Regressive Sorites of Comprehension, the middle terms are the subjects of the prior premisses and the predicates of the posterior; the middle term is here in position not intermediate between the extremes."1 § 568. The Sorites known as the Goclenian-being that first formulated by Rudolph Goclenius of Marburg 2—is the Regressive Sorites in Comprehension. The difference may be shown thus: (1.) Progressive Comprehensive, (2.) Regressive Compre A quadruped is an animal; Therefore Bucephalus is a substance. (2.) An animal is a substance; A quadruped is an animal; Bucephalus is a horse; Therefore Bucephalus is a substance. It is to be noted that these reasonings are both progressive, in the sense that prosyllogism precedes episyllogism in each. § 569. The rules of the common Sorites are as follow: "1°, The number of the premisses is unlimited. 2°, All the premisses, with the exception of the last, must be affirmative, and, with the exception of the first, definite. 3°, The first premiss may be either definite or indefinite (Universal or Singular, or Particular). 4°, The last may be either negative or affirmative." 3 The reasoning would thus be vitiated in two ways (1.) by a particular premiss in the series after the first; (2.) by a negative premiss between the first and the last. 1 Logic, iii. pp. 379, 380. 2 Goclenii Isagoge in Organum Aristotelis. Francof., 1598: p. 255. 3 Hamilton, Logic, iii. pp. 371, 372. To these it should be added that in the case of a negative conclusion in Comprehension, the mere denial of the predicate is not enough. This denial must, in accordance with the principles already laid down, be a statement of incompatibility or contradiction between subject and predicate. § 570. If it be thought necessary to resolve the Sorites into Simple Syllogisms, the rule is that there are as many simple syllogisms as there are middle terms between the subject and predicate of the conclusion, or propositions between the first and the last. But the truth is, that the Sorites is simply the natural form of a sequence in reasoning; without the useless repetition of conclusions, which everybody of ordinary intelligence is able to supply. § 571. The Enthymeme is usually regarded as an incomplete or defective reasoning, one of the premisses, major or minor, being suppressed, or retained in the mind. Thus: (a) The air has weight, for it is body. The major is here suppressed. (b) Every murderer deserves death; therefore this man deserves death. The minor is here suppressed. As Hamilton has pointed out, even the conclusion may be understood or suggested merely. Thus : "Sunt monachi nequam; nequam non unus et alter : § 572. The Enthymeme is wrongly regarded as a special form of reasoning co-ordinate with syllogism. It arises simply from the need of expressing thought in a terse and abbreviated form. As Mark Duncan has well put it: "Dicitur syllogismus imperfectus non respectu mentis, sed prolationis: nam in mente proponentis integer esse potest et solidus syllogismus, etsi proferatur truncatus." 2 Duncan and the older logicians, who really knew something of the literature of the subject, were well aware that Aristotle gave no countenance to the view of the Enthymeme as a specific form of reasoning. They were also well aware of the fact that, with Aristotle, Enthymeme does not signify a syllogism or abbreviated expression at all, but a reasoning from signs and likelihoods, a reasoning, in fact, of probability.3 1 Logic, iii. p. 393. 2 Inst. Log., L. iv. p. 252. 3 See Duncan. Inst. Log., L. iv. p. 251. On the nature and literature of the Enthymeme, see especially Hamilton, Lectures on Logic, L. xx., and Discussions, p. 154. He there clears up the whole matter,-leaving almost nothing more to be done. § 573. Enthymematic expression is not simply an accident, but a necessity of language in a rhetorical interest. What is evident is passed over. What is prolix is avoided. What is brief is sought after; and what can be left through suggestion to the imagination or reason of a hearer or reader, is allowed to make for itself its special effect. Some of the finest effects alike in oratory and in poetry are made through enthymematic expression. Thus : ̓Αθάνατον ὀργὴν μὴ φύλαττε, θνητὸς ὤν. "When, fast as shaft can fly, Lord Marmion's steed rushed by." -SCOTT. 449 CHAPTER XXXIV. INDUCTION-FORMAL AND MATERIAL-ANALOGY. § 574. According to the view of Categorical Reasoning which makes it dependent on the Law of Identity, or whole and part, it is obvious that we may reason not only from the whole or genus to the parts, but conversely from the parts to the whole. In the former case we have Deductive Categorical Reasoning, in the latter Inductive Categorical Reasoning. In the latter case we argue from "the notion of all the constituent parts discretively, to the notion of the constituted whole collectively. Its general laws are identical with those of the Deductive Categorical Syllogism, and it may be expressed, in like manner, either in the form of an Intensive or of an Extensive Syllogism." 1 $575. Strictly formal induction has been named Perfect Induction or Perfect Enumeration, as compared with Imperfect Induction or Enumeration. In the former case, there is an enumeration of all the singulars under the species, or of all the species under the genus-i.e., under the universal in question. The latter founds merely on some of the singulars under the species, or some of the species under the genusi.e., under the universal in question. Aristotle recognised the distinction of reasoning either from singulars or from parts to the whole. He regards Induction as ἐπαγωγὴ ἡ ἀπὸ τῶν καθ ̓ ἕκαστον ἐπὶ τὰ καθόλου ἔφοδος, and as ἐκ τῶν κατὰ μέρος.2 Thus, to take singulars, we have Perfect Induction in the following: ý Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus, Neptune, are opaque bodies lit by the sun; 1 Hamilton, Logic, iii. p. 318. 2 An. Post., i. 18. These are all the primary planets; Therefore all the primary planets are opaque bodies lit by the sun. To take species : Gold, silver, copper, tin, lead, zinc, platinum, iron, are (all) the most malleable metals; These are (all) the most useful; Therefore all the most malleable are the most useful metals. In Imperfect Induction we may reason thus: Or This, that, and the other magnet attracts iron; This, that, and the other magnet represent all magnets; This, that, and the other criminal was about 25 years of age; This, that, and the other criminal represent the majority of criminals; Therefore criminals of about 25 years of age are the majority. $576. Aristotle recognised Formal Induction; and thus distinguished Syllogism and Induction. In propositions which have a middle term, syllogism takes place by this middle; in those which have not, it takes place by induction. We may thus say that induction is in some sort opposed to Syllogism; for this demonstrates the extreme of the third term through the middle; that demonstrates the extreme of the middle through the third term. Thus then the syllogism which is produced by a middle term is, in nature, prior and more known; but that which is formed by induction is for us more evident.1 § 577. To illustrate this by his own example: |