say "The soul is immortal," there is affirmed of it, besides the negative notion of infinity, the positive notion of continuous existence. This is a thought very different from that of the pure negative “nonmortal." But it is impracticable to analyze exhaustively the various shades of meaning thus acquired. So, setting them aside, we shall speak only of purely negative predicates.

Affirmative judgments, having a predicate purely negative, combine an act of affirmation with an act of negation. These have been classed by Kant as a third species under quality, the negativo-affirmative, called by him "Infinite or Limitative Judgments." It will be best to give Kant's own explanation, as follows:

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In transcendental Logic, infinite must be distinguished from affirmative judgments, although in general Logic they are rightly enough classed under affirmative. General Logic abstracts all content of the predicate (though it be negative), and only considers whether the said predicate be affirmed or denied of the subject. But transcendental Logic considers also the worth or content of this logical affirmation, an affirmation by means of a merely negative predicate, and inquires how much the sum total of our cognition gains by the affirmation. For example, if I say of the soul, "It is not mortal," by this negative judgment I should at least ward off error. Now by the proposition "The soul is non-mortal," I have, in respect of the logical form, really affirmed, inasmuch as I thereby place the soul in the unlimited sphere of non-mortal beings. Now, because, of the whole sphere of possible existences, the mortal occupies one part, and the non-mortal the other, neither more nor less is affirmed by the proposition than that the soul is one among the infinite multitude of things which remain over when I take away the whole mortal part. But by this proceeding we accomplish only this much, that the infinite sphere of all possible existences is in so far limited that the mortal is excluded from it, and the soul is placed in the remaining part of the extent of this sphere. But this part remains, nothwithstanding this exception, infinite, and more and more parts may be taken away from the whole sphere without in the slightest degree thereby augmenting or affirmatively determining our conception of the soul. These judgments, therefore, infinite in respect of their logical extent, are, in respect of the content of their cognition, merely limitative.""

It remains to state here the Aristotelic rule for the distribution of

the predicate. We have shown in the previous section that the distribution of the subject is according to the quantity of the judgment; that universals distribute, and particulars do not distribute, the subject. Now the distribution of the predicate, which takes place in thought without any verbal sign, depends on the quality of the judgment. The RULE is: Negatives distribute the predicate, affirmatives do not. Some simple examples will suffice to illustrate this rule. Thus, "All houses are buildings," i. e., some buildings only, for there are some buildings that are not houses, as forts, bridges, ships, etc.; hence this predicate is undistributed or particular. Again, "No houses are pyramids;" i. e., not any pyramids, since no pyramid can be called a house; hence this predicate is distributed or universal. Again, "Some houses are dwellings," i. e., some dwellings only, for tents, caves, and ships also are dwellings; hence the predicate is particular. Again, "Some houses are not dwellings," i. e., some houses, such as shops, factories, churches, are not any dwellings; hence the predicate is here universal.

It is evident that this rule, which comes from the old Logic, and which Hamilton, as we shall see, impugns as altogether defective, has exclusive reference to the extension of the terms. Its view is that when we affirm, we thereby include the subject in the class denoted by the predicate as merely a part of it; and that when we deny, we thereby exclude the subject from that class wholly.

§ 10. In order to facilitate the statement and analysis of the syllogism, logicians combine the quantity and quality of judgments. There result four forms, which they symbolize by vowel letters," as exhibited in the following

TABLE OF THE PROPOSITIONAL FORMS.

Formulæ.

Examples.

Quantity. Quality. Symbols. Universal Affirmative,—A—All S is (some) P...... All oaks are (some) trees. Universal Negative, E-No S is (any) P..........No oaks are (any) vines. Particular Affirmative,-I-Some S is (some) P....... .Some are (some) evergreens. Particular Negative, -0-Some S is not (any) P...Some are not (any) shrubs.

15 It is curious to note that these symbolic letters were first adopted by an old logician, Petrus Hispanus; they being the first two vowels in the words affirmo and nego. We may add that the old logicians abounded in mnemonic devices, and, accordingly, the said Petrus supplied the following stanza,—

Asserit A, negat E, sed universaliter ambæ ;

Asserit I, negat O, sed particulariter ambo.

THE PROPOSITION.

CALIFORNIA

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Individual propositions (§ 8), since the subject is a total, are usually considered as universals, and symbolized by A and E.

§ 11. The fifth division is of propositions rather than of judgments. Propositions are Simple, Complex, and Compound.

A Simple proposition consists of only one judgment; i. e., it contains not more than one subject and one predicate. It may, however, consist of many grammatical elements; as, "Well-organized and skilfully administered governments are productive of happiness in their subjects."

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A Complex proposition involves with the principal judgment one or more subordinate or incidental judgments. This subordinate element appears as a clause, incidental to the principal subject or predicate. E. g., "A man who is learned is respected;" "Whoever is right is safe;" "Who steals my purse, steals trash" (Shaks.); "A little fire is quickly trodden out, which, being suffered, rivers cannot quench" (Shaks.); "Ill blows the wind that profits nobody" (Shaks.). In these the clause is in the subject, though the latter two are, the first partly, the second wholly, inverted. In the following the clause is in the predicate: "I am monarch of all I survey" (Cowper); "The cry is still They come'" (Shaks.); “When I was a boy, I used always to choose the wrong side" (Johnson); "When the age is in, the wit is out" (Shaks.); "What I have written, I have written." In the following there are incidental clauses in both subject and predicate: "They that are wise shall shine as the stars (shine);" "Shylock, who was a hard-hearted man, exacted the payment of the money he lent with such severity that he was much disliked by all good men" (Lamb).

A subdivision of incidental clauses may be made into Explicative and Limitative, or Restrictive. The Explicative clause merely unfolds the marks connoted by the notion it qualifies; as, “Man, who is born of woman, is of few days and full of trouble;" "Jonah sought to evade the God who is omnipresent." Explicative clauses express judg ments not now made, but formerly made, and now renewed subordinately. Limitative or restrictive clauses, which may also be allowed to include the concessive clause removing restriction, are those which, as the terms indicate, limit or restrict the notion they qualify; as, "Men who are avaricious are discontented." This is not said of all men, but is said of all in a limited class. So, "He is well paid that is well satisfied" (Shaks.); "Honesty, when it is more policy, is not a

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virtue." The concession in "I will trust him though he slay me" removes a conceivable restriction. So in "Live we how we can, yet die we must" (Shaks.). In "They strive that they may enter in," and They take heed lest they fall," the predicates are limited by purpose; one positively, the other negatively. When the restrictive is a condition, the categorical proposition may easily be converted into a conditional. Thus the example above may become "If men are avaricious, they are discontented."

We now observe that, these incidental clauses of all kinds being regarded merely as substantive, adjective, or adverbial elements, the complex proposition is in Logic treated as simple. It was needful to discuss it only that we may be forewarned not to mistake clauses for principal propositions; and, in reducing a proposition to strict logical form, that we may be careful to subordinate them in place to the principal subject or predicate. Thus, "He, who, though he is rich, is saving, is one that can share with him who is needy without lessening what is enjoyed;" here the form is, S is P. Indeed, the complex sentence is often directly reducible to one that is strictly simple. Thus, the first example given above, “A man who is learned is respected," reduces to "A man of learning," or "A learned man, is respected."

The Compound proposition is one that comprises two or more judgments, co-ordinate, or nearly so; and these, for logical purposes, require to be separated and stated independently. It is of two kinds, according as the compounding elements are more or less obvious. The first kind, wherein these elements are quite evident, has received no specific name, and needs only the illustration of a few examples; as, "Art is long, and life is fleeting" (Longfellow); "Every man desireth to live long, but no man would be old" (Swift).

"We are such stuff

As dreams are made on; and our little life

Is rounded with a sleep."-Shaks.

"Men may come, and men may go,

But I go on forever."-Tennyson's Brook.

"Veni, vidi, vici," contains three distinct propositions in three words. "Pompey, Crassus, and Cæsar were triumvirs;" here are three propositions: 1st. "Pompey was a triumvir;" 2d. “Crassus was a triumvir;" 3d. "Cæsar was a triumvir." If, however, we say "Pompey, Crassus, and Cæsar were the triumvirs," then the proposition is single and simple, for the three are taken collectively as one whole. So, "Roses and lilies contend for a home in her cheek," is single and

simple; but in "Darkness and silence settle on land and on sea," there are four propositions.

"Ho! hearts, tongues, figures, scribes, bards, poets cannot

Think, speak, cast, write, sing, number,-hoo!

His love to Antony."-Shaks.

In this curious sentence there are six distinct propositions, and were it not that each predicate answers to its own subject we might count thirty-six.

Compound propositions of the second class, having elements less obvious, and requiring analysis, are for this reason called Exponibles. These more than the others require special attention, since they are more intricate, and in syllogizing with them it is often requisite that they be distinctly resolved. We name three species: 1st. Exclusives and Exceptives; 2d. Comparatives; and 3d. Inceptives and Desitives. 1st. EXCLUSIVES. Compounds of this species may be formulated thus:

Only A is B=

SA is B........

{

No non-A is B.. (Faith justifies.

=A

=E

E. g., “Faith alone justifies”"={What is not faith does not justify.

It is obvious that this proposition may be inverted and the exclusive particle made to appear in the predicate; thus, "Justification is by faith alone," B is only A.

Exceptives are exemplified in "All but one were saved," which means "Nearly all were saved" and "One was not saved;" I and O.

No useful rule can be given for the resolution of these two forms of exponibles. Generally, if not always, the elementary judgments differ in quality, and one is to be noted as direct and the other as indirect or implied. The distinction between the exclusive and exceptive forms is of no practical moment, as they are readily convertible, the only difference being that what is the direct judgment in the one becomes the indirect in the other. The following are some of the exclusive and exceptive particles: only, alone, exclusively, merely, sole, solely, but, etc. These particles annexed to the subject quantify the predicate universally; as, "God alone is wise," i. c., He is all the wise. Annexed to the predicate they merely limit the subject to that predicate; as, "The sacraments are but two," i. c., there are no more. We give some examples illustrating their various modes of expression to facilitate the recognition of them hereafter. “None but the brave deserve the fair" (Dryden); "A fool thinks none except