CHAPTER IV. ARGUMENT. § 465. THUS far we have dealt with Terms as expressing the simple apprehension of the mind, and Assertions as expressing an act of Judgment; we now proceed to the subject of Argument as expressing the act of Reasoning. An ARGUMENT is defined as an Expression in which, from something laid down (assumed as true), something else is concluded to be true, as following necessarily from the other. A CONCLUSION is a proposition proved by Argument, and is always drawn from two other propositions, called the Premises. The Premises are the two propositions from which the conclusion is drawn, and are so called because they are premised, or put before it. Thus, "Every tyrant deserves death. Cæsar was a tyrant; Therefore he deserved death." Here the first proposition is a Premise; the second proposition is a Premise; the third proposition is the Conclusion. The three propositions taken together is an Argument. An Argument sometimes has only one premise expressed, while the other is suppressed, as being admitted. Thus, "Cæsar was a tyrant, therefore he deserved death." Here we have but one premise expressed, but the other is understood. indeed, is the more common form. This, Every Argument consists of two parts: that which is proved, and that by means of which it is proved; the former, before it is proved, is called the question; when proved, the conclusion ; that which is used to prove it, if stated last, is called the reason, and is introduced by the conjunction "because," or some other causal conjunction; as, "Cæsar deserved death because he was a tyrant." If the conclusion be stated last, which is the strict logical form, then that which is employed to prove it is called the premise, and the conclusion is introduced by some illative, as therefore; as, "Cæsar was a tyrant, therefore he deserved death." Arguments thus stated, without the third proposition, which is in a syllogism, are called Enthymemes. See § 467. "We are dependent, therefore we should be humble." Here the major premise is suppressed. In ordinary language, the word " Argument" is often employed to denote the Premises alone, or sometimes that one of the premises which is expressed when the other is understood; as when one speaks of proving so and so by this or that argument, meaning by such and such a Premise. SYLLOGISM. § 466. A SYLLOGISM is an argument so expressed that the conclusiveness of it is manifest from the mere form of expression alone, independently of the meaning of the words; as, Every X is Y; Z is X; therefore Z is Y. If the premises are assumed to be true, the conclusion must follow. The Premises here are, 1. Every X is Y, which is the Major Premise; 2. Z is X, which is the Minor Premise. Z is Y, is the Conclusion. Let X, Y, and Z stand for any terms whatever, the conclusion must follow from the very form of the expression, according to the following general statement: 1. Any thing whatever (as Y) affirmed of a whole class (as X), 2. Under which class something else (as Z) is comprehended, 3. May be affirmed of that (namely, Z) which is so compre hended. 1. Every Syllogism must have three, and only three, Terms; viz., the Middle term, and the two terms of the Conclusion or Question. Of these, 1. The Subject of the conclusion is called the Minor term; 2. Its predicate, the Major term; and, 3. The Middle term is that with which each of the others is separately compared, in order to judge of their agreement or disagreement with each other. Thus, in the above syllogism, Z is the minor term, Y is the major term, and X is the middle term. The major term is so called from its being of more extensive signification than the minor. 2. Every Syllogism must have three, and only three, Propositions; viz., 1. The Major Premise, in which the major term is compared with the middle; 2. The Minor Premise, in which the minor term is compared with the middle; and, 3. The Conclusion, in which the minor term is compared with the major. The Major Premise is usually placed first. When terms are said to be compared with each other, it is meant that one of them is affirmed or denied by the other. Of the two premises, the Major is, in common discourse, called the "Principle," and the Minor Premise the "Reason." CANONS AND RULES. 1st Canon.-Two terms which agree with one and the same third may be declared to agree with each other. 2d Canon.-Two terms, whereof one agrees and the other disagrees with one and the same third, may be pronounced to disagree with each other. When two terms are brought together as subject and predicate of a proposition, they are described, in technical language, as agreeing or disagreeing with each other, according as the one is affirmed or denied of the other. The former of these canons applies to affirmative, the latter to negative propositions. 1st Rule.-A Syllogism must have three, and only three, Terms. 2d Rule. It must have three, and but three, Propositions. 3d Rule. - The Middle term must be one only, i. e., not double; must be unequivocal; and must be, in one at least of the premises, distributed. 4th Rule.-No Term is to be distributed in the Conclusion that was not distributed in the Premise (or there must be no "illicit" process). 5th Rule.-One at least of the premises must be affirmative; since, if both were negative, the Middle term would not be pronounced either to agree with each of the "Extremes," or to agree with one and to disagree with the other, but to disagree with both; whence nothing can be inferred; as, "No X is Y, and Z is not X," evidently affords no ground for comparing Y and Z together. 6th Rule. If one premise be negative, the Conclusion must be negative; since, inasmuch as the other premise must be af firmative, the Middle will have been assumed to agree with one of the "Extremes," and to disagree with the other. EXERCISE. Point out the three Propositions in each of the following Syllogisms, and name them; also each Subject, Predicate, and Copula; also the Major term, the Minor term, and the Middle term: 1. Every dispensation of Providence is beneficial; Afflictions are dispensations of Providence; Therefore they are beneficial. 2. No predaceous animals are ruminant; The lion is a predaceous animal; Therefore the lion is not ruminant. 3. All tyrants deserve death; Cæsar was a tyrant; Therefore he deserved death. 4. No one who lives on terms of confidence with another is justified in killing him; Brutus lived on terms of confidence with Cæsar; Brutus, therefore, was not justified in killing Cæsar. The MODE of a Syllogism is the designation of the three Propositions it contains (in the order in which they stand), according to their respective Quantity and Quality; that is, according as each proposition is universal or particular, affirmative or negative; that is, according as each proposition is A, E, S, or O. Out of sixty-four combinations obtained by 4×4 × 4, there are only eleven modes in which any syllogism can be expressed. The FIGURE of a Syllogism is the situation of the Middle term in the two premises respectively with relation to the two Extremes (or Terms) of the conclusion, namely, the Major and Mi nor terms. Let X be the Middle term, Y the Major term, and Z the Minor term. In the FIRST FIGURE the Middle term is made the Subject of the Major premise, and the Predicate of the Minor; as, Every X is Y; Z is X; therefore Z is Y. All electrical phenomena (X) are measurable (Y); Here the middle term is less extensive than the major, and more extensive than the minor. In the SECOND FIGURE the Middle term is the Predicate of each Premise. In this, none but negative conclusions can be proved, since one of the premises must be negative, in order that the Middle term may be (by being the predicate of a Negative) distributed; as, No Y is X; Z is X; therefore Z is not Y. The nervous fluid will not travel along a tied nerve; Electricity will travel along a tied nerve; Therefore Electricity is not the nervous fluid. Here the Middle term is more extensive than the major or the minor term. In the THIRD FIGURE the Middle term is the Subject of each premise. In this Figure none but particular conclusions can fol low; as, Every X is Y; every X is Z; therefore some Z is Y. All virtuous men are conscientious; All virtuous men are happy; Therefore some who are happy are conscientious. Here the Middle term, "virtuous men," is less extensive than either the major or the minor term. The FOURTH FIGURE (Y is X; X is Z; therefore Z is Y) is omitted by some logicians as awkward and unnecessary. THE ENTHYMEME. § 467. An ENTHYMEME is a syllogism with one premise suppressed. It is an abridged form of an argument. This is the ordinary form of speaking and writing. See § 465. EXERCISE. Draw out the following Enthymemes into regular syllogisms: 1. Cæsar was a tyrant, therefore he deserved death. 2. The Epicureans can not be regarded as true philosophers, for they did not reckon virtue as a good in itself. 3. Some reviewers do not refrain from condemning books which they have not read; they are, therefore, not candid. 4. How can ye believe who receive honor one of another? |