conversion, and these only so far as our subsequent need in syllogizing requires, which is, that we be able to convert each of the four judgments A, E, I, O.

1st. Simple conversion transposes the terms without changing the quantity or the quality of the proposition. It may be applied to E, and to I. Thus,

Since No one without warm sympathics is a true poet;.....
Then No true poet is without warm sympathies;.....

Since Some good mathematicians are poor financiers;
Then Some poor financiers are good mathematicians...

E

= E

=

I

I

The judgment of degree (i, § 13), symbolized by A or E, is always and only simply convertible.

2d. Conversion per accidens reduces the quantity of a proposition (hence also called C. by limitation), but leaves its quality unchanged. It is applied to A, and the converse is I. Thus,

Since All plane triangles are rectilinear figures;..
Then Some rectilinear figures are plane triangles...

= A

= I

The name was given by Boethius, because it is not a conversion of the universal per se, but only of a particular which the universal includes. If we hold to the rule that affirmatives do not distribute the predicate, it is evident that the predicate of the convertend, "rectilinear figures," does not change its quantity in becoming the subject of the converse. But, for the same reason, the subject of the convertend, "plane triangles," in becoming the predicate of the affirmative converse, has its quantification reduced. Also observe that our general rule (§ 3) forbids us to retrace this step-to reconvert the I into A. E also may be converted per accidens.

3d. Conversion by contraposition changes the quality but not the quantity of the proposition. It is applied to the remaining judgment. O, and the converse is I. In order to contrapone we have the following RULE: Infinitate and then convert simply. Thus,

Since Some pure air is not wholesome;.
Then Some unwholesome air is pure...

= 0
I

This is of course a compound process, and was devised to convert O, which cannot be converted simply, or per accidens. It has been also called "conversion by negation."

Upon a slight inspection it is sufficiently obvious that the doctrine of conversion has respect to judgments in extension. An intensive

judgment cannot be converted without at the same time changing its subject into a mark, and its predicate into a concept; as, "All men are mortal" converts to "Some mortals are human." Otherwise the view in converting must be changed to extension.

Again, since an individual cannot become a predicate (i, § 6), it follows that no individual judgment (i, § 8) can be converted. The symbol A or E (i, § 10), when used to represent it, must be held inconvertible. We say "Venus is pretty," and may say, "Something pretty is Venus;" but this apparent conversion per accidens is only a rhetorical inversion; the subject of thought is still Venus. This gives occasion to remark that no mere inversion is a logical conversion.

§ 8. Opposition. A subject and predicate given in either one of the four forms A, E, I, O, is in opposition to the same matter in each of the other three forms. The opposition is such that if the given proposition be taken as true, or as false, we can immediately infer the truth or falsity of at least some of the others. It is of four kinds, usually exhibited upon a diagram, thus,

1st. Contradictory opposition exists between propositions having the same naked or unquantified subject and predicate, but which differ in both quantity and quality. Both cannot be true, and both cannot be false. This is merely a specific statement of the laws of Contradiction and Excluded Middle. E. g., If A, “All Salt is Pure," be sublated (denied), then by an immediate inference we can posit (affirm) O, "Some Salt is not Pure." If I, "Some Salt is Pure," be posited, then we can immediately sublate E,"No Salt is Pure." If it is true that "Every man has a conscience," then it cannot be said that "Some men have no conscience." Again, if you prove that “A doctrine, such as the connection between mind and body, is to be believed, though it is not comprehensible," you have thereby shown that "No doctrine is to be disbelieved because it is incomprehensible."

Such propositions are said, in common phrase, to be diametrically opposed. Aristotle used the diagonal for the contrary opposition of A and E, and for this reason, perhaps, the phrase "diametrically opposed" is ambiguous, it being applied both to contraries and to contradictories. Contradictory opposition is the only perfect form of opposition, all others being more or less imperfect.

Proof is direct and indirect. If we wish to refute an adversary, we may show that his arguments are false, do not sustain his assertion, which, being unsupported, fails. The result is merely negative, and is often sufficient. But we may wish to go further, and prove his assertion positively false. If this is done by an attack upon his own assertion, the method is direct. But if we affirm the contradictory proposition, and, having established it, immediately infer his assertion false, the method is indirect. Thus, if one affirms with Hobbes that "All human motives are always ultimately selfish," we may undertake to prove that "Some one motive in some single case was unselfish." If this be established, then the immediate, necessary inference from this O is, that his A is false. The proof called reductio ad absurdum is indirect and quite similar. Euclid makes much use of it. Instead of demonstrating a proposition directly, he demonstrates that its contradictory is absurd and thence infers its truth.

2d. Contrary opposition exists between A and E, universal propositions differing in quality only. Both cannot be true, but both may be false. Between these propositions there is a tertium quid, namely I and O. If A, "All S is P," be posited, E, "No S is P," is sublated, and vice versa. But if either is sublated, this does not posit the other, for it may be that "Only some S is P"I and O. To deny that "All Stars are Planets" does not afford the inference that "No Stars are Planets;" for it may be, and in this case is, true that some are, and some are not. To sublate "No wars are evil" does not give position to "All wars are evil;" for if some are, and some are not, then both the others are false.

When, however, the judgment or proposition is individual, all dis

The Aristotelic doctrine of Opposition differs considerably from the one here given, which is the approved Scholastic form. Saint-Hilaire represents the former thus: "L'opposition (rà ȧvrieípeva) peut être de quatre espèces. Il y a 1o celle des relatifs; 2° celle des contraires; 3° celle de la privation et de la possession (répηois kai žıç); 4o enfin celle de l'affirmation et de la negation. Cette théorie des oppositions joue un grand rôle dans le système d'Aristote."—De la Logique D'Aristote, Tome i, p. 172 sq. (Paris, 1838). See Aristotle's Categoriæ, ch. x.

tinctions in opposition disappear, or rather become merged into the simple negative, which, in such case, is the true contradictory. E. g., "Caliban is a man," and "Caliban is not a man."

In controversy opponents often take contrary positions, and either failing to establish his own gives to the other an apparent victory. E. g., One asserts that "All men are to be trusted." Another opposes this with "No men are to be trusted," but being unable to prove it in face of cited cases of some who are to be trusted, leaves the question in confusion, and his opponent in possession of the field. Indeed, they have not squarely faced each other. The opposer, in adopting the indirect method, should have undertaken, not the contrary, which is too much, but the diametrical contradictory, that "Some men are not to be trusted," which in this case would insure an easy victory.

3d. Subcontrary opposition exists between I and O, particular propositions differing in quality only. Both may be true, but both cannot be false. Hamilton calls these subaltern contraries, "compossible." If I, "Some S is P," be taken as true, it may be that O, "Some S is not P," is also true. But if I is false, then O must be true. If "Some Sighs are Prayers," it may also be true that "Some Sighs are not Prayers." But if it is false to say that "Some Sighs are Prayers," then it must be true that "Some are not."

Let it be noticed, however, that if, in "Some S is P," and "Some S is not P," the same "Some" is intended, then the propositions are “incompossible." In strictness they become contraries, and hence pure Logic, which takes it thus, knows no subcontrary opposition. But usually the sphere of the "Some" in the one is different from that in the other. Thus, if I observe that "Some metals (some at least, perhaps all) are fusible," it may be that "Some others, for aught I know, are infusible." Here the "Some" is wholly indefinite, and our rule holds good. But, further, if the "Some" be thought as semidefinite (i, § 8), then our rule changes from "Both may be true" to "Both must be true." Thus, I know that "Some flowers (some at most, not all) are fragrant;" then it must be true that "Some flowers are not fragrant." This Hamilton calls "integration," since the two "Somes," taken together, constitute the whole.

4th. Subalternate opposition exists between propositions differing in quantity only. If the universal is true, the particular is true; if the particular is false, the universal is false. If I have $100 at my credit in bank, it is evident I may draw for $5 or $10. If I have not $10 at my credit, I cannot draw $100. This is a specific application

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of the law of Identity. If it is true that " All Sin must be Punished," then we can infer that "Some, or any one, Sin must be Punished." If "Some Sin, even one, will not be Punished" be proved false, then we cannot say that "No Sin will be Punished." The reverse of the rule, however, does not hold. From "Some S is P," it does not follow that "All S is P." If " No S is P" is a false statement, we cannot infer that "Some S is P" is also false. Though to say that "No Subjects can become Predicates" is untrue, still it is true that "Some Subjects, as individuals, cannot become Predicates."

An exception is to be taken also here. If a particular proposition is thought as semi- definite, it follows that the universal is false. If "Only some flowers are fragrant,” I and O, then it is false to say either that "All are," or that "None are." Also, if a universal is true, then its subalternate particular is false. If "All Scripture is Profitable," then we cannot think that "Some (some at most, not all) Scripture is Profitable." If we accept that "No Scripture should be Profaned," then we cannot consistently think that "Some (some only) Scripture should not be Profaned." In semi-definite thought the rule for subalternate opposition becomes "If either is true, the other is false." This modified form of the opposition Hamilton calls "inconsistency."

Let us repeat here an exceptive remark made above, that individual propositions have only one opposite. The subject being an individual total, its quantity cannot be reduced. Hence there is no subaltern, nor diagonal contradictory. The simple contrary or negative is a complete contradiction. E. g., "Diogenes was a fool," and "Diogenes was not a fool."

The relation between subcontraries, as well as that between subalterns, is not strictly opposition. Between subcontraries there is no real contrariety, but rather a presumption of agreement, a presumption that both are true. Between subalterns the relation is that of a partial agreement, or subordination, which Hamilton calls "restriction." But for convenience and brevity, logicians treat them as species under opposition."

Logic, pp. 530-535. Aristotle never recognizes the semi-definite judgment. With him a particular proposition is always construed as wholly indefinite.

Aristotle does not mention subalternate opposition. He names subcontrary opposition, but declares it to be merely verbal, not real. He speaks of contradictories as opposites (ávrikeiμevai), apparently considering these alone as really opposed. See Waitz, Comment, on Organ. 11b 16. Cf. Cic. Top. xi, § 47.