it is a humiliating reflection that mankind never reasoned so ill as when they most professed to cultivate the art of reasoning.—life of galileo, p. 1. society for the diffusion of useful knowledge.
common sense—the foundation of logic—first received (to a limited extent) the regularity of an art and the certainty of a science, from the master hand of aristotle. impartial scholars, familiar with his writings on logic, allow them to have not only ingenuity but real merit; and his admirers contend that he has been misunderstood by some and abused by others. this is highly probable, as we are certain that when his works were interpreted by the schools, and his logic proclaimed the great text-book of knowledge and the only weapon of truth, 'men's minds, instead of studying nature, were in an endless ferment about occult qualities and imaginary essences; little was talked of but intention and remission, proportion and degree, infinity, formality, quiddity and individuality.'* logic then was jargon, controversy chicane, and truth a shuttlecock, with which the disputants respectively played, or the object which they mutually disguised. logic was a labyrinth in which the subtlest lost their way—a bourne from which the traveller after truth seldom returned.
* account of lord bacon's novum organon scientiarum, lib. of
useful knowledge, p. 4.
a striking illustration of this has been furnished by a candid and distinguished writer—dr. reid. 'of the analytics and of the topics of aristotle, ingenuousness requires me to confess, that though i have often purposed to read the whole with care, and to understand what is intelligible, yet my courage and patience always failed me before i had done. why should i throw away so much time and painful attention upon a thing of so little real use? if i had lived in those ages when the knowledge of aristotle's organon entitled a man to the highest rank in philosophy, ambition might have induced me to employ upon it some years of painful study; and, less, i conceive, would not be sufficient. such reflections as these always got the better of my resolution.'*
dr. whately, who has for many years occupied the throne of logic and whose work maybe taken, from its currency in our colleges and academies, as the representative of the logic of the schools, seems to obviate all objections to the abstruseness of this subject by a counter charge, to the effect that logic is now underrated only because it has been overrated. but it is not the complexity found in it, but the laudations bestowed upon it which have brought it into neglect. dr. whately contends that certain writers, 'by representing logic as furnishing the sole instrument for the discovery of truth in all subjects, and as teaching the use of the intellectual faculties in general, raised expectations which could not be realised, and which naturally led to a reaction—to logic being regarded as utterly futile and empty.'** deeply deploring this kind of injury, from which many important arts have suffered, i am neither disposed to defend such a course, nor to imitate it. but i demur to the truth of this representation with regard to logic. if logic be not the 'sole instrument for the discovery of truth in all subjects,' it is certainly the principal one. instead of charging scholastic logicians with having unduly 'raised,' it would be nearer the truth, in my opinion, to say that they have confused 'expectations' by intricate machinery and extreme elaborations.
* lord kamet's sketches vol. 8, chap. s. aristotle's
logic.
** dr. whately: elements of logic, preface, p. vii. second
edition.
intricacy and minuteness of detail might be a trifling disqualification did they lead to something immediately practical. but dr. whately contends that logic, in the most extensive sense which the name can, with propriety, be made to bear, is that of the science, and also the art of reasonings 'inasmuch as logic institutes an analysis of the process of the mind in reasoning, it is strictly a science, while considered in reference to the practical rules it furnishes it is an art.'* he confines the province of logic, as an art, to 'employing language properly for the purpose of reasoning,' and restricts the logician to the use of the syllogism as the sole test of argument. mr. augustus de morgan thus exhibits the spirit of whately's restriction:—
logic has nothing to do with the truth of the facts, opinions, or presumptions, from which an inference is derived; but simply takes care that the inference shall certainly be true if the premises be true.'
it has been, and is to be, objected, that logic, thus confined, 'leaves untouched the greatest difficulties, and those which are the sources of the greatest errors in reasoning.' to this powerful objection dr. whately thinks it sufficient to reply, that 'no art is to be censured for not teaching more than falls within its province, and, indeed, more than can be taught by any conceivable art. such a system of universal knowledge as should instruct us in the full meaning or meanings of every term, and the truth or falsity, certainty or uncertainty of every proposition, thus superseding all other studies, it is most unphilosophical to expect, or even to imagine. and to find fault with logic for not performing this, is as if one should object to optics for not giving sight to the blind—or complain of a reading glass for being of no service to a person who had never learnt to read.'*** this would be a most conclusive answer if confident assertion could be accepted in lieu of proof. the objection still remains to be removed. we may still demand, does it not fall within the legitimate province of logic to provide means of encountering the 'greatest difficulties' with which it is confessed logic is beset? true, there is no art can teach everything, but is that a reason why logic should teach nothing, or next to nothing, compared with what seems essentially necessary?
* intro., p. 1.
** klein. of logic, synthetical compendium, chap. 2, part
1, sec. 9.
*** elem. of logic, intro., pp. 12, 13.
dr. whately contends that the 'difficulties' and 'errors' in the objection adduced, are in the subject matter about which logic is employed, and not in the process of reasoning—which alone is the appropriate province of logic. but it seems to me that dr. whately has found it impossible to keep within the bounds of the restriction he thus endeavours to establish.
in treating upon 'apprehension,' he introduces, as indeed he was obliged to do, from the department of metaphysics, several speculations on 'generalisation' and 'abstractions,' and from ontology (the science which explains the most general conceptions respecting the phenomena of nature) he borrows the leading principles of definition. because he thus goes so far, it is not to be contended that therefore he should have gone further; but when he found he must depart from his rule and borrow from other branches of knowledge (no matter for what end), why did he not depart from it to some purpose, and borrow from natural philosophy such rules as would have guarded the logician from the 'chief errors' into which he may fall?
dr. whately informs us, indeed, that logic furnishes certain syllogistic forms to which all sound arguments may be reduced, and thus establishes universal tests for the detection of fallacy—but it is to be observed that it is only such fallacy as may creep in between the premises and the conclusion of an argument. it is to this narrow and aristotelian object that logic is restricted. 'the process of reasoning itself is alone the appropriate province of logic. this process will have been correctly conducted if it have conformed to the logical rules, which preclude the possibility of any error creeping in between the principles from which we are arguing, and the conclusions we deduce from them.'* we learn from our authority, that as arithmetic does not profess to introduce any notice of the things, whether coins, persons, or dimensions, respecting which calculations are made; neither does logic undertake 'the ascertainment of facts, or the degree of evidence of doubtful propositions.' and just as an arithmetical result will be useless if the data of the calculation be incorrect, so a logical conclusion is liable to be false if the premises are so. neither does the logic, now under consideration, concern itself with the 'discovery of truth,' excepting so far as that may be said to be implied by the detection of error in a false inference.** logic thus, confined to the actual process of reasoning, however important its functions there, evidently leaves us in the dark as to the value of what we reason about. for the information thus missing, this logic refers us to knowledge in general—to grammar and composition for the art of expressing, with correctness and perspicuity, the terms of propositions—to natural, moral, political, or other philosophy, for the facts which alone can establish the truth of the premises reasoned from.
* intro., p. 13.
** for the grounds of these representations, see
dissertation on the province of reasoning, chap. 2, sec. 4
dr. whately's logic.
the exclusion from logic of all consideration of the facts on which propositions are founded, is thus endeavoured to be justified by the archbishop of dublin:—'no arithmetical skill will secure a correct result, unless the data are correct from which we calculate: nor does any one on that account undervalue arithmetic; and yet the objection against logic rests on no better foundation.' this is true, but is it true that arithmetic is on this account to be imitated? if the arithmetician must take his data for granted, it is what the searcher after truth must never do—he must use his eyes and examine for himself, in all cases, as far as possible, unless he intends to be deceived. and for want of such precaution as this, the arithmetician is at sea the moment he steps out of the narrow path of mechanical routine. who is not aware of the failures of calculation when applied to the general business of life—to statistics, moral and political? every day, facts have to be called in to correct the egregious blunders of figures.* the calculations are conducted in most approved form, but are of no use. does not this demonstrate that when arithmetic, like logic, is applied to the business of life, general rules for securing the accuracy of data would be of essential service? supposing, however, that arithmetic could do very well without them, does it follow that logic should, when it would be safer and more efficient with them?
* 'in art, in practice, innumerable critics will demonstrate
that most things are impossible. it was proved by fluxionary
calculus, that steam-ships could never get across from the
farthest point of ireland to the nearest of newfoundland;
impelling force, resisting force, maximum here, minimum
there; by law of nature, and geometric demonstration—what
could be done? the great western could weigh anchor from
bristol port; that could be done. the great western,
bounding safe through the gullets of the hudson, threw her
cable out on the capstan of new york, and left our still
moist paper-demonstration to dry itself at leisure.'—
thomas carlyle, chartism, pp. 96-7.
since our author's canons are held absolute in the schools, it may be useful to consider this last cited argument in another light. a stronger objection may be urged, one which particularly addresses itself to those who mistake mere pertinence for general relevance, and suppose that a single analogy decides a case.
his grace reasons, that, because arithmetic does not concern itself about its data, logic should follow the same example. but why overlooks he pure mathematics—a much higher science than arithmetic? surely geometry, which through all time has been the model of the sciences, was better worthy than arithmetic to be the model of logic! was it classical in the principal of st. alban's college to abandon euclid and cleave unto cocker or walkingame?
arithmetic is mechanical—geometry is reasoning; surely it was more befitting to compare reason with reason, when endeavouring to discover the true way of perfecting reason. geometry is, of all sciences, reputed the most conclusive in its arguments—and we know it is distinguished above all sciences for carefulness in its data. it begins with axioms, the most indubitable of all data, and its subsequent conclusions are founded only on established facts—and to be sure that they are established facts, the geometer, before he employs them, establishes them himself. if an analogy is to decide the province of logic, here is an analogy whose pretensions over those of arithmetic are eminent.
so conclusive did dr. whately deem the argument just examined, that he many times, in various forms, reproduced it. one of the last instances is under the head of 'fallacies.' 'it has been made a subject of bitter complaint against logic, that it presupposes the most difficult point to be already accomplished; viz., the sense of the terms to be ascertained. a similar objection might be urged against every other art in existence e.g., against agriculture, that all the precepts for the cultivation of land presuppose the possession of a farm.'*
* logic, chap. 3. fallacies, sec. 2.
already has been pointed out what may reasonably induce a suspicion of the soundness of these analogies; viz., that their author found it necessary to disregard them and introduce, from other branches of knowledge, certain disquisitions on the 'sense of terms.' with regard to this particular instance, it may be observed, that though treatises on agriculture do presuppose the possession of a farm, they do not presuppose the knowledge requisite for cultivating it, but inform fully of soil, and seed, and crops. so logic may be allowed to presuppose the existence of the universe, whence truth is drawn, or the existence of language, 'whereby it is expressed; but it is surely not to pre-suppose the knowledge of facts and terms, the great instruments for the cultivation of truth. agricultural treatises hardly warrant this inference. there are the representations that induced the confession that 'logic is not so much an instrument of acquirement as of defence. it is a good armour to buckle on when compelled to battle for our heritage, but a poor implement for its cultivation.'*
all practical arts include a knowledge of materials as well as implements. platers, ignorant of the nature of metals, cabinetmakers, of the different species of wood, make but sorry artizans; and in like manner, reasoners, unacquainted, at least in a general way, with the accuracy of what is reasoned about, make but sorry logicians.**
it will readily be expected that in the modern progress of knowledge, the aristotelian province of logic would be enlarged. the far-seeing intellect of lord verulam heralded the innovation—'our glorious bacon led philosophy forth from the jargon of schools and the fopperies of sects. he made her to be—the handmaid of nature, friendly to her creatures, and faithful to her laws.'***
* w. j. fox, mon. rep., p. 45: 1835.
** the reader will find that logician is need in the sense
of skilfulness in eliciting and exhibiting reality. by that
which i call logical is meant that which is truthful. i
presume that is the sense to which this high word should be
confined. it is the lax application of this term to mere
dexterity in evading the truth according to rule, that has
so increased the unsatisfactory race of professed sceptics.
—see scepticism, chap. xii.
*** langhornea' preface to the lives of plutarch.
the general object of lord bacon's philosophy, writes bruce, an edinburgh professor of logic of the last century, is to connect the reasoning powers of man with experiments for the improvement of natural knowledge.
to create a just taste for philosophical investigation, required—
1. a display of the true, that they may be distinguished from the false subjects of inquiry.
2. scientific rules to direct the discovery of the laws of nature.
but to 'display the true,' is to display the facts on which the truth rests. the 'discovery of the laws of nature' implies observation of the operations of nature. the philosophy of bacon, says macaulay, began in observation and ended in arts.
it is most obvious, as the reader will gather from what has been advanced, that for guarding, to the greatest possible extent, against error in conclusions, it is necessary to take into consideration the character of the data from which we reason—and to do this, we must draw from the general sources of knowledge to which the logic of the schools refers us. if we happen not to possess an accurate acquaintance with these branches, we must draw upon the best notions we have of them, or apply such natural sagacity as we happen to possess. but whether the information we happen to possess be complete or partial, it is not well that we are left to apply it at random, without any definite mode of procedure; and if logic refuses to assist us, and gives only a vague reference elsewhere, we must endeavour to assist ourselves. the datum of all arguments is a proposition, an assertion, or denial; and to ascertain its truth (upon which the value of the whole reasoning depends) we have to do with the facts upon which it rests, and the terms in which it is expressed. for it may be here observed, that the truth or falsity of every proposition depends upon facts. to ascertain the general accuracy of facts, we have to appeal to received standards of certainty; and to fix the meaning of terms, we have recourse to a plain principle of definition. in the task of recognising truth, so necessary in examining the premises of an argument, one is wonderfully assisted by being familiarised with the sources of truth, and the mode of its discovery. in these operations the tutored and untutored may alike be assisted by simple general rules. if these rules prove not infallible in every case, they will prove successful in the majority of cases.
since general rules are the only, rules that the vast field of facts admits of, they are not to be rejected on light grounds. they enable us to set forth intelligibly the reasons of our own conviction, and to detect and expose the fundamental fallacies of apparent arguments. since they direct us where the logic of the schools leaves us without a guide, their value is apparent.
the logical management of the syllogism involves much abstruseness respecting 'genus' and 'species,' the 'quantity' and 'quality' of 'propositions', 'contraries,' 'sub-contraries,' 'contradictions,' and 'subalterns.' stepping by 'illative conversion,' 'six rules to be observed with respect to categorical syllogism' next demand attention, followed hard by eleven moods which can be used in a legitimate syllogism, viz.—— a, a, a, a, a, i, a., e, e, a, e, o, a, i, i, a, o, o, e, a, e, e, a, o, e, i, o, i, a, i, o, a, o.' in the middle of this abstract train march the 'undistributed middle' and the 'illicit process,' attended by four figures represented by the following mnemonic lines, which must be carefully committed to memory:'—
fig. 1. barbara, celarent, darii, ferioque prioris.
fig. 2. cesare, damestres, festino, baroko,* secund?.
fig. 3. tertia, darapti, disamis, datisi, felapton, bokardo,** ferlso, habet; quarta insuper addit.
fig. 4. bramantip, camenes, dimaris, fesapo, fresison.
a motley group, too numerous to be particularised, bring up the complex rear of 'modals,' 'hypotheticals,' 'conditionals,' and 'disjunctives.' this is certainly not the portal through which the populace can at present pass to logic, even if such logic helped them to all truth, and saved them from all fallacy.
but this species of logic is not without interest. symbolic letters and mnemonic lines are not without attractions to those who understand them. there is poetry in an algebraic sign, when it is the emblem of a difficulty solved, and a wonderful result simply arrived at. to try the whole power of words, and discover every form of language in which a legitimate deduction can be expressed, is no ignoble task. it is a high discipline, but it belongs rather to the age of leisure than this of 'copperasfames, cotton-fuz, gin-riot, wrath, and toil'—to the luxuries rather than the utilities of learning.
there is the inefficiency of the syllogism, and also the vitiation produced by its employment.
1. it corrupts the taste for philosophical invention by placing philosophy in abstractions, and withdrawing it from the observation of nature.
2. it creates a reliance on principles, which originate in the hypotheses of philosophers, not in the laws of nature.
3. it makes truth the result of the forms of argument, not of scientific evidence.***
* or, fakoro, as indeed all the particulars in this place
recited.
** or, dokamo. but a brief summary of the subjects
comprised in his logic in reference to the syllogism.
***bruce. these references to fakoro and dokamo are whately's.
lord kames cites from the father of logic the following syllogism, which will bear repetition as an extraordinary instance of that assumption for which the logic of the schools provides no remedy:—
heavy bodies naturally tend to the centre of the universe.
we know, by experience, that heavy bodies tend to the centre of the earth.
therefore the centre of the earth is the centre of the universe.
but by what experience did aristotle discover the centre of the universe, so as to become aware that heavy bodies naturally tend there? on what facts rest the measurement of the radii from our earth to the boundless circumference of space? how did he ascertain the limits of that which has no limits? yet, strange to say, the logic of the schools prides itself in leaving us where the stagyrite left us.
'when mankind began to reason on the phenomena of nature, they were solicitous to abstract, and they formed general propositions from a limited observation. though these propositions were assumed, they were admitted as true. they were not examined by appeals to nature, but by comparison with other propositions.'*
in this syllogism from aristotle, there is the usual compliance with accredited rules, and the same defiance of common sense. such examples are deemed perfect reasoning and legitimate argument; but is it not a mockery to encourage the belief that we can have reason and argument, without the truth? only this shallow consolation remains to us. if the logician of the schoole does not enlighten the understanding, he is at least reputed not to offend the taste, and he wins the equivocal praise of butler:—
'he'll run in debt by disputation,
and pay with ratiocination;
all this by syllogism, true
in mood and figure, he will do.'
syllogisms are to truth what rhyme is to poetry. 'it is a well known fact that verse, faultless in form, may be utterly destitute of poetic fire or feeling.'**
* bruce.
** a. j. d. d'orsey, eng. gram., part 2, article prosody.
according to the logic of the schools, 'the question respecting the validity of an argument is not whether the conclusion be true, but whether it follows from the premises adduced.' it was the bitter experience of bordon of the delusiveness of such partial logic that induced him to exclaim, 'one fact is worth fifty arguments.'
with such authorities, 'a valid argument is that which it so stated that its conclusiveness is evident from the mere form of the expression.' but since it is admitted that if the data reasoned upon be incorrect, no logical skill can secure a correct result; it is evident that however faultless the form, the inquirer after truth is in no way nearer his object, unless he be instructed how to lay a foundation of faultless facts. he then, who is in love with truth rather than logomachy, will admit, in spite of the most ingenious analogies, that there is some room for a logic of facts, as well as a logic of words.
