Part 12

No doubt it is, for in contemplating a thing we can mentally enter it into all the classes to which it appears 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 that _for logical purposes_ every 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,' which means 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 paper has the property or attribute of whiteness. In logic it is interpreted to mean that paper is an individual of the class _white_. 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 are _partial_ recognitions 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--something which 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 man _is_ a British subject'--classifying him; we say also 'The man _is_ cold'--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 no _object_ corresponding 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 property of 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,'[23] and 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 that _Nothing_ is 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 there _ought to be_ sixty-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, thus admitting that the former are only intermediate halting places between the natural speech and the fundamental moods. It is _expected_ that 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 which has 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.

A A /\B /\ B / /\C / \ /\C / / /\ / \ / /\ / / / \ / \ / / \ / / / \ / \ / / \ / / / \ / \ / / \ +------------+ +------------+ +----------+ _Barbara._ _Celarent._

A A /\B /\ B / /\ C / \ /\ C / / \ : / \ / \ : / / \: : / \ / \: : / / /\ : / \ / /\ : / / / \ : / \ / / \ : +------------+... +------------+ +----------+... _Darii._ _Ferio._

The first mood _Barbara_ is formed by placing the cards on top of each other, so that B is within the margin 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 is _Celarent_: 'No B is A, all C is B, therefore no C is A.'

In _Darii_ the 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.'

In _Ferio_ A 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 reduce _Darii_ to _Barbara_ all 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 the _Barbara_ syllogism: '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.'

_Ferio_ in the same manner is reduced to _Celarent_. 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.'

Finally _Celarent_ can be reduced to _Barbara_. B cannot indeed be enclosed in A, but we assume the existence of a whole having all the characters which A has _not_, or having none of the characters which A has. This is the whole F = Not-A. Then _Celarent_ becomes _Barbara_ thus: '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.

[Footnote 20: _Logic_, Book I. § 3.]

[Footnote 21: _Logic_, Book II. c. 3. § 2.]

[Footnote 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!]

[Footnote 23: _Laws of Thought_, p. 35.]

[Footnote 24: _Ibid._ p. 47.]

STUDIES IN DIALECTIC

XXXIX

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.

***

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.

I. Cloven feet | inhere with horns -------------------------+------------------- Fossil animal appears to | _it is probable he have had cloven feet | had horns_

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's _Seventh 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 which _should_ have been vaulted, have wholly perished. _Imagination may supply_ them 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 hall _were probably_ two lateral ones, communicating with each other, and capable of being entered either from the hall or from the outer air. Beyond the great hall _was probably_ a domed chamber equalling it in width, and opening upon a court, round which were a number of moderate-sized apartments. The entire building _was no doubt_ an oblong square, of which the shorter sides seem to have measured 370 feet. It had at least three, and _may not improbably have had_ a 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--

III. That church | is 100 yards off --------------------+---------------------- A man appears on | _he is_ 100 _ys. off_ the roof of the ch. |

And this--

III. That distant house | is 60 ft. high ----------------------------+------------------------ It appears to be scaffolded | _the scaffold is about_ to a third of its height | 20 _feet high_

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--

I. Louis | is a good king -----------------------+--------------------------- The governor of France | _therefore the g. of F. is is Louis | a good king_

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 matters of fact), there is no rational imagination involved in rearranging these data as in the proposed conclusion.

***

'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.

All fools | are men --------------+-------- You are a man | _N. C._

***

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