Chapter 16

THE SYLLOGISTIC ANALYSIS OF PROPOSITIONS INTO TERMS.

I.--THE BARE ANALYTIC FORMS.

The word "term" is loosely used as a mere synonym for a name: strictly speaking, a term ([Greek: horos], a boundary) is one of the parts of a proposition as analysed into Subject and Predicate. In Logic, a term is a technical word in an analysis made for a special purpose, that purpose being to test the mutual consistency of propositions.

For this purpose, the propositions of common speech may be viewed as consisting of two TERMS, a linkword called the copula (positive or negative) expressing a relation between them, and certain symbols of quantity used to express that relation more precisely.

Let us indicate the Subject term by S, and the Predicate term by P.

All propositions may be analysed into one or other of four forms:--

All S is P, No S is P, Some S is P, Some S is not P.

All S is P is called the UNIVERSAL AFFIRMATIVE, and is indicated by the symbol A (the first vowel of Affirmo).

No S is P is called the UNIVERSAL NEGATIVE, symbol E (the first vowel of Nego).

Some S is P is called the PARTICULAR AFFIRMATIVE, symbol I (the second vowel of _aff_Irmo).

Some S is not P is called the PARTICULAR NEGATIVE, symbol O (the second vowel of _neg_O).

The distinction between Universal and Particular is called a distinction in QUANTITY; between Affirmative and Negative, a distinction in QUALITY. A and E, I and O, are of the same quantity, but of different quality: A and I, E and O, same in quality, different in quantity.

In this symbolism, no provision is made for expressing degrees of particular quantity. _Some_ stands for any number short of all: it may be one, few, most, or all but one. The debates in which Aristotle's pupils were interested turned mainly on the proof or disproof of general propositions; if only a proposition could be shown to be not universal, it did not matter how far or how little short it came. In the Logic of Probability, the degree becomes of importance.

Distinguish, in this Analysis, to avoid subsequent confusion, between the Subject and the Subject Term, the Predicate and the Predicate Term. The Subject is the Subject Term quantified: in A and E,[1] "All S"; in I and O, "Some S". The Predicate is the Predicate Term with the Copula, positive or negative: in A and I, "is P"; in E and O, "is not P".

It is important also, in the interest of exactness, to note that S and P, with one exception, represent general names. They are symbols for classes. P is so always: S also except when the Subject is an individual object. In the machinery of the Syllogism, predications about a Singular term are treated as Universal Affirmatives. "Socrates is a wise man" is of the form All S is P.

S and P being general names, the signification of the symbol "is" is not the same as the "is" of common speech, whether the substantive verb or the verb of incomplete predication. In the syllogistic form, "is" means _is contained in_, "is not," _is not contained in_.

The relations between the terms in the four forms are represented by simple diagrams known as Euler's circles.

Diagram 5 is a purely artificial form, having no representative in common speech. In the affirmations of common speech, P is always a term of greater extent than S.

No. 2 represents the special case where S and P are coextensive, as in All equiangular triangles are equilateral.

S and P being general names, they are said to be DISTRIBUTED when the proposition applies to them in their whole extent, that is, when the assertion covers every individual in the class.

In E, the Universal Negative, both terms are distributed: "No S is P" wholly excludes the two classes one from the other, imports that not one individual of either is in the other.

In A, S is distributed, but not P. S is wholly in P, but nothing is said about the extent of P beyond S.

In O, S is undistributed, P is distributed. A part of S is declared to be wholly excluded from P.

In I, neither S nor P is distributed.

It will be seen that the Predicate term of a Negative proposition is always distributed, of an Affirmative, always undistributed.

A little indistinctness in the signification of P crept into mediaeval text-books, and has tended to confuse modern disputation about the import of Predication. Unless P is a class name, the ordinary doctrine of distribution is nonsense; and Euler's diagrams are meaningless. Yet many writers who adopt both follow mediaeval usage in treating P as the equivalent of an adjective, and consequently "is" as identical with the verb of incomplete predication in common speech.

It should be recognised that these syllogistic forms are purely artificial, invented for a purpose, namely, the simplification of syllogising. Aristotle indicated the precise usage on which his syllogism is based (_Prior Analytics_, i. 1 and 4). His form[2] for All S is P, is S is wholly in P; for No S is P, S is wholly not in P. His copula is not "is," but "is in," and it is a pity that this usage was not kept. "All S is in P" would have saved much confusion. But, doubtless for the sake of simplicity, the besetting sin of tutorial handbooks, All S is P crept in instead, illustrated by such examples as "All men are mortal".

Thus the "is" of the syllogistic form became confused with the "is" of common speech, and the syllogistic view of predication as being equivalent to inclusion in, or exclusion from a class, was misunderstood. The true Aristotelian doctrine is not that predication consists in referring subjects to classes, but only that for certain logical purposes it may be so regarded. The syllogistic forms are artificial forms. They were not originally intended to represent the actual processes of thought expressed in common speech. To argue that when I say "All crows are black," I do not form a class of black things, and contemplate crows within it as one circle is within another, is to contradict no intelligent logical doctrine.

The root of the confusion lies in quoting sentences from common speech as examples of the logical forms, forgetting that those forms are purely artificial. "Omnis homo est mortalis," "All men are mortal," is not an example formally of All S is P. P is a symbol for a substantive word or combination of words, and mortal is an adjective. Strictly speaking, there is no formal equivalent in common speech, that is, in the forms of ordinary use--no strict grammatical formal equivalent--for the syllogistic propositional symbols. We can make an equivalent, but it is not a form that men would use in ordinary intercourse. "All man is in mortal being" would be a strict equivalent, but it is not English grammar.

Instead of disputing confusedly whether All S is P should be interpreted in extension or in comprehension, it would be better to recognise the original and traditional use of the symbols S and P as class names, and employ other symbols for the expression in comprehension or connotation. Thus, let _s_ and _p_ stand for the connotation. Then the equivalent for All S is P would be All S has _p_, or _p_ always accompanies _s_, or _p_ belongs to all S.

It may be said that if predication is treated in this way, Logic is simplified to the extent of childishness. And indeed, the manipulation of the bare forms with the help of diagrams and mnemonics is a very humble exercise. The real discipline of Syllogistic Logic lies in the reduction of common speech to these forms.

This exercise is valuable because it promotes clear ideas about the use of general names in predication, their ground in thought and reality, and the liabilities to error that lurk in this fundamental instrument of speech.

[Footnote 1: For perfect symmetry, the form of E should be All S is not P. "No S is P" is adopted for E to avoid conflict with a form of common speech, in which All S is not P conveys the meaning of the Particular Negative. "All advices are not safe" does not mean that safeness is denied of all advices, but that safeness cannot be affirmed of all, _i.e._, Not all advices are safe, _i.e._, some are not.]

[Footnote 2: His most precise form, I should say, for in "P is predicated of every S" he virtually follows common speech.]

II.--THE PRACTICE OF SYLLOGISTIC ANALYSIS.

The basis of the analysis is the use of general names in predication. To say that in predication a subject is referred to a class, is only another way of saying that in every categorical sentence the predicate is a general name express or implied: that it is by means of general names that we convey our thoughts about things to others.

"Milton is a great poet." "Quoth Hudibras, _I smell a rat_." _Great poet_ is a general name: it means certain qualities, and applies to anybody possessing them. _Quoth_ implies a general name, a name for persons _speaking_, connoting or meaning a certain act and applicable to anybody in the performance of it. _Quoth_ expresses also past time: thus it implies another general name, a name for persons _in past time_, connoting a quality which differentiates a species in the genus persons speaking, and making the predicate term "persons speaking in past time". Thus the proposition _Quoth Hudibras_, analysed into the syllogistic form S is in P, becomes S (Hudibras) is in P (persons speaking in past time). The Predicate term P is a class constituted on those properties. _Smell a rat_ also implies a general name, meaning an act or state predicable of many individuals.

Even if we add the grammatical object of _Quoth_ to the analysis, the Predicate term is still a general name. Hudibras is only one of the persons speaking in past time who have spoken of themselves as being in a certain mood of suspicion.[1]

The learner may well ask what is the use of twisting plain speech into these uncouth forms. The use is certainly not obvious. The analysis may be directly useful, as Aristotle claimed for it, when we wish to ascertain exactly whether one proposition contradicts another, or forms with another or others a valid link in an argument. This is to admit that it is only in perplexing cases that the analysis is of direct use. The indirect use is to familiarise us with what the forms of common speech imply, and thus strengthen the intellect for interpreting the condensed and elliptical expression in which common speech abounds.

There are certain technical names applied to the components of many-worded general names, CATEGOREMATIC and SYNCATEGOREMATIC, SUBJECT and ATTRIBUTIVE. The distinctions are really grammatical rather than logical, and of little practical value.

A word that can stand by itself as a term is said to be Categorematic. _Man_, _poet_, or any other common noun.

A word that can only form part of a term is Syncategorematic. Under this definition come all adjectives and adverbs.

The student's ingenuity may be exercised in applying the distinction to the various parts of speech. A verb may be said to be _Hypercategorematic_, implying, as it does, not only a term, but also a copula.

A nice point is whether the Adjective is categorematic or syncategorematic. The question depends on the definition of "term" in Logic. In common speech an adjective may stand by itself as a predicate, and so might be said to be Categorematic. "This heart is merry." But if a term is a class, or the name of a class, it is not Categorematic in the above definition. It can only help to specify a class when attached to the name of a higher genus.

Mr. Fowler's words SUBJECT and ATTRIBUTIVE express practically the same distinction, except that Attributive is of narrower extent than syncategorematic. An Attributive is a word that connotes an attribute or property, as _hot_, _valorous_, and is always grammatically an adjective.

The EXPRESSION OF QUANTITY, that is, of Universality or non-universality, is all-important in syllogistic formulae. In them universality is expressed by _All_ or _None_. In ordinary speech universality is expressed in various forms, concrete and abstract, plain and figurative, without the use of "all" or "none".

Uneasy lies the head that wears a crown. He can't be wrong whose life is in the right. What cat's averse to fish? Can the leopard change his spots? The longest road has an end. Suspicion ever haunts the guilty mind. Irresolution is always a sign of weakness. Treason never prospers.

A proposition in which the quantity is not expressed is called by Aristotle INDEFINITE ([Greek: adioristos]). For "indefinite"[2] Hamilton suggests PREINDESIGNATE, undesignated, that is, before being received from common speech for the syllogistic mill. A proposition is PREDESIGNATE when the quantity is definitely indicated. All the above propositions are "Predesignate" universals, and reducible to the form All S is P, or No S is P.

The following propositions are no less definitely particular, reducible to the form I or O. In them as in the preceding quantity is formally expressed, though the forms used are not the artificial syllogistic forms:--

Afflictions are often salutary. Not every advice is a safe one. All that glitters is not gold. Rivers generally[3] run into the sea.

Often, however, it is really uncertain from the form of common speech whether it is intended to express a universal or a particular. The quantity is not formally expressed. This is especially the case with proverbs and loose floating sayings of a general tendency. For example:--

Haste makes waste. Knowledge is power. Light come, light go. Left-handed men are awkward antagonists. Veteran soldiers are the steadiest in fight.

Such sayings are in actual speech for the most part delivered as universals.[4] It is a useful exercise of the Socratic kind to decide whether they are really so. This can only be determined by a survey of facts. The best method of conducting such a survey is probably (1) to pick out the concrete subject, "hasty actions," "men possessed of knowledge," "things lightly acquired"; (2) to fix the attribute or attributes predicated; (3) to run over the individuals of the subject class and settle whether the attribute is as a matter of fact meant to be predicated of each and every one.

This is the operation of INDUCTION. If one individual can be found of whom the attribute is not meant to be predicated, the proposition is not intended as Universal.

Mark the difference between settling what is intended and settling what is true. The conditions of truth and the errors incident to the attempt to determine it, are the business of the Logic of Rational Belief, commonly entitled Inductive Logic. The kind of "induction" here contemplated has for its aim merely to determine the quantity of a proposition in common acceptation, which can be done by considering in what cases the proposition would generally be alleged. This corresponds nearly as we shall see to Aristotelian Induction, the acceptance of a universal statement when no instance to the contrary is alleged.

It is to be observed that for this operation we do not practically use the syllogistic form All S is P. We do not raise the question Is All S, P? That is, we do not constitute in thought a class P: the class in our minds is S, and what we ask is whether an attribute predicated of this class is truly predicated of every individual of it.

Suppose we indicate by _p_ the attribute, knot of attributes, or concept on which the class P is constituted, then All S is P is equivalent to "All S has _p_": and Has All S _p_? is the form of a question that we have in our minds when we make an inductive survey on the above method. I point this out to emphasise the fact that there is no prerogative in the form All S is P except for syllogistic purposes.

This inductive survey may be made a useful COLLATERAL DISCIPLINE. The bare forms of Syllogistic are a useless item of knowledge unless they are applied to concrete thought. And determining the quantity of a common aphorism or saw, the limits within which it is meant to hold good, is a valuable discipline in exactness of understanding. In trying to penetrate to the inner intention of a loose general maxim, we discover that what it is really intended to assert is a general connexion of attributes, and a survey of concrete cases leads to a more exact apprehension of those attributes. Thus in considering whether _Knowledge is power_ is meant to be asserted of all knowledge, we encounter along with such examples as the sailor's knowledge that wetting a rope shortens it, which enabled some masons to raise a stone to its desired position, or the knowledge of French roads possessed by the German invaders,--along with such examples as these we encounter cases where a knowledge of difficulties without a knowledge of the means of overcoming them is paralysing to action. Samuel Daniel says:--

Where timid knowledge stands considering Audacious ignorance has done the deed.

Studying numerous cases where "Knowledge is power" is alleged or denied, we find that what is meant is that a knowledge of the right means of doing anything is power--in short, that the predicate is not made of all knowledge, but only of a species of knowledge.

Take, again, _Custom blunts sensibility_. Putting this in the concrete, and inquiring what predicate is made about "men accustomed to anything" (S), we have no difficulty in finding examples where such men are said to become indifferent to it. We find such illustrations as Lovelace's famous "Paradox":--

Through foul we follow fair For had the world one face And earth been bright as air We had known neither place. Indians smell not their nest The Swiss and Finn taste best The spices of the East.

So men accustomed to riches are not acutely sensible of their advantages: dwellers in noisy streets cease to be distracted by the din: the watchmaker ceases to hear the multitudinous ticking in his shop: the neighbours of chemical works are not annoyed by the smells like the casual passenger. But we find also that wine-tasters acquire by practice an unusual delicacy of sense; that the eyes once accustomed to a dim light begin to distinguish objects that were at first indistinguishable; and so on. What meanings of "custom" and of "sensibility" will reconcile these apparently conflicting examples? What are the exact attributes signified by the names? We should probably find that by sensibility is meant emotional sensibility as distinguished from intellectual discrimination, and that by custom is meant familiarity with impressions whose variations are not attended to, or subjection to one unvarying impression.

To verify the meaning of abstract proverbs in this way is to travel over the road by which the Greek dialecticians were led to feel the importance of definition. Of this more will be said presently. If it is contended that such excursions are beyond the bounds of Formal Logic, the answer is that the exercise is a useful one and that it starts naturally and conveniently from the formulae of Logic. It is the practice and discipline that historically preceded the Aristotelian Logic, and in the absence of which the Aristotelian formulae would have a narrowing and cramping effect.

CAN ALL PROPOSITIONS BE REDUCED TO THE SYLLOGISTIC FORM? Probably: but this is a purely scientific inquiry, collateral to Practical Logic. The concern of Practical Logic is chiefly with forms of proposition that favour inaccuracy or inexactness of thought. When there is no room for ambiguity or other error, there is no virtue in artificial syllogistic form. The attempt so to reduce any and every proposition may lead, however, to the study of what Mr. Bosanquet happily calls the "Morphology" of Judgment, Judgment being the technical name for the mental act that accompanies the utterance of a proposition. Even in such sentences as "How hot it is!" or "It rains," the rudiment of subject and predicate may be detected. When a man says "How hot it is," he conveys the meaning, though there is no definitely formed subject in his mind, that the outer world at the moment of his speaking has a certain quality or attribute. So with "It rains". The study of such examples in their context, however, reveals the fact that the same form of Common speech may cover different subjects and predicates in different connexions. Thus in the argument:--

"Whatever is, is best. It rains!"--

the Subject is _Rain_ and the Predicate _is now_, "is at the present time," "is in the class of present events".

[Footnote 1: Remember that when we speak of a general name, we do not necessarily mean a single word. A general name, logically viewed, is simply the name of a _genus_, kind, or class: and whether this is single-worded or many-worded is, strictly speaking, a grammatical question. "Man," "man-of-ability," "man-of-ability-and-courage," "man-of-ability-and-courage-and-gigantic-stature," "man-who-fought-at-Marathon"--these are all general names in their logical function. No matter how the constitutive properties of the class are indicated, by one word or in combination, that word or combination is a general name. In actual speech we can seldom indicate by a single word the meaning predicated.]

[Footnote 2: The objection taken to the word "indefinite," that the quantity of particular propositions is indefinite, _some_ meaning any quantity less than all, is an example of the misplaced and frivolous subtlety that has done so much to disorder the tradition of Logic. By "indefinite" is simply meant not definitely expressed as either Universal or Particular, Total or Partial. The same objection might be taken to any word used to express the distinction: the degree of quantity in Some S is not "designate" any more than it is "definite" or "dioristic".]

[Footnote 3: _Generally._ In this word we have an instance of the frequent conflict between the words of common speech and logical terminology. How it arises shall be explained in next chapter. A General proposition is a synonym for a Universal proposition (if the forms A and E are so termed): but "generally" in common speech means "for the most part," and is represented by the symbol of particular quantity, _Some_.]

[Footnote 4: With some logicians it is a mechanical rule in reducing to syllogistic form to treat as I or O all sentences in which there is no formal expression of quantity. This is to err on the safe side, but common speakers are not so guarded, and it is to be presumed rather that they have a universal application in their minds when they do not expressly qualify.]

III.--SOME TECHNICAL DIFFICULTIES.

_The formula for_ EXCLUSIVE PROPOSITIONS. "None but the brave deserve the fair": "No admittance except on business": "Only Protestants can sit on the throne of England".

These propositions exemplify different ways in common speech of naming a subject _exclusively_, the predication being made of all outside a certain term. "None that are not brave, etc.;" "none that are not on business, etc.;" "none that are not Protestants, etc.". No not-S is P. It is only about all outside the given term that the universal assertion is made: we say nothing universally about the individuals within the term: we do not say that all Protestants are eligible, nor that all persons on business are admitted, nor that every one of the brave deserves the fair. All that we say is that the possession of the attribute named is an indispensable condition: a person may possess the attribute, and yet on other grounds may not be entitled to the predicate.

The justification for taking special note of this form in Logic is that we are apt by inadvertence to make an inclusive inference from it. Let it be said that None but those who work hard can reasonably expect to pass, and we are apt to take this as meaning that all who work hard may reasonably expect to pass. But what is denied of every Not-S is not necessarily affirmed of every S.

_The expression of_ TENSE or TIME _in the Syllogistic Forms_. Seeing that the Copula in S is P or S is in P does not express time, but only a certain relation between S and P, the question arises Where are we to put time in the analytic formula? "Wheat is dear;" "All had fled;" time is expressed in these propositions, and our formula should render the whole content of what is given. Are we to include it in the Predicate term or in the Subject term? If it must not be left out altogether, and we cannot put it with the copula, we have a choice between the two terms.

It is a purely scholastic question. The common technical treatment is to view the tense as part of the predicate. "All had fled," All S is P, _i.e._, the whole subject is included in a class constituted on the attributes of flight at a given time. It may be that the Predicate is solely a predicate of time. "The Board met yesterday at noon." S is P, _i.e._, the meeting of the Board is one of the events characterised by having happened at a certain time, agreeing with other events in that respect.

But in some cases the time is more properly regarded as part of the subject. _E.g._, "Wheat is dear". S does not here stand for wheat collectively, but for the wheat now in the market, the wheat of the present time: it is concerning this that the attribute of dearness is predicated; it is this that is in the class of dear things.

_The expression of_ MODALITY _in the Syllogistic Forms_. Propositions in which the predicate is qualified by an expression of necessity, contingency, possibility or impossibility [_i.e._, in English by _must_, _may_, _can_, or _cannot_], were called in Mediaeval Logic _Modal_ Propositions. "Two and two _must_ make four." "Grubs _may_ become butterflies." "Z _can_ paint." "Y _cannot_ fly."

There are two recognised ways of reducing such propositions to the form S is P. One is to distinguish between the _Dictum_ and the _Mode_, the proposition and the qualification of its certainty, and to treat the _Dictum_ as the Subject and the _Mode_ as the Predicate. Thus: "That two and two make four is necessary"; "That Y can fly is impossible".

The other way is to treat the Mode as part of the predicate. The propriety of this is not obvious in the case of Necessary propositions, but it is unobjectionable in the case of the other three modes. Thus: "Grubs are things that have the potentiality of becoming butterflies"; "Z has the faculty of painting"; "Y has not the faculty of flying".

The chief risk of error is in determining the quantity of the subject about which the Contingent or Possible predicate is made. When it is said that "Victories may be gained by accident," is the predicate made concerning All victories or Some only? Here we are apt to confuse the meaning of the contingent assertion with the matter of fact on which in common belief it rests. It is true only that some victories have been gained by accident, and it is on this ground that we assert in the absence of certain knowledge concerning any victory that it may have been so gained. The latter is the effect of the contingent assertion: it is made about any victory in the absence of certain knowledge, that is to say, formally about all.

The history of Modals in Logic is a good illustration of intricate confusion arising from disregard of a clear traditional definition. The treatment of them by Aristotle was simple, and had direct reference to tricks of disputation practised in his time. He specified four "modes," the four that descended to mediaeval logic, and he concerned himself chiefly with the import of contradicting these modals. What is the true contradictory of such propositions as, "It is possible to be" ([Greek: dynaton einai]), "It admits of being" ([Greek: endechetai einai]), "It must be" ([Greek: anankaion einai]), "It is impossible to be" ([Greek: adynaton einai])? What is implied in saying "No" to such propositions put interrogatively? "Is it possible for Socrates to fly?" "No." Does this mean that it is not possible for Socrates to fly, or that it is possible for Socrates not to fly?

A disputant who had trapped a respondent into admitting that it is possible for Socrates not to fly, might have pushed the concession farther in some such way as this: "Is it possible for Socrates not to walk?" "Certainly." "Is it possible for him to walk?" "Yes." "When you say that it is possible for a man to do anything do you not believe that it is possible for him to do it?" "Yes." "But you have admitted that it is possible for Socrates not to fly?"

It was in view of such perplexities as these that Aristotle set forth the true contradictories of his four Modals. We may laugh at such quibbles now and wonder that a grave logician should have thought them worth guarding against. But historically this is the origin of the Modals of Formal Logic, and to divert the names of them to signify other distinctions than those between modes of qualifying the certainty of a statement is to introduce confusion.

Thus we find "Alexander was a great general," given as an example of a Contingent Modal, on the ground that though as a matter of fact Alexander was so he might have been otherwise. It was not _necessary_ that Alexander should be a great general: therefore the proposition is _contingent_. Now the distinction between Necessary truth and Contingent truth may be important philosophically: but it is merely confusing to call the character of propositions as one or the other by the name of Modality. The original Modality is a mode of expression: to apply the name to this character is to shift its meaning.

A more simple and obviously unwarrantable departure from tradition is to extend the name Modality to any grammatical qualification of a single verb in common speech. On this understanding "Alexander conquered Darius" is given by Hamilton as a _Pure_ proposition, and "Alexander conquered Darius honourably" as a _Modal_. This is a merely grammatical distinction, a distinction in the mode of composing the predicate term in common speech. In logical tradition Modality is a mode of qualifying the certainty of an affirmation. "The conquest of Darius by Alexander was honourable," or "Alexander in conquering Darius was an honourable conqueror," is the syllogistic form of the proposition: it is simply assertory, not qualified in any "mode".

There is a similar misunderstanding in Mr. Shedden's treatment of "generally" as constituting a Modal in such sentences, as "Rivers _generally_ flow into the sea". He argues that as _generally_ is not part either of the Subject term or of the Predicate term, it must belong to the Copula, and is therefore a _modal_ qualification of the whole assertion. He overlooked the fact that the word "generally" is an expression of Quantity: it determines the quantity of the Subject term.

Finally it is sometimes held (_e.g._, by Mr. Venn) that the question of Modality belongs properly to Scientific or Inductive Logic, and is out of place in Formal Logic. This is so far accurate that it is for Inductive Logic to expound the conditions of various degrees of certainty. The consideration of Modality is pertinent to Formal Logic only in so far as concerns special perplexities in the expression of it. The treatment of it by Logicians has been rendered intricate by torturing the old tradition to suit different conceptions of the end and aim of Logic.