned him that those premises could not prove in the instance of Commodus, what they were inadequate137 to prove in any collection of cases in which his was included.
The advantage, in judging whether any controverted138 inference is legitimate, of referring to a parallel case, is universally acknowledged. But by ascending139 to the general proposition, we bring under our view not one parallel case only, but all possible parallel cases at once; all cases to which the same set of evidentiary considerations are applicable.
When, therefore, we argue from a number of known cases to another case supposed to be analogous140, it is always possible, and generally advantageous141, to divert our argument into the circuitous channel of an induction from those known cases to a general proposition, and a subsequent application of that general proposition to the unknown case. This second part of the operation, which, as before observed, is essentially142 a process of interpretation, will be resolvable into a syllogism or a series of syllogisms, the majors of which will be general propositions embracing whole classes of cases; every one of which propositions must be true in all its extent, if the argument is maintainable. If, therefore, any fact fairly coming within the range of one of these general propositions, and consequently asserted by it, is known or suspected to be other than the proposition asserts it to be, this mode of stating the argument causes us to know or to suspect that the original observations, which are the real grounds of our conclusion, are not sufficient to support it. And in proportion to the greater chance of our detecting the inconclusiveness of our evidence, will be the increased reliance we are entitled to place in it if no such evidence of defect shall appear.
The value, therefore, of the syllogistic form, and of the [Pg 221]rules for using it correctly, does not consist in their being the form and the rules according to which our reasonings are necessarily, or even usually, made; but in their furnishing us with a mode in which those reasonings may always be represented, and which is admirably calculated, if they are inconclusive, to bring their inconclusiveness to light. An induction from particulars to generals, followed by a syllogistic process from those generals to other particulars, is a form in which we may always state our reasonings if we please. It is not a form in which we must reason, but it is a form in which we may reason, and into which it is indispensable to throw our reasoning, when there is any doubt of its validity: though when the case is familiar and little complicated, and there is no suspicion of error, we may, and do, reason at once from the known particular cases to unknown ones.[9]
These are the uses of syllogism, as a mode of verifying any given argument. Its ulterior uses, as respects the general course of our intellectual operations, hardly require illustration, being in fact the acknowledged uses of general language. They amount substantially to this, that the inductions143 may be made once for all: a single careful interrogation of experience may suffice, and the result may be registered in the form of a general proposition, which is committed to memory or to writing, and from which afterwards we have only to syllogize. The particulars of our experiments may then be dismissed from the memory, in which it would be impossible to retain so great a multitude of details; while the knowledge which those details afforded for future use, and which would otherwise be lost as soon as the observations were forgotten, [Pg 222]or as their record became too bulky for reference, is retained in a commodious144 and immediately available shape by means of general language.
Against this advantage is to be set the countervailing inconvenience, that inferences originally made on insufficient evidence, become consecrated145, and, as it were, hardened into general maxims; and the mind cleaves146 to them from habit, after it has outgrown147 any liability to be misled by similar fallacious appearances if they were now for the first time presented; but having forgotten the particulars, it does not think of revising its own former decision. An inevitable drawback, which, however considerable in itself, forms evidently but a small set-off against the immense benefits of general language.
The use of the syllogism is in truth no other than the use of general propositions in reasoning. We can reason without them; in simple and obvious cases we habitually148 do so; minds of great sagacity can do it in cases not simple and obvious, provided their experience supplies them with instances essentially similar to every combination of circumstances likely to arise. But other minds, and the same minds where they have not the same pre-eminent advantages of personal experience, are quite helpless without the aid of general propositions, wherever the case presents the smallest complication; and if we made no general propositions, few persons would get much beyond those simple inferences which are drawn by the more intelligent of the brutes. Though not necessary to reasoning, general propositions are necessary to any considerable progress in reasoning. It is, therefore, natural and indispensable to separate the process of investigation149 into two parts; and obtain general formul? for determining what inferences may be drawn, before the occasion arises for drawing the inferences. The work of drawing them is then that of applying the formul?; and the rules of syllogism are a system of securities for the correctness of the application.
§ 6. To complete the series of considerations connected [Pg 223]with the philosophical character of the syllogism, it is requisite to consider, since the syllogism is not the universal type of the reasoning process, what is the real type. This resolves itself into the question, what is the nature of the minor150 premise, and in what manner it contributes to establish the conclusion: for as to the major, we now fully124 understand, that the place which it nominally151 occupies in our reasonings, properly belongs to the individual facts or observations of which it expresses the general result; the major itself being no real part of the argument, but an intermediate halting-place for the mind, interposed by an artifice152 of language between the real premises and the conclusion, by way of a security, which it is in a most material degree, for the correctness of the process. The minor, however, being an indispensable part of the syllogistic expression of an argument, without doubt either is, or corresponds to, an equally indispensable part of the argument itself, and we have only to inquire what part.
It is perhaps worth while to notice here a speculation153 of a philosopher to whom mental science is much indebted, but who, though a very penetrating154, was a very hasty thinker, and whose want of due circumspection155 rendered him fully as remarkable156 for what he did not see, as for what he saw. I allude157 to Dr. Thomas Brown, whose theory of ratiocination is peculiar. He saw the petitio principii which is inherent in every syllogism, if we consider the major to be itself the evidence by which the conclusion is proved, instead of being, what in fact it is, an assertion of the existence of evidence sufficient to prove any conclusion of a given description. Seeing this, Dr. Brown not only failed to see the immense advantage, in point of security for correctness, which is gained by interposing this step between the real evidence and the conclusion; but he thought it incumbent158 on him to strike out the major altogether from the reasoning process, without substituting anything else, and maintained that our reasonings consist only of the minor premise and the conclusion, Socrates is a man, therefore Socrates is mortal: thus actually suppressing, as an unnecessary step in the argument, [Pg 224]the appeal to former experience. The absurdity159 of this was disguised from him by the opinion he adopted, that reasoning is merely analysing our own general notions, or abstract ideas; and that the proposition, Socrates is mortal, is evolved from the proposition, Socrates is a man, simply by recognising the notion of mortality as already contained in the notion we form of a man.
After the explanations so fully entered into on the subject of propositions, much further discussion cannot be necessary to make the radical160 error of this view of ratiocination apparent. If the word man connoted mortality; if the meaning of "mortal" were involved in the meaning of "man;" we might, undoubtedly, evolve the conclusion from the minor alone, because the minor would have already asserted it. But if, as is in fact the case, the word man does not connote mortality, how does it appear that in the mind of every person who admits Socrates to be a man, the idea of man must include the idea of mortality? Dr. Brown could not help seeing this difficulty, and in order to avoid it, was led, contrary to his intention, to re-establish, under another name, that step in the argument which corresponds to the major, by affirming the necessity of previously perceiving the relation between the idea of man and the idea of mortal. If the reasoner has not previously perceived this relation, he will not, says Dr. Brown, infer because Socrates is a man, that Socrates is mortal. But even this admission, though amounting to a surrender of the doctrine that an argument consists of the minor and the conclusion alone, will not save the remainder of Dr. Brown's theory. The failure of assent to the argument does not take place merely because the reasoner, for want of due analysis, does not perceive that his idea of man includes the idea of mortality; it takes place, much more commonly, because in his mind that relation between the two ideas has never existed. And in truth it never does exist, except as the result of experience. Consenting, for the sake of the argument, to discuss the question on a supposition of which we have recognised the radical incorrectness, namely, that the meaning of a proposition relates to the ideas of the things [Pg 225]spoken of, and not to the things themselves; I must yet observe, that the idea of man, as an universal idea, the common property of all rational creatures, cannot involve anything but what is strictly161 implied in the name. If any one includes in his own private idea of man, as no doubt is always the case, some other attributes, such for instance as mortality, he does so only as the consequence of experience, after having satisfied himself that all men possess that attribute: so that whatever the idea contains, in any person's mind, beyond what is included in the conventional signification of the word, has been added to it as the result of assent to a proposition; while Dr. Brown's theory requires us to suppose, on the contrary, that assent to the proposition is produced by evolving, through an analytic162 process, this very element out of the idea. This theory, therefore, may be considered as sufficiently23 refuted; and the minor premise must be regarded as totally insufficient to prove the conclusion, except with the assistance of the major, or of that which the major represents, namely, the various singular propositions expressive163 of the series of observations, of which the generalization called the major premise is the result.
In the argument, then, which proves that Socrates is mortal, one indispensable part of the premises will be as follows: "My father, and my father's father, A, B, C, and an indefinite number of other persons, were mortal;" which is only an expression in different words of the observed fact that they have died. This is the major premise divested164 of the petitio principii, and cut down to as much as is really known by direct evidence.
In order to connect this proposition with the conclusion Socrates is mortal, the additional link necessary is such a proposition as the following: "Socrates resembles my father, and my father's father, and the other individuals specified165." This proposition we assert when we say that Socrates is a man. By saying so we likewise assert in what respect he resembles them, namely, in the attributes connoted by the word man. And we conclude that he further resembles them in the attribute mortality.
[Pg 226]
§ 7. We have thus obtained what we were seeking, an universal type of the reasoning process. We find it resolvable in all cases into the following elements: Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute. This type of ratiocination does not claim, like the syllogism, to be conclusive3, from the mere form of the expression; nor can it possibly be so. That one proposition does or does not assert the very fact which was already asserted in another, may appear from the form of the expression, that is, from a comparison of the language; but when the two propositions assert facts which are bona fide different, whether the one fact proves the other or not can never appear from the language, but must depend on other considerations. Whether, from the attributes in which Socrates resembles those men who have heretofore died, it is allowable to infer that he resembles them also in being mortal, is a question of Induction; and is to be decided166 by the principles or canons which we shall hereafter recognise as tests of the correct performance of that great mental operation.
Meanwhile, however, it is certain, as before remarked, that if this inference can be drawn as to Socrates, it can be drawn as to all others who resemble the observed individuals in the same attributes in which he resembles them; that is (to express the thing concisely) of all mankind. If, therefore, the argument be admissible in the case of Socrates, we are at liberty, once for all, to treat the possession of the attributes of man as a mark, or satisfactory evidence, of the attribute of mortality. This we do by laying down the universal proposition, All men are mortal, and interpreting this, as occasion arises, in its application to Socrates and others. By this means we establish a very convenient division of the entire logical operation into two steps; first, that of ascertaining167 what attributes are marks of mortality; and, secondly168, whether any given individuals possess those marks. And it will generally be advisable, in our speculations169 on the reasoning process, to consider this double operation as in [Pg 227]fact taking place, and all reasoning as carried on in the form into which it must necessarily be thrown to enable us to apply to it any test of its correct performance.
Although, therefore, all processes of thought in which the ultimate premises are particulars, whether we conclude from particulars to a general formula, or from particulars to other particulars according to that formula, are equally Induction: we shall yet, conformably to usage, consider the name Induction as more peculiarly belonging to the process of establishing the general proposition, and the remaining operation, which is substantially that of interpreting the general proposition, we shall call by its usual name, Deduction170. And we shall consider every process by which anything is inferred respecting an unobserved case, as consisting of an Induction followed by a Deduction; because, although the process needs not necessarily be carried on in this form, it is always susceptible of the form, and must be thrown into it when assurance of scientific accuracy is needed and desired.
§ 8. The theory of the syllogism, laid down in the preceding pages, has obtained, among other important adhesions, three of peculiar value; those of Sir John Herschel,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir John Herschel considering the doctrine, though not strictly "a discovery,"[13] to be "one of the greatest steps which have yet been made in the philosophy of Logic6." "When we consider" (to quote the further words of the same authority) "the inveteracy171 of the habits and prejudices which it has cast to the winds," there is no cause for misgiving172 in the fact that other thinkers, no less entitled to consideration, have formed a very different estimate [Pg 228]of it. Their principal objection cannot be better or more succinctly173 stated than by borrowing a sentence from Archbishop Whately.[14] "In every case where an inference is drawn from Induction (unless that name is to be given to a mere random174 guess without any grounds at all) we must form a judgment that the instance or instances adduced are sufficient to authorize128 the conclusion; that it is allowable to take these instances as a sample warranting an inference respecting the whole class;" and the expression of this judgment in words (it has been said by several of my critics) is the major premise.
I quite admit that the major is an affirmation of the sufficiency of the evidence on which the conclusion rests. That it is so, is the very essence of my own theory. And whoever admits that the major premise is only this, adopts the theory in its essentials.
But I cannot concede that this recognition of the sufficiency of the evidence—that is, of the correctness of the induction—is a part of the induction itself; unless we ought to say that it is a part of everything we do, to satisfy ourselves that it has been done rightly. We conclude from known instances to unknown by the impulse of the generalizing propensity175; and (until after a considerable amount of practice and mental discipline) the question of the sufficiency of the evidence is only raised by a retrospective act, turning back upon our own footsteps, and examining whether we were warranted in doing what we have already done. To speak of this reflex operation as part of the original one, requiring to be expressed in words in order that the verbal formula may correctly represent the psychological process, appears to me false psychology176.[15] We review our syllogistic as well as our inductive processes, and recognise that they have been correctly performed; but logicians do not add a third premise to the syllogism, to express this act of recognition. A careful copyist verifies his transcript177 by collating178 it with the original; and [Pg 229]if no error appears, he recognises that the transcript has been correctly made. But we do not call the examination of the copy a part of the act of copying.
The conclusion in an induction is inferred from the evidence itself, and not from a recognition of the sufficiency of the evidence; as I infer that my friend is walking towards me because I see him, and not because I recognise that my eyes are open, and that eyesight is a means of knowledge. In all operations which require care, it is good to assure ourselves that the process has been performed accurately179; but the testing of the process is not the process itself; and, besides, may have been omitted altogether, and yet the process be correct. It is precisely because that operation is omitted in ordinary unscientific reasoning, that there is anything gained in certainty by throwing reasoning into the syllogistic form. To make sure, as far as possible, that it shall not be omitted, we make the testing operation a part of the reasoning process itself. We insist that the inference from particulars to particulars shall pass through a general proposition. But this is a security for good reasoning, not a condition of all reasoning; and in some cases not even a security. Our most familiar inferences are all made before we learn the use of general propositions; and a person of untutored sagacity will skilfully180 apply his acquired experience to adjacent cases, though he would bungle181 grievously in fixing the limits of the appropriate general theorem. But though he may conclude rightly, he never, properly speaking, knows whether he has done so or not; he has not tested his reasoning. Now, this is precisely what forms of reasoning do for us. We do not need them to enable us to reason, but to enable us to know whether we reason correctly.
In still further answer to the objection, it may be added that, even when the test has been applied, and the sufficiency of the evidence recognised,—if it is sufficient to support the general proposition, it is sufficient also to support an inference from particulars to particulars without passing through the general proposition. The inquirer who has logically satisfied himself that the conditions of legitimate induction were [Pg 230]realized in the cases A, B, C, would be as much justified182 in concluding directly to the Duke of Wellington as in concluding to all men. The general conclusion is never legitimate, unless the particular one would be so too; and in no sense, intelligible to me, can the particular conclusion be said to be drawn from the general one. Whenever there is ground for drawing any conclusion at all from particular instances, there is ground for a general conclusion; but that this general conclusion should be actually drawn, however useful, cannot be an indispensable condition of the validity of the inference in the particular case. A man gives away sixpence by the same power by which he disposes of his whole fortune; but it is not necessary to the legality of the smaller act, that he should make a formal assertion of his right to the greater one.
Some additional remarks, in reply to minor objections, are appended.[16]
[Pg 231]
§ 9. The preceding considerations enable us to understand the true nature of what is termed, by recent writers, Formal Logic, and the relation between it and Logic in the widest sense. Logic, as I conceive it, is the entire theory of [Pg 232]the ascertainment183 of reasoned or inferred truth. Formal Logic, therefore, which Sir William Hamilton from his own point of view, and Archbishop Whately from his, have represented as the whole of Logic properly so called, is really a very subordinate part of it, not being directly concerned with the process of Reasoning or Inference in the sense in which that process is a part of the Investigation of Truth. What, then, is Formal Logic? The name seems to be properly applied to all that portion of doctrine which relates to the equivalence of different modes of expression; the rules for determining when assertions in a given form imply or suppose the truth or falsity of other assertions. This includes the theory of the Import of Propositions, and of their Conversion184, [Pg 233]?quipollence, and Opposition185; of those falsely called Inductions (to be hereafter spoken of[17]), in which the apparent generalization is a mere abridged statement of cases known individually; and finally, of the syllogism: while the theory of Naming, and of (what is inseparably connected with it) Definition, though belonging still more to the other and larger kind of logic than to this, is a necessary preliminary to this. The end aimed at by Formal Logic, and attained186 by the observance of its precepts187, is not truth, but consistency. It has been seen that this is the only direct purpose of the rules of the syllogism; the intention and effect of which is simply to keep our inferences or conclusions in complete consistency with our general formul? or directions for drawing them. The Logic of Consistency is a necessary auxiliary188 to the logic of truth, not only because what is inconsistent with itself or with other truths cannot be true, but also because truth can only be successfully pursued by drawing inferences from experience, which, if warrantable at all, admit of being generalized, and, to test their warrantableness, require to be exhibited in a generalized form; after which the correctness of their application to particular cases is a question which specially189 concerns the Logic of Consistency. This Logic, not requiring any preliminary knowledge of the processes or conclusions of the various sciences, may be studied with benefit in a much earlier stage of education than the Logic of Truth: and the practice which has empirically obtained of teaching it apart, through elementary treatises190 which do not attempt to include anything else, though the reasons assigned for the practice are in general very far from philosophical, admits of a philosophical justification.
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syllogism
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| n.演绎法，三段论法 | |
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conversant
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| adj.亲近的，有交情的，熟悉的 | |
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conclusive
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| adj.最后的，结论的；确凿的，消除怀疑的 | |
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conclusiveness
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| n.最后； 释疑； 确定性； 结论性 | |
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syllogistic
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| adj.三段论法的，演绎的，演绎性的 | |
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logic
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| n.逻辑(学)；逻辑性 | |
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remarkably
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| ad.不同寻常地，相当地 | |
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premise
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| n.前提；v.提论，预述 | |
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premises
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| n.建筑物，房屋 | |
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ratiocination
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| n.推理；推断 | |
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inevitable
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| adj.不可避免的，必然发生的 | |
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doctrine
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| n.教义；主义；学说 | |
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explicitly
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| ad.明确地，显然地 | |
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explicit
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| adj.详述的，明确的；坦率的；显然的 | |
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consistency
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| n.一贯性，前后一致，稳定性；(液体的)浓度 | |
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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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impute
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| v.归咎于 | |
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frivolity
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| n.轻松的乐事，兴高采烈；轻浮的举止 | |
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allege
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| vt.宣称，申述，主张，断言 | |
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appreciation
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| n.评价；欣赏；感谢；领会，理解；价格上涨 | |
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insufficient
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| adj.(for，of)不足的，不够的 | |
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insufficiently
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| adv.不够地，不能胜任地 | |
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sufficiently
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| adv.足够地，充分地 | |
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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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defenders
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| n.防御者( defender的名词复数 )；守卫者；保护者；辩护者 | |
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adversaries
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| n.对手，敌手( adversary的名词复数 ) | |
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uncertainty
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| n.易变，靠不住，不确知，不确定的事物 | |
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dispelled
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| v.驱散，赶跑( dispel的过去式和过去分词 ) | |
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remains
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| n.剩余物，残留物；遗体，遗迹 | |
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disposition
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| n.性情，性格；意向，倾向；排列，部署 | |
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previously
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| adv.以前，先前（地） | |
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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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mere
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| adj.纯粹的；仅仅，只不过 | |
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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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accusation
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| n.控告，指责，谴责 | |
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entrapped
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| v.使陷入圈套，使入陷阱( entrap的过去式和过去分词 ) | |
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catching
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| adj.易传染的，有魅力的，迷人的，接住 | |
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memorandum
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| n.备忘录，便笺 | |
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quill
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| n.羽毛管；v.给（织物或衣服）作皱褶 | |
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derive
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| v.取得；导出；引申；来自；源自；出自 | |
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aggregate
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| adj.总计的，集合的；n.总数；v.合计；集合 | |
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compendious
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| adj.简要的，精简的 | |
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recording
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| n.录音，记录 | |
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generalization
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| n.普遍性，一般性，概括 | |
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concise
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| adj.简洁的，简明的 | |
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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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philosophical
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| adj.哲学家的，哲学上的，达观的 | |
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deference
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| n.尊重，顺从；敬意 | |
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iota
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| n.些微，一点儿 | |
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constrained
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| adj.束缚的,节制的 | |
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fiat
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| n.命令，法令，批准；vt.批准，颁布 | |
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52
perfectly
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| adv.完美地，无可非议地，彻底地 | |
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53
maxim
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| n.格言，箴言 | |
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54
lame
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| adj.跛的，(辩解、论据等)无说服力的 | |
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55
brutes
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| 兽( brute的名词复数 )； 畜生； 残酷无情的人； 兽性 | |
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56
dreads
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| n.恐惧，畏惧( dread的名词复数 )；令人恐惧的事物v.害怕，恐惧，担心( dread的第三人称单数 ) | |
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57
maxims
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| n.格言，座右铭( maxim的名词复数 ) | |
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58
erect
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| n./v.树立，建立，使竖立；adj.直立的，垂直的 | |
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59
recollecting
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| v.记起，想起( recollect的现在分词 ) | |
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60
consultation
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| n.咨询；商量；商议；会议 | |
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61
steer
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| vt.驾驶，为…操舵；引导；vi.驾驶 | |
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62
judgment
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| n.审判；判断力，识别力，看法，意见 | |
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63
utterly
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| adv.完全地，绝对地 | |
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64
incapable
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| adj.无能力的，不能做某事的 | |
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65
justifying
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| 证明…有理( justify的现在分词 )； 为…辩护； 对…作出解释； 为…辩解（或辩护） | |
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66
applied
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| adj.应用的；v.应用，适用 | |
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67
recondite
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| adj.深奥的，难解的 | |
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68
warrior
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| n.勇士，武士，斗士 | |
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69
skilful
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| (=skillful)adj.灵巧的，熟练的 | |
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70
judicious
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| adj.明智的，明断的，能作出明智决定的 | |
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71
precisely
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| adv.恰好，正好，精确地，细致地 | |
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72
savage
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| adj.野蛮的；凶恶的，残暴的；n.未开化的人 | |
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73
dexterity
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| n.(手的)灵巧，灵活 | |
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74
scotch
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| n.伤口，刻痕；苏格兰威士忌酒；v.粉碎，消灭，阻止；adj.苏格兰(人)的 | |
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75
procured
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| v.（努力）取得， （设法）获得( procure的过去式和过去分词 )；拉皮条 | |
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76
proceeding
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| n.行动，进行，(pl.)会议录，学报 | |
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77
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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78
ascertain
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| vt.发现，确定，查明，弄清 | |
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79
judicial
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| adj.司法的，法庭的，审判的，明断的，公正的 | |
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80
uncommon
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|
| adj.罕见的，非凡的，不平常的 | |
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81
circuitous
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|
| adj.迂回的路的，迂曲的，绕行的 | |
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82
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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83
induction
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| n.感应，感应现象 | |
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84
justification
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| n.正当的理由；辩解的理由 | |
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85
judgments
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| 判断( judgment的名词复数 )； 鉴定； 评价； 审判 | |
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86
systematic
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| adj.有系统的，有计划的，有方法的 | |
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87
revert
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| v.恢复，复归，回到 | |
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88
entirely
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| ad.全部地，完整地；完全地，彻底地 | |
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89
assent
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| v.批准，认可；n.批准，认可 | |
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90
impairing
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| v.损害，削弱( impair的现在分词 ) | |
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91
peculiarity
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| n.独特性，特色；特殊的东西；怪癖 | |
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92
synthetically
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| adv. 综合地，合成地 | |
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93
dynamics
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| n.力学，动力学，动力，原动力；动态 | |
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94
mobility
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| n.可动性，变动性，情感不定 | |
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95
annihilate
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| v.使无效；毁灭；取消 | |
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96
demonstration
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| n.表明，示范，论证，示威 | |
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97
talismanic
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| adj.护身符的，避邪的 | |
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98
virtue
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| n.德行，美德；贞操；优点；功效，效力 | |
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99
conjuring
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| n.魔术 | |
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100
equilibrium
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| n.平衡，均衡，相称，均势，平静 | |
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101
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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102
radii
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|
| n.半径；半径（距离）( radius的名词复数 )；用半径度量的圆形面积；半径范围；桡骨 | |
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103
enunciation
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| n.清晰的发音；表明，宣言；口齿 | |
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104
abridged
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| 削减的，删节的 | |
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105
specimen
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| n.样本，标本 | |
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106
paradigm
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| n.例子，模范，词形变化表 | |
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107
undoubtedly
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| adv.确实地，无疑地 | |
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108
requisite
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| adj.需要的，必不可少的；n.必需品 | |
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109
configuration
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| n.结构，布局，形态，(计算机)配置 | |
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110
rendering
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| n.表现，描写 | |
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111
configurations
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|
| n.[化学]结构( configuration的名词复数 )；构造；（计算机的）配置；构形（原子在分子中的相对空间位置） | |
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112
distinguished
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| adj.卓越的，杰出的，著名的 | |
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113
favourable
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| adj.赞成的，称赞的，有利的，良好的，顺利的 | |
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114
testimony
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| n.证词；见证，证明 | |
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115
authoritative
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| adj.有权威的，可相信的；命令式的；官方的 | |
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116
scripture
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| n.经文，圣书，手稿；Scripture:(常用复数)《圣经》，《圣经》中的一段 | |
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117
volition
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| n.意志；决意 | |
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118
elicited
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| 引出，探出( elicit的过去式和过去分词 ) | |
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119
determined
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| adj.坚定的；有决心的 | |
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120
certify
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| vt.证明，证实；发证书(或执照)给 | |
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121
inquiry
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| n.打听，询问，调查，查问 | |
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122
interpretation
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| n.解释，说明，描述；艺术处理 | |
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123
formerly
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| adv.从前，以前 | |
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124
fully
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| adv.完全地，全部地，彻底地；充分地 | |
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125
intelligible
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| adj.可理解的，明白易懂的，清楚的 | |
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126
assenting
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| 同意，赞成( assent的现在分词 ) | |
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127
authorized
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| a.委任的，许可的 | |
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128
authorize
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| v.授权，委任；批准，认可 | |
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129
collateral
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| adj.平行的；旁系的；n.担保品 | |
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130
legitimately
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| ad.合法地；正当地，合理地 | |
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131
justifies
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| 证明…有理( justify的第三人称单数 )； 为…辩护； 对…作出解释； 为…辩解（或辩护） | |
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132
bestow
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| v.把…赠与，把…授予；花费 | |
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133
negligence
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| n.疏忽，玩忽，粗心大意 | |
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134
bias
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| n.偏见，偏心，偏袒；vt.使有偏见 | |
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135
reign
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| n.统治时期，统治，支配，盛行；v.占优势 | |
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136
justifiable
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| adj.有理由的，无可非议的 | |
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137
inadequate
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| adj.(for,to)不充足的，不适当的 | |
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138
controverted
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| v.争论，反驳，否定( controvert的过去式和过去分词 ) | |
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139
ascending
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| adj.上升的，向上的 | |
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140
analogous
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| adj.相似的；类似的 | |
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141
advantageous
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| adj.有利的；有帮助的 | |
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142
essentially
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| adv.本质上，实质上，基本上 | |
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143
inductions
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| 归纳（法）( induction的名词复数 )； （电或磁的）感应； 就职； 吸入 | |
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144
commodious
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| adj.宽敞的；使用方便的 | |
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145
consecrated
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| adj.神圣的，被视为神圣的v.把…奉为神圣，给…祝圣( consecrate的过去式和过去分词 )；奉献 | |
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146
cleaves
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| v.劈开，剁开，割开( cleave的第三人称单数 ) | |
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147
outgrown
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| 长[发展] 得超过（某物）的范围( outgrow的过去分词 )； 长[发展]得不能再要（某物）； 长得比…快； 生长速度超过 | |
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148
habitually
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| ad.习惯地，通常地 | |
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149
investigation
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| n.调查，调查研究 | |
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150
minor
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| adj.较小(少)的，较次要的；n.辅修学科；vi.辅修 | |
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151
nominally
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| 在名义上，表面地； 应名儿 | |
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152
artifice
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| n.妙计，高明的手段；狡诈，诡计 | |
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153
speculation
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| n.思索，沉思；猜测；投机 | |
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154
penetrating
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| adj.（声音）响亮的，尖锐的adj.（气味）刺激的adj.（思想）敏锐的，有洞察力的 | |
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155
circumspection
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| n.细心，慎重 | |
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156
remarkable
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| adj.显著的，异常的，非凡的，值得注意的 | |
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157
allude
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| v.提及，暗指 | |
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158
incumbent
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| adj.成为责任的，有义务的；现任的，在职的 | |
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159
absurdity
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| n.荒谬，愚蠢；谬论 | |
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160
radical
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| n.激进份子，原子团，根号；adj.根本的，激进的，彻底的 | |
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161
strictly
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| adv.严厉地，严格地；严密地 | |
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162
analytic
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| adj.分析的，用分析方法的 | |
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163
expressive
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| adj.表现的，表达…的，富于表情的 | |
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164
divested
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| v.剥夺( divest的过去式和过去分词 )；脱去（衣服）；2。从…取去…；1。（给某人）脱衣服 | |
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165
specified
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| adj.特定的 | |
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166
decided
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| adj.决定了的，坚决的；明显的，明确的 | |
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167
ascertaining
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| v.弄清，确定，查明( ascertain的现在分词 ) | |
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168
secondly
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| adv.第二，其次 | |
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169
speculations
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| n.投机买卖( speculation的名词复数 )；思考；投机活动；推断 | |
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170
deduction
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| n.减除，扣除，减除额；推论，推理，演绎 | |
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171
inveteracy
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| n.根深蒂固，积习 | |
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172
misgiving
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| n.疑虑，担忧，害怕 | |
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173
succinctly
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| adv.简洁地；简洁地，简便地 | |
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174
random
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| adj.随机的；任意的；n.偶然的(或随便的)行动 | |
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175
propensity
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| n.倾向；习性 | |
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176
psychology
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| n.心理，心理学，心理状态 | |
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177
transcript
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|
| n.抄本，誊本，副本，肄业证书 | |
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178
collating
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| v.校对( collate的现在分词 )；整理；核对；整理（文件或书等） | |
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179
accurately
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| adv.准确地，精确地 | |
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180
skilfully
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| adv. (美skillfully)熟练地 | |
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181
bungle
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| v.搞糟；n.拙劣的工作 | |
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182
justified
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| a.正当的，有理的 | |
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183
ascertainment
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| n.探查，发现，确认 | |
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184
conversion
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| n.转化，转换，转变 | |
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185
opposition
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| n.反对，敌对 | |
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186
attained
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| （通常经过努力）实现( attain的过去式和过去分词 )； 达到； 获得； 达到（某年龄、水平、状况） | |
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187
precepts
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| n.规诫，戒律，箴言( precept的名词复数 ) | |
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188
auxiliary
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| adj.辅助的，备用的 | |
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189
specially
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| adv.特定地；特殊地；明确地 | |
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190
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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