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The word "term" is loosely used as a mere synonym for a name: strictly speaking, a term (ὅρος, 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 affIrmo).

Some S is not P is called the Particular Negative, symbol O (the second vowel of negO).

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 mediæval 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 mediæval 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 form² 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.