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.