sion is thus shown to remain always the same. That of the Converse is exactly equal to that of the convertend or original proposition. Logicians, looking only to the quantity of the subject, and not considering that the predicate has always a quantity in thought as well, called the one proposition universal, and the other particular, whereas in quantity they were precisely equivalent-All X is (some) Y is precisely equivalent to Some Y is all X. It is not maintained that this express quantification of the predicate is always necessary in ordinary thought and language. It is sufficient if the predicate be as extensive as the subject, which every affirmative judgment must assume. Whether it be in itself more extensive is generally of little moment. But as soon as we have to find its immediate implicate by Conversion, we must ask the quantity of the predicate which subsists in thought to be explicitly stated. This being done, all Conversion of Propositions becomes one-simple, natural, and thorough-going. There can be no doubt that Hamilton has for the first time clearly shown the true character of Conversion, its requisite, and its rule. Wherever thought needs to seek the converse of a proposition, its best, easiest, and most scientific way is to conform to the simple principle which Hamilton has given. § 434. The table of Hamilton, with the Eight Propositional Forms, shows at a glance the convertibility of each: AfA, All X is all Y = AfA. IfA, Some X is all Y = AfI. (I) IfI, Some X is some Y = IfI. (0) InA, Some X is not any Y=An I. (a) The attempts at modifying the current doctrine of conversion by the older logicians are curious and suggestive. Universal Negative is twofold,-(1) in which the predicate is distributed, as no man is an ass; (2) in which the predicate is not distributed, as when the predicate precedes the negation, as omnis homo animal non est (every man is not animal.) In the first case, the conversion is simple, as every suppositum in the subject is removed from it in the predicate, so every suppositum in the predicate is removed from it in the subject. In the second case, there cannot be simple conversion, as every phanix is not animal (omnis phœnix animal non est), therefore, some animal is not phoenix. This per accidens.-(Duns Scotus, In An. Pr., L. i. c. xii.) The particular affirmative proposition is of two sorts, (1) with the predicate discrete, as some man is Socrates. This cannot be converted simply, but only per accidens into one singular, Socrates is a man. But, with addition, this can be converted simply, as aliquid quod est Socrates est homo. Such a particular implies a universal from the terms transposed, as some man is Socrates, therefore, all which is Socrates is man. This does not hold in divine things, as, this essence is the father, therefore, everything which is this divine essence is the father. The son is this divine essence, and he is not the father. This consequence is, therefore, not formal.-(Duns Scotus, In An. Pr., L. i. c. xiii.) Scotus recognises a particular affirmative proposition with a distributed predicate, as some moon is every moon (quædam luna est omnis luna). This can be simply converted, every moon is (the) moon. Here the predicate stands for every one of its supposita; the subject for one suppositum, and these are equivalent.—(Ibid.) (b) Equalis vero est subjectus terminus prædicato, ut si quis dicat "homo risibilis est"; ut vero id quod subjectum est majus possit esse prædicato, nulla prorsus enuntiatione contingit, ipsa enim prædicata natura minora esse non patitur.-(Boethius, Introd. ad Syll. Cat., p. 562. Prantl, i. p. 696.) (c) Mark Duncan argues against simple conversion of Particular Negative thus: Some man is not stone; e converso, some stone is not man. This is not formally good. For, by parity of conversion, if some animal is not man, some man is not animal; therefore some stone is not man, not because some man is not stone, but because no man is stone.—(Inst. Log., L. ii. c. v. § 5.) (d) The particular affirmative is not converted per contrapositionem— Something intelligent is man; something not man is not intelligent.— (Shyrewood. Prantl, iii. 15.) On Conversion, see especially Marsilius von Inghen.—(Prantl, iv. 97.) § 435. Some logicians, among others Thomson, regard the following as cases of Immediate Negative Conceptions. A statement made in a positive predicate regarding a subject inference, implies a statement regarding its opposite, or contradictory. The bodily organism is material; this implies that it is not immaterial. All human virtues are not without alloy or imperfection. This implies that all human virtues are short of their type, and that a perfect act of virtue is not within the power of man. These are virtually the same statements, but they are made from different points of view, and they may be supposed to bring out what is implied in the original statements. It is clear, however, that, unless in the case of the simple contradictory, there is here no purely formal inference. It is either a case of the same predicate in other words; or of a predicate implied through a medium or process of reasoning. All actual human virtues may be imperfect, without the consequence that all possible virtues of man are so. There is no immediate connection between those two statements. This so-called form of immediate inference, in so far as it is noncontradictory, comes properly under the head of Equipollence, -being purely terminal. § 436. Immediate Inference through Determination.-Determination means adding a predicate or term to a notion, so as to make it more specific or determinate. We determine every time we proceed from higher genera to lower species. Thus, an animal is like ourselves a sentient creature; therefore, an animal struck or wounded is a creature in suffering like ourselves. There is here no purely formal immediate inference; the connection between a sentient creature, struck or wounded and suffering, is known through induction, and is here inferred through a major. Sentiency, wounded, suffering, are after observation associated or connected, but the concept of the one does not necessarily lead in any way to that of the other. § 437. Immediate Inference by Complex Conceptions.-This arises when the subject and predicate, that is, the entire proposition, is added comprehensively to the original conception. Thus, the molecule of sand consists of silicon and oxygen; therefore, the analysis of the molecule of sand into those elements would be an analysis of a molecule. Not, certainly, of a molecule, meaning any molecule, but simply of the molecule of sand. But to call this an inference, immediate or other, is a simple misnomer. It is a mere tautology. The doctrine of Exponibles, with the old logicians, and the propositional implicates unfolded according to their rules, were much better grounded than this. 347 CHAPTER XXVII. IMMEDIATE INFERENCE-OPPOSITION-CONTRARY AND CONTRADICTORY. § 438. "Since it may happen that what is may be enunciated as if it were not, and what is not as if it were, and what is as if it were, and what is not as if it were not; further, as this applies equally to the present and to other times, therefore it is lawful to deny all those things which any one has affirmed, as well as to affirm those things which any one has denied. Whence it appears that to every affirmation is opposed a negation, to every negation an affirmation; let this be contradiction (avríparis), the affirmation and negation of the opposite. But I call opposed that which is of the same concerning the same, not the species alone of one expression." " 1 $439. Aristotle here raises a very important and fundamental question. We seek frequently to deny or contradict, to state the opposite of a given proposition. The question arises, How can we best do so? In other words, how are we to make a statement which shall deny a given statement or proposition without doing more than exactly denying itthat is, without doing more than is logically required of us? Out of this need or question arises what is called the doctrine of the Opposition of Propositions. And this is one of the most important and also one of the nicest points in Logic. It depends essentially on the negation or negative proposition which is strictly implied in any advanced or given proposition. The proposition we advance may be an affirmative. In this case, what we have to look for is the negative which 1 De Int., c. 6. will precisely deny it, and do nothing more. The proposition advanced may be a negative. In this case, what we have to look for is the affirmative which will directly confront and conflict with it, and which, if established, will render it untenable. These propositions will be regarded as opposites of various kinds, and the test of them in each case will be the strictness of the Immediate Inference with which, as negatives or affirmatives, they are implied in and follow from the original proposition. He who makes a statement is bound to accept all that which it logically implies, and only that which it logically implies,-in affirmation, therefore, to exclude the immediately involved negation; in negation to exclude the immediately conflictive affirmation. § 440. In dealing with this point, it may be well to sketch generally, before proceeding to detail, the main forms and features of the Opposition of propositions. This will be found to admit of degrees. Let us take, first, universal affirmative and universal negative propositions. If it is said that every X is Y, I can deny this by saying that no X is Y. Or, to take a concrete example, if it is said that every planet is inhabited, this may be denied by saying that no planet is inhabited. Now, look at these two propositions. The one, every planet is inhabited, is a universal affirmative; the other, no planet is inhabited, is a universal negative. They agree in quantity, but they differ in quality. They are both universals: they speak of the whole of the subject; but the one is affirmative, and the other negative. The opposition, therefore, here is tolerably complete; for the one affirms universally of the subject, or affirms of the whole subject; the other denies universally of the subject, or of the whole subject. Yet this is not the highest or the extreme form of opposition. For while the assertion or the truth of the one proposition implies the denial or the falsity of the other, the denial or the falsity of the one does not imply the affirmation or the truth of the other. Thus it cannot possibly be asserted or be true that every planet is inhabited, and that no planet is inhabited; that every X is Y, and that no X is Y. If the former of these statements be true, the latter is false. But the denial of the former statement does not imply the truth of the latter. may be false that every planet is inhabited, yet it does not follow that all planets are not inhabited; for if even one planet, It |