by an old acquaintance and he qualifies his sweeping condemnation. "Some people are trustworthy", he now says, implying that all but a chosen few are unreliable. After a while, however, he learns the value of cautious statements, and if he should then go to a new place and be fortunate in his first acquaintances he might say "Some people here are trustworthy", implying nothing whatever about the rest except, perhaps, that he did not know them. In short, the development of particular propositions is a mark of increasing caution and accuracy. The end which they serve is therefore defeated, at least in part, when they are understood to imply more than they state. Often they do imply more—but merely because a speaker or hearer is not yet sufficiently well trained to realize that a qualified statement can be made on general principles. Here again one must take care to speak in such a way as to be understood aright by his hearers (whoever they may be), and to try and find a definite interpretation for the statements of others which they themselves would accept. Instead of being ambiguous, words used to denote quantity and quality are often lacking altogether. Undesignated Sometimes the meaning is clear enough without quantity or quality. them; but sometimes it is not. The term indefinite, indesignate, or preindesignate is applied to propositions whose form does not show whether they are intended to be universals or particulars. When, for example, we say that dogs delight to bark and bite, or that republics are more free than monarchies, or that crows are black, do we mean the statement to apply to every dog, every republic, every crow, or only to some larger or smaller number of them? Indefinite propositions must not be confused with particulars. The quantity of a particular proposition is perfectly clear, but the object to which it refers is not definitely designated. The quantity of an indefinite proposition, on the other hand, is not clear, and for that reason it is impossible to say whether it is meant to refer to any definitely designated objects or not. Particular propositions are indefinite in their reference; indefinite propositions, ambiguous. When the form of a proposition gives no indication of its quantity it is very easy to accept it or prove it true when interpreted as a particular and then use it as though it were true as a universal. Here is an example: "Improbable events happen almost every day; events which happen almost every day are probable events; therefore improbable events are probable events." When the first premise of this argument is assumed to be true it is evidently understood to mean that some improbable event or other happens almost every day; and from it in conjunction with the other premise we have the right to conclude that the occurrence of some improbable event or other is probable, but nothing more. When the premise is understood in this sense throughout it certainly will not help us to conclude that improbable events are probable events. It is capable, however, of being interpreted to mean that every improbable event happens almost every day; and when taken in this latter sense it certainly will help us to reach the conclusion. Every improbable event happens almost every day; events which happen almost every day are probable events; therefore every improbable event is a probable event. But, then, when the premise is understood in this sense nobody would admit its truth. We must not assume, however, that the quantity or quality of a proposition has not been indicated merely because it has not been expressed formally by one of the words 'some', 'all', 'none', 'not'. Minto puts the matter as follows: "The expression of Quantity, that is, of universality or non-universality, is all-important in syllogistic formulæ. 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'. In Uneasy lies the head that wears a crown. 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. "All the above propositions are Pre-designate' [i.e., definite] 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 [i.e., Some S is P, or Some S is not P]. 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. Rivers generally 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. Such sayings are in actual speech for the most part delivered as universals. It is a useful exercise of the Socratic kind to decide whether they are really so. This can only 6 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 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.” * When the function of a proposition is, not to describe some one object or set of objects, but to tell of a causal or other relation which exists between several (e.g., Double quantity. John strikes James; David defeated the Philistines), it is rather arbitrary to determine the quantity of the proposition with reference merely to what happens to be named in the subject. It would be fairer to recognize both parties to the relation, and to determine the quantity of the proposition with reference to each. Each of these hunters shot a bird' is a universal proposition with reference to the hunters, but particular with reference to the birds. ' Almost any Turk hates a Greek' is particular with reference to the Turks, universal with reference to the Greeks. 'All Turks and Greeks hate each other' is universal with reference to both. 'There are many thieves in the land' is particular with reference to the thieves, singular with reference to the land. * William Minto, "Logic, Inductive and Deductive", Scribners, 1895, pp. 70-73. Let it be remembered, therefore, that though it may sometimes be convenient to describe the quantity of such a proposition with reference to only one of the related parties, such a description is both arbitrary and incomplete. There are two closely allied kinds of propositions, much harder to define than to deal with in practice, called respectively exceptive and exclusive. The subject of Exclusives each kind contains some such limiting phrase as and exceptives. none but, only, alone, except; and on this account they are often confused, in spite of a real contrast between them. Exceptive propositions state that something is true of all the members of a given group of objects except those specified. Exclusive propositions, on the other hand, state that something is true of certain specified members of a group only. Here are some examples of the two: 66 Exceptive affirmative: All but the Germans departed. : The Germans alone departed. No one but the Germans departed. : The Germans alone did not depart. Exclusive Exceptive affirmative: All but the brave deserve the fair. 66 Exclusive : The brave alone deserve the fair. None but the brave deserve the fair. : The brave are the only ones who do not deserve the fair. It will be noticed that each kind of proposition can be either affirmative or negative,* and that the exclusive affir * The fact that each kind of proposition can be either affirmative or negative is overlooked in some of the text-books. Jevons, for example, assumes in the following definitions that both kinds must be affirmative: Exceptive propositions affirm a predicate of all the subject with the exception of certain defined cases, to which, as is implied, the predicate does not belong." "Exclusive propositions contain some words, such as only, alone, none but, which limit the predicate to the subject." Where a predicate is limited to a subject', it is certainly affirmed and not |