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It will be evident that from the affirmation of universals more information is derived than from the affirmation of particulars. It follows that more information can be derived from the denial of particulars than from the denial of universals, that is to say, there are less cases left doubtful, as in the above table.

The reader may well be cautioned, however, against an ambiguity which has misled some even of the most eminent logicians. In particular propositions the adjective some is to be carefully interpreted as some, and there may or may not be more or all. Were we to interpret it as some, not more nor all, then it would really give to the proposition the force of I and O combined. If I say "some men are sincere," I must not be taken as implying that 66 'some men are not sincere," I must be understood to predicate sincerity of some men, leaving the character of the remainder wholly unaffected. It follows from this that, when I deny the truth of a particular, I must not be understood as implying the truth of the universal of the same quality. To deny the truth of "some men are mortal" might seem very natural, on the ground that not some but all men are mortal; but then the proposition denied would really be some men are not mortal, i. e. O not I. Hence when I deny that " some men are immortal" I mean that "no men are immortal;" and when I deny that 66 some men are not mortal," I mean that "all men are mortal."

It has long been usual to compare propositions as

regards the quality of the subject matter to which they refer, and what is technically called the matter was distinguished into three kinds, necessary, contingent, and impossible. Necessary matter consists of any subject in which the proposition A may be affirmed; impossible in which E may be affirmed. Any subject or branch of knowledge in which universal statements cannot usually be made is called contingent matter, and it implies the truth of I and O. Thus "comets are subject to gravitation," though an indefinite or indesignate proposition (p. 65), may be interpreted as A, because it refers to a part of natural science where such general laws obtain. But "men are sincere" would be properly interpreted as particular or I, because the matter is clearly contingent. The truth of the following statements is evident.

In necessary matter A and I are true; E and O false. In contingent matter I and O are true; A and E false. Inimpossible matter E and O are true; A and I false. In reality, however, this part of logical doctrine is thoroughly illogical, because in treating a proposition we have no right, as already explained (p. 70), to assume ourselves acquainted with the science to which it refers. Our duty is to elicit the exact consequences of any statements given to us. We must learn in logic to transform information in every possible way, but not to add extraneous facts.

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WE are said to infer whenever we draw one truth from another truth, or pass from one proposition to another. As Sir W. Hamilton says, Inference is "the carrying out into the last proposition what was virtually contained in the antecedent judgments." The true sphere of the science of logic indeed is to teach the principles on which this act of inference must be performed, and all the previous consideration of terms and propositions is only useful or pertinent so far as it assists us to understand the processes of inference. We have to consider in succession all the modes in which the same information may be moulded into different forms of expression often implying results of an apparently different character, Logicians are not agreed exactly as to what we may include under the name Inference, and what we should not. All would allow that there is an act of inference when we see drops of water on the ground and believe that it has rained. This is a somewhat complicated act of inference, which we shall consider in later lessons under the subject of Induction. Few or none would say that there is an act of inference in passing from "The Duke of Cambridge is the Commander-in-chief," to "The Commander-inchief is the Duke of Cambridge." But without paying

82 CONVERSION OF PROPOSITIONS, [LESS.

lesson point out all the ways in which we can from a single proposition of the forms A, E, I or O, pass to another proposition.

We are said to convert a proposition when we transpose its subject and predicate; but in order that the converse or converted proposition shall be inferred from the convertend, or that which was to be converted, we must observe two rules (1) the quality of the proposition (affirmative or negative) must be preserved, and (2) no term must be distributed in the Converse unless it was distributed in the Convertend.

If in "all metals are elements" we were simply to transpose the terms, thus-" all elements are metals," we imply a certain knowledge about all elements, whereas it has been clearly shewn that the predicate of A is undistributed, and that the convertend does not really give us any information concerning all elements. All that we can infer is that "some elements are metals;" this converse proposition agrees with the rule, and the process by which we thus pass from A to I is called Conversion by Limitation, or Per accidens.

When the converse is a proposition of exactly the same form as the convertend the process is called simple conversion. Thus from " some metals are brittle substances" I can infer "some brittle substances are metals," as all the terms are here undistributed. I is simply converted into I.

Thus

Again, from "no metals are compounds," I can pass directly to "no compounds are metals," because these propositions are both in E, and all the terms are therefore distributed. Euler's diagram (p. 73, Fig. 3) clearly shows, that if all the metals are separated from all the compounds all the compounds are necessarily separated

But in attempting to convert the proposition 0 we encounter a peculiar difficulty, because its subject is undistributed; and yet the subject should become by conversion the predicate of a negative proposition, which distributes its predicate. Take for example the proposition, "some existing things are not material substances." By direct conversion this would become "all material substances are not existing things;" which is evidently absurd. The fallacy arises from existing things being distributed in the converse, whereas it is particular in the convertend; and the rules of the Aristotelian logic prevent us from inserting the sign of particular quantity before the predicate. The converse would be equally untrue and fallacious were we to make the subject particular, as in " some material substances are not existing things." We must conclude, then, that the proposition O cannot be treated either by simple conversion or conversion by limitation. It is requisite to apply a new process, which may be called Conversion by Negation, and which consists in first changing the convertend into an affirmative proposition, and then converting it simply. If we attach the negation to the predicate instead of to the copula, the proposition becomes "some existing things are immaterial substances," and, converting simply, we have-"some immaterial substances are existing things," which may truly be inferred from the convertend. The proposition 0, then, is only to be converted by this exceptional method of negation.

Another process of conversion can be applied to the proposition A, and is known as conversion by contraposition. From "all metals are elements," it necessarily follows that "all not-elements are not metals." If this be not at the first moment apparent, a little reflection will render it so, and from fig. 5 we see that if all the metals be among the elements, whatever is not ele

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