STUDIES IN DIALECTIC

All Englishmen are Europeans;John Smith is an Englishman;therefore John Smith is a European.

Observe the difference between this theorem and that adduced in illustration of the Dictum (xxxvi). In the latter the first premise is a categorical judgment and so therefore is the conclusion; in the theorem just given the first premise is a classification, and the conclusion is necessarily a classification.

We first remark that such an 'argument' is never met with in real spontaneous thinking—it occurs only in logic books. It is manufactured exclusively for Peripatetic consumption. The reason it is not to be found is simple—the conclusion it yields is a classification, and that is not enough for valid argument. In reasoning we may introduce a classification as theminor premise—that is, the proposition which brings the case under the precedent—but the applicate is never a general or class idea. It is one or more properties abstracted from the subject (whether the latter be a single object or general idea), and applied to the case. Merely to classify a case and so leave it would answer no rational purpose.

Logicians urge in recommendation of this syllogism that it gives a certain conclusion. The premises being correct, the conclusion is infallibly true.

No doubt it is, for in contemplating a thing we can mentally enter it into all the classes to which itappears to belong, whatever be their generality. Knowing the class European and the individual John Smith, we see at once that the latter is contained in the former, and we can do this without putting him first in the minor class English. It is like saying, 'The pavilion is in the garden, John Smith is in the pavilion, therefore he is in the garden.' Of course he is! The minor premise of a double classification is superfluous. The fact that such conclusions are certain, shows how nugatory they are. We are not certain of anything till it has been experienced. In legitimate reasoning the conclusion is never more than probable. The certainty of these double classifications shows that we are stating what we already know—not imagining an ideal addition to our positive knowledge.

Doctrine of the Predicate.So long as logicians are permitted to fabricate their own examples, all is plain sailing with the syllogism. But they are sometimes obliged to deal with genuine arguments. In this case what they do is to assume thatfor logical purposesevery predicate of the precedent—that is, the applicate—is a general or class term. Even when an argument is good they spoil it with a bad theory.

Sir William Hamilton states that up to his time logicians recognised but one type of proposition—that called by him the proposition 'in extension,' whichmeans the classifying of the subject. He announced that he intended to introduce a proposition 'in comprehension,' meaning a judgment in the category of inherence—as for instance, 'man is responsible.' He further said that he recognised a third type of proposition, that concerning 'cause and effect.'

But in the course of working out these logical novelties he seems to have discovered that they were irreconcilable with conversion, and so he dropped them. The judgment in comprehension, he then declared, was to all intents and purposes the same as one in extension, and as to causation—why, a cause is a class, and an effect is an individual belonging to that class!22

Let us see what is the result of treating applicates as general ideas. Take an example in each of the categories.

'The paper is white.' This means that the paperhas the property or attribute of whiteness. In logic it is interpreted to mean that paper is an individual of the classwhite. This is wrong, for there is no such class. No sane person would form a class out of salt, snow, milk, china, silver, the moon, and other white things; for though they have a common property it is not the sign of a common human utility.

The confusing a single property with a class is not always owing to exigencies of syllogism. It pervades the writings of most Western metaphysicians, and may be accounted for in this manner.

General ideas and abstract properties or ideas have in common that they arepartialrecognitions of what we perceive (xiv). The partition in each is however made in a different way, and for a different purpose. In generalisation the selection is done almost mechanically. We see many things that have some common relation, function, or utility for us, and we remember only so much of them as appears to be necessary for the recognition of that relation or utility—just so much of the Intellectual experience as has always accompanied the Sentimental experience. The process is very like that of putting a piece of wood or ivory in a turning-lathe, and whittling off all that we do not want. A general idea is the useful core of a multitude of superposed observations, each of which had something irrelevant—somethingwhich it is better to forget. We whittle this off and remember only the core.

Abstraction, on the other hand, is a conscious and deliberate operation from beginning to end. It consists in distinguishing one by one the properties of a thing, and even treating each property as if it had an independent existence. For this exercise it is not necessary to observe many things: we can analyse one alone, though an acquaintance with other cognate objects is sometimes necessary to call our attention to single properties. We need the shock of difference to be able to distinguish well a fine abstraction—the difference between shades of colours, for example. Abstraction is thus a minute attention to individuals, and need not for a moment be confounded with generalisation.

Another cause of the confusion in question can be traced to the use of the verb 'is' to represent both the relation of a thing to the general idea it has contributed to form, and the relation of a single property to the thing in which it inheres. We say 'The manisa British subject'—classifying him; we say also 'The maniscold'—mentioning one of his attributes. There is no class of cold men, and the two relations have nothing in common. A class does not inhere in a man as cold inheres in him. There is noobjectcorresponding to class—it is a conceptual creation.

The ambiguity of 'is' favours the syllogistic doctrine of predication, and there is a rule to the effect that in syllogising propositions, all verbs are to be converted into 'is' (or its conjugates) with a participle or noun, so that if they were not before statements of classification they now become such. 'He walks' is clearly no classification; but 'he is walking' is assimilated by false analogy to such a classification as 'he is human,' and so is treated as a classification by those who reason according to the Letter.

The substantive verb has no positive and uniform meaning. As an auxiliary it is a mere sign of tense, and in other positions it is an indefinite mark of relationship, the precise meaning of which must be determined by the subject and the context. It may sometimes be dispensed with in classification, as 'Victoria Regina'—'Phillips, Dentist.'

In the second category we have such propositions as 'the book lies on the table.' In syllogistic this is first altered to 'the book is lying on the table,' and it is feigned that 'lying on the table' is a class or general idea, and 'book' an individual of that class. To interpret 'the groom stands by the horse' a class has to be created, composed of the persons who happen to be standing by horses.

'The mountain is ten miles off' is a judgment in perspection. Syllogistically we are asked to believe that a class of things exists having the common propertyof being ten miles off, and that the mountain is entered in that class. The absurdity of this doctrine is self-evident.

In the remaining categories the reduction to 'is' has, if possible, a worse effect. In changing 'Canada lies west of Ireland' into 'Canada is a country lying west of Ireland,' we lose the relation in concretion, and express instead a verbal definition. Instead of affirming a position we explain a name. In such a proposition as 'the town of A lies 100 miles due north of B,' it is plain the predicate cannot be a class, for only one place has the quality expressed.

In the fifth category we have such a proposition as 'water freezes when the temperature falls to zero Centigrade.' This is turned into a substantive sentence by saying 'water is that liquid which freezes,' &c., which is a verbal or identical proposition.

'Cecrops founded Athens' is a judgment in causation. In turning it into 'Cecrops was (or is) the founder of Athens,' we emphasise the man's name, but the relation signified by 'founded' is slurred over or lost sight of. Boole converts 'Caesar conquered the Gauls' into 'Caesar is he who conquered the Gauls,'23and this he interpreted as classification. We need not be surprised that he should suppose a class could be formed by one individual, for he elsewhere tells us thatNothingis a class.24

Classification is not judgment of any sort—it is a variety of recollection. Logicians imagine it is the only judgment, and so far as they can they degrade true judgments to that spurious form.

Moods of the Syllogism.Having persuaded themselves that classification is the beginning, middle, and end of reasoning, logicians next proceed to divide the matter of their science.

Modern logicians who have some acquaintance with real thinking as exemplified in works of physical science, can, if acting according to their natural intelligence, lay down correct rules for dividing a subject. These are simple and obvious: divide according to fundamental resemblance—let each division correspond to some definite human utility—let the more important properties take precedence of the less important, and so forth: the merest common sense.

But in the division of their own subject they follow Aristotle, and so lose their way.

It is plain that an act of reasoning is a mental thing in the first place, and only when uttered, and thus in a secondary sense, is it a material object. The classification of arguments should therefore follow mental characteristics. Logicians make it follow the material characteristics of the terms in which the arguments are uttered. Their moods of the syllogism are mere varieties of expression, not varieties of reason.

The number of these moods is accidental, depending on flexibility of language and ingenuity in inventing varieties of syntax. Mere transposition of premises constitutes a difference of mood. Logicians however pretend to base their numeration on a more general necessity. They calculate from the distinctive parts of the three propositions forming a syllogism, varied by negation, &c., that thereought to besixty-four moods. Experience proves that in spite of their free and easy method of multiplying syllogistic varieties they cannot produce anything like that number. One logician has thirty-six moods, another thirty-two, a third eleven; the more orthodox fix the number at nineteen. But they all admit that every argument can be reduced to one of four fundamental types—the moods of the First Figure. Why then have more classes than these four? Because, says Whately, it would be 'occasionally tedious' to reduce every argument to the first figure.

If the 11, 19, 32, or 36 classes were natural arguments taken down untouched from men's lips, and it was found to be useless and troublesome to reduce them to four artificial forms, the plea might be admitted. But the so-called valid syllogisms are themselves artificial, and just as tedious to make as the moods of the first figure. Not only so, but an elaborate system of mnemonic rules is provided for reducing the valid moods to the fundamental moods, thusadmitting that the former are only intermediate halting places between the natural speech and the fundamental moods. It isexpectedthat the intermediates should be reduced to the first figure.

Is there anything analogous to this sort of division in any science or branch of practical thought? Would logicians themselves sanction such a classification in a natural science? If a zoologist, for example, were to determine beforehand how many classes of animals there ought to be, would they not say he was acting improperly? If, after discovering that he had five times as many classes as he could find animals to put into them, he still retained his classification and required his pupils to write out the names or symbols of all the useless classes—would not logicians be apt to call him a pedant? Yet in a modern work on logic such a task is prescribed for students:—

'Write out the sixty-four moods of the syllogism,and strike out the fifty-three invalid ones.'

We might have excused the existence of a merely verbal classification in logic, if it were accompanied by and subordinated to a classification of theorems considered as mental facts. But in syllogistic the verbal is the dominant classification, and we have seen from the procedure of Sir William Hamilton—in dropping his categorical judgments—that when the two principles of division conflict, it is the mental whichhas to give way. The Letter is allowed to kill the Spirit.

All the Moods reducible to One.Syllogists appear not to know their own schematism very well. They say there are four ultimate moods, which it is impossible to reduce to any lower number. But since each of the four is, mentally, a double classification, it must be possible to reflect this common property in the mode of expression. The difference between them can only be verbal. Let us adopt another than the ordinary symbolism.

Cut a card into three triangular pieces of unequal size, and call them by the letters A, B, C, beginning with the largest. These are the terms of the syllogism.

syllogismBarbara.Celarent.

Barbara.Celarent.

syllogismDarii.Ferio.

Darii.Ferio.

The first moodBarbarais formed by placing the cards on top of each other, so that B is within themargin of A, and C within the margin of B. This is the syllogism, 'All B is A, all C is B, therefore all C is A.'

Next let B and C be as above, but let A be wholly apart from both. This isCelarent: 'No B is A, all C is B, therefore no C is A.'

InDariithe whole of B is in A, but only a part of C coincides with B. The syllogism is: 'All B is A, some C is B, therefore some C is A.'

InFerioA is again wholly separated from the others, and C is only partially in B. Argument: 'No B is A, some C is B, therefore some C is not A.'

It is to be remembered that all the other figures and moods are reducible to the above figure of four moods, so that the reduction applicable to the latter is equally applicable to the former.

To reduceDariitoBarbaraall that is necessary is to ignore the dotted part of C. That is suggested by the use of the word 'some,' which has a correlative 'all' or 'others.' But the correlative quantity does not enter into the syllogism, and we know nothing about it. It may not even exist. We are therefore at liberty to substitute for 'some C' the name D, and consider it an integer instead of a fraction. Then we have theBarbarasyllogism: 'All B is A, all D (= some C) is B, therefore all D is A.' The phrase 'all of some' is quite allowable: 'I met some firemen, all of whom wore brass helmets.'

Ferioin the same manner is reduced toCelarent. The dotted part of C is cut away, and the part really significant in the syllogism is called E. Then 'No B is A, all E is B, no E is A.'

FinallyCelarentcan be reduced toBarbara. B cannot indeed be enclosed in A, but we assume the existence of a whole having all the characters which A hasnot, or having none of the characters which A has. This is the whole F = Not-A. ThenCelarentbecomesBarbarathus: 'All B is F, all C is B, therefore all C is F.'

This demonstrates that there is only one fundamental operation where syllogists suppose there are at least four. The difference is wholly a matter of language, and disappears on changing the names of the terms and ignoring irrelevant suggestions. But the syllogism, I repeat, does not represent the act of reasoning, and its moods and figures are fit only to be a game for children.

20:Logic, Book I. § 3.

21:Logic, Book II. c. 3. § 2.

22:Lectures, iii. pp. 287 and 356. The impossibility of reconciling their definitions and rules to real thinking and argument is the despair of logicians. Most of them take to symbols, which are more accommodating than real experience, having just such properties as their makers choose to put in them. Sir William Hamilton had the courage to declare that a logician might use arguments of a concrete or real form, but that it is not necessary they should agree with real fact. 'The logician has a right to suppose any material impossibility, any material falsity; he takes no account of what is objectively impossible or false, he has a right to assume what premises he please, provided that they do not involve a contradiction in terms.'—Id.322. That means in plain English that a logician may misrepresent matters of fact, if he cannot otherwise establish his theory!

23:Laws of Thought, p. 35.

24:Ibid.p. 47.

The theorems given for practice in logic books are useful dialectic material, but they do not fully illustrate all the categories. Logicians have no definite categories, and in selecting examples they are unconsciously biassed in favour of those that can be most easily interpreted to signify classification. The really generalistic examples are rare; the most are judgments of inherence, admitted in virtue of the assumption that inherent properties can—when it is needful to preserve the traditional notion of predication—be considered class-ideas. Theorems in perspection and concretion we do not expect to find in logic books, for these, in so far as they are distinct from association, are categories peculiar to the Berkeleyan philosophy.

Whately has the following example in association—'Lias lies above red sandstone; red sandstone lies above coal; therefore lias lies above coal.' No doubt Whately would, in syllogising this, have changed the propositions to 'Red sandstone is lying,' &c., and have assumed that 'lying above coal' is a class to which red sandstone belongs.

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Here are examples of arguments in inherence—

A hot skin, quick pulse, intense thirst have invariably in my experience coexisted with fever; the person now examined exhibits these symptoms, so I infer that he has a fever.

Great width of skull between the ears is invariably found united with a destructive temperament; this animal's skull is very wide between the ears; hence it may be concluded that he has a destructive temperament.

Cloven feet belong universally—i.e.as far as our experience goes—to horned animals; we may conclude that this fossil animal, since it appears to have had cloven feet, was horned.

When an architect, contemplating the fragments of a building, restores it in imagination after the analogy of similar buildings, we have an argument in inherence. Such speculations are generally too long and complex for analysis, but an instructive example occurs in Canon Rawlinson'sSeventh Oriental Monarchy, which I will venture to quote, marking the phrases that introduce or express the rational idea. Observe the difference of style between this, which is real practical reasoning, and the trivial certainties of Syllogistic.

'What remains of this massive erection [the Takht-i-Khosru, or palace of Chosroës Anushirwan, at Ctesiphon] is a mere fragment, which,to judge from the other extant Sassanian ruins, cannot have formed so much as one fourth part of the original edifice. Nothing has come down to our day but a single vaulted hall on the grandest scale, together with the mere outer wall of what no doubt constituted the main facade of the building. The apartments, which,according to all analogy, must have existed at the two sides, and in the rear, of the great hall, some of whichshouldhave been vaulted, have wholly perished.Imagination may supplythem from the Firuzabad, or the Mashita palace; but not a trace, even of their foundations, is extant; and the details consequently are uncertain, though the general plan can scarcely be doubted. At each side of the great hallwere probablytwo lateral ones, communicating with each other, and capable of being entered either from thehall or from the outer air. Beyond the great hallwas probablya domed chamber equalling it in width, and opening upon a court, round which were a number of moderate-sized apartments. The entire buildingwas no doubtan oblong square, of which the shorter sides seem to have measured 370 feet. It had at least three, andmay not improbably have hada larger number of entrances, since it belongs to tranquil times and a secure locality.'

***

The most notable argument in the category of concretion is undoubtedly the inference as to the sphericity of the earth. Next is the sub-inference by Columbus that China could be reached by sailing westward from Portugal. If the syllogistic opinion were valid—that a conclusion must be absolutely true or absolutely false—the expedition of Columbus was based on a fallacy. Most people think it was eminently rational.

No one has seen the north or the south poles, and the conviction that they could be realised, if certain difficulties of transport were overcome, is a sub-inference of the same character.

Here is a common type of inference in perspection—

And this—

In these cases we have not seen the man or the scaffolding before, and have not measured the latter or the distance to the former: the conclusions are imaginary judgments fairly drawn from known premises.

***

The deciphering of hieroglyphics, cuneiform inscriptions, and remains of other dead and forgotten languages, is argument in causation. Examples cannot conveniently be quoted even in a condensed form, but this kind of reasoning is most interesting dialectically from the slightness of the analogies that are nevertheless found to give valid conclusions.

***

This is considered argument by Whately—

The supposed case is a verbal proposition, serving to rename the subject of precedent. There is no reasoning. If we already know that Louis is a good king and is also the governor of France (the given mattersof fact), there is no rational imagination involved in rearranging these data as in the proposed conclusion.

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'He who calls you a man speaks truly; he who calls you a fool calls you a man; therefore he who calls you a fool speaks truly.'—A fallacy of cross reasoning, and the predicate is a class.

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'Nothing is heavier than platina; feathers are heavier than nothing; therefore feathers are heavier than platina.'—A trivial equivoque.

The following is more subtle. 'Theft is a crime; theft was encouraged by the laws of Sparta; therefore the laws of Sparta encouraged crime.'—At most the laws of Sparta encouraged one crime; but there is a fallacy of equivocation. Taking things surreptitiously from the person in whose possession they may be, is not a crime—is not theft—in a society so communistic as the Spartan. There it was encouraged as an exercise in adroitness. This example shows the necessity of knowing the matter of the argument.

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'Warm countries alone produce wine; Spain is a warm country; therefore Spain produces wine.'

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'Meat and drink are necessaries of life; the revenues of Vitellius were spent in meat and drink; therefore the revenues of Vitellius were spent on the necessaries of life.'—Fallacy of composition: meat and drink in moderate quantities are necessaries of one life, but not food of every kind and in excessive quantities.

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'He who is most hungry eats most; he who eats least is most hungry; therefore he who eats least eats most.'—A fallacy of accident: he who eats least does notat the same timeeat most.

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'Whatever body is in motion must move either in the place where it is, or in the place where it is not; neither of these is possible; therefore there is no such thing as motion.'—It is an abuse of reason to attempt to disprove matters of fact. The conclusion of an argument being always problematical, it can have no force against actual experience. We experience motion, therefore it cannot be disproved.

***

'A wise lawgiver must either recognise the rewards and punishments of a future state, or he must be ableto appeal to an extraordinary Providence, dispensing them regularly in this life; Moses did not do the former, therefore he must have done the latter'—(Warburton, from Whately).—The reasoner omitted to establish that Moses was a wise lawgiver, so that the precedent does not apply to his case, except by courtesy.

***

'That man is independent of the caprices of fortune who places his chief happiness in moral and intellectual excellence; a true philosopher is independent of the caprices of fortune; therefore a true philosopher is one who places his chief happiness in moral and intellectual excellence.' An instance of cross reasoning.

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'For those who are bent on cultivating their minds by diligent study, the incitement of academical honours is unnecessary; and for the idle it is ineffectual, for such are indifferent to mental improvement; therefore the incitement of academical honours is either unnecessary or ineffectual.'

A fallacy of doubtful precedent: because two kinds of students are not benefited by the hope of honoursit is prematurely concluded that no others exist who may be so benefited.

***

'He who bears arms at the command of the magistrate does what is lawful for a Christian; the Swiss in the French service, and the British in the American service, bore arms at the command of the magistrate; therefore they did what is lawful for a Christian.'

The conclusion is valid so far as the information given enables us to judge. If we know from other sources that the Swiss and British who are referred to, committed atrocities at the command of the magistrate, the conclusion is a fallacy of accident. In general it is lawful to obey a magistrate, but there may be particular cases when it is not.

***

'Anyone who is candid will refrain from condemning a book without reading it; some reviewers do not refrain from this; therefore some reviewers are not candid.'—This is cross reasoning and invalid. It is one thing to say that the uncandid do not refrain, and another that all who do not refrain are uncandid. The conclusion is taken from the latter proposition, which is not asserted.

***

'Everyone desires happiness; virtue is happiness; therefore everyone desires virtue.'

The case is manifestly untrue.

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'He who has a confirmed habit of any kind of action exercises no self-denial in the practice of that action; a good man has a confirmed habit of virtue; therefore he who exercises self-denial in the practice of virtue is not a good man.'—(Arist.Eth.Bk. II., from Whately.)

The conclusion drawn is fallacious, the second theorem being based on contrast.

***

'According to theologians, a man must possess faith to be acceptable to the Deity; now he who believes all the fables of heathen mythology must possess faith; therefore such a one must, according to theologians, be acceptable to the Deity.'

'Faith' is ambiguous, meaning in the precedent,spiritual aspiration, and in the case ignorant credulity.

***

'No evil should be allowed that good may come of it; all punishment is an evil; therefore no punishment should be allowed that good may come of it.'—'Evil' is ambiguous, meaning wrong-doing in the precedent and pain in the case; the conclusion is therefore fallacious.

***

'The principles of justice are variable; the appointments of nature are invariable; therefore the principles of justice are no appointments of nature.'—(Arist.Eth.Bk. V., from Whately.) The terms 'principles of justice' and 'nature' require to be defined. It might be said that justice is one principle, everywhere and always the same, and that only its embodiments in law and custom are variable.

***

'What happens every day is not improbable; some things, against which the chances are many thousands to one, happen every day; therefore some things against which the chances are many thousands to one, are not improbable.'—A fallacy of division: that improbable things in general happen every day does not render the occurrence of any one a probable event.

***

'Protection from punishment is plainly due to the innocent; therefore, as you maintain that this person ought not to be punished, it appears that you are convinced of his innocence.'—A fallacy of cross reasoning.

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'He who cannot possibly act otherwise than he does, has neither merit nor demerit in his action; a liberal and benevolent man cannot possibly act otherwise than he does in relieving the poor; therefore such a man has neither merit nor demerit in his action.'—To 'have merit in an action' is scarcely intelligible. A man's merit is in his character, and his actions are effects and signs of character.

***

'All the fish that the net inclosed were an indiscriminate mixture of various kinds; those that were set aside and saved as valuable were fish that the net inclosed; therefore those that were set aside and saved as valuable were an indiscriminate mixture of various kinds.'

An instance of the fallacy of division: what is true of the whole contents of the net is not necessarily true of a portion of the contents.

***

'A desire to gain by another's loss is a violation of the tenth commandment; all gaming, therefore, since it implies a desire to profit at the expense of another, involves a breach of the tenth commandment.'—A valid argument in inherence.

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'He that destroys a man who usurps despotic power in a free country, deserves well of his countrymen; Brutus destroyed Caesar, who usurped despotic power in Rome; therefore he deserved well of the Romans.'—If Rome was 'a free country' the conclusion is valid.

***

'No fish suckles its young; the whale suckles its young; the whale is therefore no fish.'

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'This explosion must have been occasioned by gunpowder, for nothing else would have possessed sufficient force.'

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'Every man should be moderate, for excess will cause disease.'

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'Blessed are the merciful, for they shall obtain mercy.'

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'Some speculative men are unworthy of trust; for they are unwise, and no unwise man can be trusted.'

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