tive syllogism in which the premises contain less (or more) than the whole truth. Logicians sometimes distinguish between the reasoning a minore ad majus, and that a majore ad minus; but the distinction is superficial, since one is simply convertible into the other." Let us now examine analytically some miscellaneous examples. Our typical syllogism above may be analyzed thus: The tree is higher than the man; This may be re-dressed as follows: The height of the tree is greater than the height of the man; The height of the spire is greater than the height of the tree; .. The height of the spire is still greater than that of the man. These propositions may be further analyzed, thus: The height of the tree is as much as that of the man (and more), etc. Very often we do not need the pleonastic conclusion; in which case the argument may be resolved thus: The sea is broader than the lake; The ocean is as broad as the sea (and more); .. The ocean is broader than the lake. Here the second premise contains a surplus which is elided in thought. The syllogism may then be construed into Barbara, by taking for the middle term "what is as broad as the sea." It is evident that this treatment considers the judgments as compound, and views the reasoning as complex. Also, that both kinds of judgments of degree may occur in the same reasoning. Sometimes the judgments are triplex, as: A includes B; B includes C; .. A includes C. "De Morgan gives a more elaborate analysis of this argument than others of our common authorities. See his Formal Logic, pp. 20–22. The first premise says three things. It says that "A is greater than B," which is compounded of, 1st," as much as," and, 2dly, "more;" also it says, 3dly, that "A partially coincides with," or "is the same as, B." Not only do both kinds of judgments of degree occur in the same reasoning, but qualitative judgments also often combine with quantitative. For example,— The sun is a star revolving about a remote celestial centre; The form is M is contained under P....... Qualitative. M is the same as S... .. S is contained under P.. ..Quantitative. ....Qualitative. The Canon of Replacement is well suited to such cases. Nothing is more common in reasoning than to have the minor premise declare simply the equivalence of notions, one of which then replaces the other in the major premise to constitute the conclusion. The equivalence in such cases, however, amounts to identity, and should be read "is the same as." We append a single example of reasoning from the mathematical whole to the part, as follows: A minute is a part of a degree; A degree is a part of a circle; .. A minute is a part of a circle. 5. It is sufficiently manifest how readily, in a large number of cases, the quantitative syllogism may be converted into qualitative. There are, however, many cases when this cannot be done without great violence, and some perhaps wherein it is wholly impracticable. On the other hand, qualitative syllogisms may as often be readily transmuted into quantitative, sometimes by violence, sometimes not at all. The frequent practicability of this change may have been the origin of so many attempts of recent logicians, they not recognizing the fundamental distinction of these two wholes, to reduce all propcsitions to equations, proposing thereby to modify, or rather to supersede, the whole Aristotelic system. The best illustration of this perhaps is Hamilton's "Unfigured Syllogism," " the Canon of which has already been given in i, § 4. He says that any syllogism whatever 12 See Appendix to his Logic, p. 626; cf. Discussions, p. 604. may be transmuted as in the following example, and find adequate expression in the unfigured form: All patriots are brave; Some who flee are patriots; ..Some who flee are brave. Unfigured Syllogism. All patriots and some brave men are equal; Some who flee and some patriots are equal; ..Some who flee and some brave men are equal. It will be observed that the change involves the quantified predicate. Hamilton says, "This form has been overlooked by logicians, while, in fact, it affords a key to the whole mystery of syllogism." Evidently it is only a forcing the qualitative reasoning into the quantitative mould, and making the expression needlessly awkward, in order to avoid even the mere appearance of figure. The innovation and the claim have been received with a just coldness by all except the most devoted followers of Hamilton. § 6. It is needful to observe, before closing, that there is another class of judgments, one which cannot be regarded as either qualitative or quantitative. These are causal judgments. Besides the two modes of thought we have discussed, there is that in which we think events, one as causing, bringing about, or determining another. With such judgments we syllogize, pursuing a train of causes and effects. The elementary form of this syllogism stands thus: A causes B; B causes C; .. A causes C. This is not reducible without violence to any of the forms we have been considering, but logically it is quite similar to the quantitative syllogism. The copula is "causes," and, in converting, this is to be changed to the notion of effect. Obviously there is no more important reasoning in life or in science than that which follows the chain. of cause and effect, fixing human responsibility, or explaining the facts of nature. But the logic involved does not seem to call for special discussion after what has been said of similar forms. It may be well to remark, however, that the copula is often absorbed in verb forms, as "A governs B," "A lifts B," "A excites B," etc. These, for simplicity's sake, may be allowed to stand in the place of the more formal copula, provided the causal relation is continuously maintained in the reasoning. Just that event, and no other, which was the effect of one must be the cause of the next, and so on in a chain throughout the series of propositions. § 7. Praxis. Name the class to which each of the following rea sonings belongs. Supply any lacking proposition. Re-dress, if need be, analytically, and exhibit the copula. Explicate the several syllogisms that may be involved in one example. Construc two or three as qualitative: 1. The favorite pupil of the Academy was Aristotle; Aristotle became the head of the rival Lyceum; .. Plato's favorite became his rival. 2. The author of Athalie was the greatest French dramatist; Racine was the author of Athalie; .. Racine was the greatest French dramatist. 3. The sting of death is sin; And the strength of sin is the law.-1 Cor. xv, 56. 4. John knew more than Peter; Peter knew more than Mark; .. John knew more than Mark. 5. Aristotle lived after Plato; Plato lived after Socrates; .. Aristotle lived after Socrates. 6. Virginia is one of the Southern States; The Southern States are a part of the Union; .. Virginia is a part of the Union. 7. All the vexations of this life, including the most petty, are not as numerous as its duties; Its duties are its delights; .. The vexations of life are less than its delights. 8. Lias lies above Red Sandstone; Red Sandstone lies above Coal; .. Lias lies above Coal.13 9. Wisdom is more precious than rubies; And rubies than gold; .. Wisdom is of yet higher value than gold. 10. A follows B; B. follows C; .. A follows C. 13 This example is given by Whately without remark. It has been a sore trouble to his successors. See Fowler's Deductive Logic, pp. 168–70, for what the head of Lincoln College, Oxford, thinks about it; and compare Dr. McCosh's summary treatment of it in his Logic, p. 144. 11. If God so clothe the grass of the field, more clothe you?-Matt. vi, 30. 12. The orbit of Venus is within that of the earth; And this within that of Jupiter; .. The orbit of Venus is within that of Jupiter. shall he not much 13. The radius perpendicular to a chord bisects the chord and the subtended arc. For in the right-angled trian gles A D C and B D C, A C is equal to C B, 14. The dome is under the sky; The altar is under the dome; .. The altar is under the sky. A D E 15. Behold, the heaven and heaven of heavens cannot contain thee; how much less this house that I have builded.-1 Kings viii, 27. 16. To practise self-denial is to overcome temptation; To overcome temptation is to conquer Satan; .. Self-denial is a mastery of Satan also. 17. If two straight lines cut each other, the A -B E vertical or opposite angles will be 18. Cocoanuts contain milk; These barrels contain cocoanuts; .. These barrels contain milk. |