A modal proposition of this description consists of what is termed the dictum and the modus. The dictum is the subject, and the modus the predicate. In the examples given already, there is no difficulty in distinguishing the subject from the predicate, for they stand in their legitimate order, while the nature of their relation is determined by the word qualifying the copula; and the relation may be either that of necessity, possibility, impossibility, or contingency. But propositions often occur, usually considered modal, in which it is often requisite to alter the arrangement of the words in which they are expressed, in order to see clearly which is the dictum, and which the modus. In such cases, it is necessary first to ascertain the term, or the particular number of words constituting a term, which represents the dictum; and when this is ascertained, all that remains is, to connect the term constituting the modus with the copula,-for the modus must be always joined to the copula,-and what is so joined is the predicate. In the following proposition, viz.,

It is necessary that a man should be an animal,

there is a necessity of agreement asserted between the subject and predicate, and on examining the proposition, we find 'that a man should be an animal' is the dictum or subject, and 'necessary' the modus or predicate. By uniting the modus with the copula, the proposition will stand thus:

That a man should be an animal is necessary.

It is evident that the first kind of modal propositions mentioned, (viz., those in which the subject and predicate occupy their legitimate places) may be multiplied to any extent; for any adverb affecting the copula, and thereby qualifying the predicate, or even an adjective qualifying the subject, is sufficient to rank the proposition in which it occurs in this class of modals. It may be remarked, however, that this indefinite multiplication of modals is not to be attributed to Aristotle;

it originated with his Greek commentators, and was followed out by subsequent logicians. On the other hand, the various forms under which modal propositions of the latter description appear, although, as well as the former, easily reducible to the categorical form, will, if they are to be resolved into the dictum and modus, which they easily may be, constitute a second class of modals equally numerous. If, however, modality is to be restricted to one or both of these classes (and it would appear that these are the only kinds of it recognisable in pure logic, as they necessitate, under certain conditions, a corresponding modification of their immediate or mediate consequents), a little consideration will suffice to show, that the propositions falling under either of the classes should be designated propositions verbally modal-their modality being expressed, not implied; for in all cases, by a slight alteration in the phraseology, or a different arrangement of the order of the terms, they may be reduced to pure categorical propositions.

Whether modality, either expressed or implied in a proposition, should be relegated from the domain of pure logic, is a question among logicians. Some, holding the formal view, admit the expressed, but reject the implied; while others exclude both. No sufficient reason has been shown, however, why expressed modality should be banished from pure logic; for if a premiss is assumed under a necessity, or probability, or possibility, of being true, any of these conditions will, in a corresponding degree, determine the conclusion to be deduced, which, under any of these assumptions will be as purely logical as that the truth of the conclusion follows from the truth of the premisses, or the falsity of the conclusion from the falsity of the premisses.

In applied logic, on the other hand, there seems no reason why implied modality should not be recognised; and hence the modality of a proposition would depend, in many cases, not on the effect a qualifying epithet may have on the copula,

but on the degree of certainty a thinker may entertain regarding a judgment, and in contradistinction to verbal modality, it might be very properly designated material modality. Aristotle, whose view of modality may be, with some straining, interpreted either as expressed or understood in a proposition, enumerates four modes, viz., the necessary (avaynaιov), the impossible (aduvarov), the contingent (evdexoμevov), and the possible (duvarov). Whether he added the true (aλŋles) and the false (oux aλndes) is not quite clear. From his classification of judgments, however, and the grounds on which they must be explained, it may be presumed that he would not exclude implied modality from applied logic. In this view, therefore, the modality of a judgment in applied logic may depend on our knowledge of facts and things, or the degree of certainty with which we can assert the agreement or disagreement of any given subject and predicate. Hence the modality of our judgments will vary with the increase of our knowledge, and what is problematical at one time may amount to belief at another. The objective facts and things concerning which we judge remain the same, whatever changes may take place in the mind of the thinker as to clearer apprehensions of them. The change is subjective, not objective.

On examining Aristotle's four modes, it will appear that all possible judgments may be reduced to three classes, viz., the

Problematical,
Assertory, and
Demonstrable.

This is Aristotle's distribution. All judgments which are merely matters of opinion come under the class 'problematical;' all judgments founded on belief may be referred to the class assertory;' while all judgments resulting from the axioms and deductions of pure science belong to the class 'demonstrable.'

Of the three, the problematical judgment is obviously the weakest, for it is neither regarded as true by the thinker, nor can it be shown to be a true decision in reference to the object or thing concerning which the judgment is made. Consequently, it cannot be laid down as truth either in a subjective or objective sense. In illustration, let us take the following example:

The solar system may be a gradual projection from the sun.

In this judgment, there may be either a total, partial, or no agreement between the subject and predicate; but from our imperfect knowledge of the object-matter of the judgment, we can only affirm a possible dependence or agreement between them. The judgment may indeed be true, and farther knowledge may prove it so, but now it is merely matter of opinion.

All judgments which rest on possibility or probability, or to which doubt attaches in the mind of the thinking subject, may be classed under problematical judgments.

The learner should observe, that in propositions the words 'may be' often occur in two different senses. In the proposition, The world may be circumnavigated, ' may be' means is capable of being, and the proposition is assertory; while in the proposition, All the species in the world may be the offspring of a few primary species, may be' means are, for anything we know, and the proposition is problematical.

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An assertory judgment implies belief in addition to opinion, and is therefore subjectively true, i. e., held as true by the thinker. An assertory judgment may also be true with respect to the fact or object regarding which it is made, but its truth objectively is indemonstrable. An assertory judgment is therefore subjectively true, but not objectively certain. The following is an example of an assertory judgment:

A mixed monarchy is the best form of government;

and to a person holding this opinion as belief, the judgment is subjectively true, inasmuch as the thinking subject believes it to be so. Objectively, however, it is not certain, for one may believe the democratic, a second the despotic, and a third the patriarchal, to be the best form of government. An assertory differs from a demonstrable judgment in this, that however firm our own belief may be in the truth of an assertory judgment, we cannot compel men in general to acquiesce in it, because however strong the evidence in its favour may be, it cannot amount to absolute demonstration.

Belief in the truth of an assertory judgment may be confined to one thinking subject, because he may have examined the object-matter of it more carefully and minutely than other thinking subjects, or he may have been influenced by prejudice, interest, or any other adequate cause.

Belief in the truth of an assertory judgment may be common to any particular sect or school, e. g., Calvinists may believe in common that Calvin's Institutes are the best compend of Theology. The same holds true in the case of political classes, or in philosophical schools, &c. This coincidence of belief may arise from similarity in habits of thought, or from educational training, or any cause sufficient to present a judgment to the mind of the thinking subject as true.

Belief in the truth of an assertory judgment may be common to all, e. g., That there is a First Cause; That there is a day of final retribution; That there is a future state; are matters to which universal belief is acceded, although not susceptible of absolute demonstration.

In every case, the truth of an assertory proposition, whether held by an individual, or a class, or men in general, depends on moral not on demonstrable certainty.

Belief in the truth of a demonstrable judgment occupies the highest place in the scale of credibility. It is not only subjectively, but also objectively true, and differs, consequently, both from the problematical and assertory judgment.