common proposition is the conclusion is called Prosyllogismus, and that in which it is the premise, Episyllogismus. The advance from the prosyllogismus to the episyllogismus (a principiis ad principata) is called episyllogistic, or progressive, or synthetic, and the advance from episyllogismus to prosyllogismus (a principiatis ad principia) is called prosyllogistic, or regressive, or analytic.

Thus, e.g. Boëthius' concludes episyllogistically or progressively, for he first forms the syllogism: what furthers (prodest) is good; what exercises or improves, furthers: Therefore what exercises or improves is good,-and continues using the conclusion attained as a premise (the major premise) of a new syllogism: misfortune, which happens to the good, serves either (if he is a wise man) to train him, or (if he is a proficient) to improve him. Hence misfortune which befalls the good is good.

on.

In the long mathematical example § 110, the conclusion of 1 is minor premise in 3; the conclusion of 3 is minor premise in 4, and so In this reference the course of demonstration is progressive. This chain of inference is episyllogistic or progressive. If there is a medium obstructing the motion of the planets, then the path of the earth cannot be constant nor periodical, but must always become less: If this be the case, then the existence of organisms on the earth cannot have been (nor can remain) eternal. Hence, if there is this medium, organisms must have at one time come into existence, and will wholly pass away. If organisms once existed for the first time on the earth, they must have arisen out of inorganic matter. If this is the case, there has been an original production (generatio aequivoca). Hence, if this obstructive medium exists, there has been an original production.

Cato argues prosyllogistically or regressively in Cicero: 2

1 De Consol. Philos. iv. pt. vii.

2 De Fin. iii. 8, 27.

quod est bonum, omne laudabile est; quod autem laudabile est, omne honestum est: bonum igitur quod est, honestum est. This syllogism is supported by a supplementary proof of a premise (the minor: quod est bonum omne laudabile est).

If the major premise be proved supplementarily, the inference is also made prosyllogistically or regressively. The historical development of the sciences in its length and breadth should take this course. For certain general propositions are first discovered (as, e.g. the laws of Kepler) under which the individual facts are syllogistically subsumed. The highest principles are discovered later (e. g. the Newtonian law of Gravitation) from which those general propositions are necessary deductions. A like course is to be preserved in many cases for didactic reasons in the exposition of the sciences. In psychology a similar significance might belong to the fundamental processes of Beneke the formation of sensations in consequence of external affections, the formation of traces or unconscious constructions of memory, of the internal affections, to which also belongs the calling into consciousness of like thoughts by the like, and the reconstruction of mental (psychic) powerswhich belongs in Astronomy to Kepler's laws; for from these processes the individual phenomena of the mental (psychic) life may be genetically explained. The prosyllogism which deduces these processes from higher principles has yet to be sought for. The Herbartian hypotheses, which, even if they were correct, could not be placed in the same rank with the principles of Newton, are insufficiently established, and, although enunciated to avoid contradictions, are not free from internal contradiction. (The monads or the real essences are not in space, and yet are the substantial elements of what exists in space; self-maintenance suffices only to maintain what exists, and yet is sufficient to establish the new, which remains as a conception after the removal of the existing cause, and affects in manifold relations other results of self-maintenance.) Hence they are untenable.

The exposition of the different forms which a combination of syllogisms admits or excludes, whether they take the form

H H

of inferences of the First or the other Figures, appears to be unnecessary, for the general syllogistic rules enable us to deal securely with every given case in the enunciation and testing of chains of reasoning.

§ 125. An ENTHYMEME (9μnua, syllogismus decurtatus) is a simple inference abbreviated in the expression by the omission of one of the two premises. The premise which remains unexpressed must be completed in thought, and thus the enthymeme is logically equivalent to a fully expressed syllogism. If one or both of the premises of a simple inference he enlarged by the addition of reasons, the EPICHEIREMA results (nure, aggressio), which is, therefore, an abbreviated compound inference. The abbreviation, however, has to do only with the form of the syllogism reduced to a subordinated proposition which is given as the cause of one of the premises.

An episyllogistic chain of reasoning whose expression is simplified by the omission of all the conclusions save the last, and where those suppressed conclusions are identical with the major or minor premises of the following syllogisms, is called a Chain-syllogism or a SORITES (@psits, sorites, acerbus, syllogismus acervatus). The Aristotelian Sorites differs from the Goclenian by the arrangement in which the premises follow each other. The former has the form: A is B, B is C, C is D. A is D. It advances from the lower notion to the higher. The minor premises of all the syllogisms save the first (e.g. A is c) are not expressed, but are to be added in thought in the analysis which completes them. The Goclenian Sorites, on the other hand, has the opposite succession of premises: c is D, B is Cc, a is

B: .. A is D. It advances, so far as the succession of premises is concerned (and if, as in Aristotle's Sorites, the predicate be enunciated before its subject, so far as the succession of notions also is concerned), from the more universal to the less universal. The major premise of all the syllogisms except the first (e.g. B is D) is to be added in thought.

The scheme may be given for the sake of distinctness :

In the Aristotelian Sorites that conclusion which in the following (or in a great number of members, in each of the following) syllogism becomes the minor premise is not expressed (but is to be added in an analysis which completes the thought). In the Goclenian Sorites that conclusion which in (each of) the following syllogisms becomes the major is omitted. Both forms, the Aristotelian and Goclenian, agree in this, that the conclusion of the first syllogism is the premise (major or minor) of the second. The characteristic (§ 124) of episyllogistic procedure lies in this, that one advances from previous to consequent inferences. Hence, both in the Goclenian and in the Aristotelian Sorites the advance is episyllogistic. It is a mistake to think the Goclenian prosyllogistic or regressive.

The Enthymeme must not be considered to be an immediate, nor the Epicheirema a simple influence. The abbreviation of expression does not change the form of thought.

Examples of Chain-syllogisms may be seen in great numbers in scientific writings which advance from given hypotheses to final results. In such writings the form of a chain of thoughts is more frequently shortly indicated than completely expressed according to the logical schematism. For example, Aristotle' concludes that the exposition of action, the combination of events into the unity of a complete action or the μos, is the most important of the elements of Tragedy, from the following premises: Action is that in which happiness lies; what contains happiness is the end and aim; the end and aim is what is highest: Therefore action is what is highest. This is true in actual life. But the unspoken thought must be added: The reproduction of what is actually the highest in the objects reproduced in Tragedy (Action, Character, Thought) is the highest in Tragedy. Hence it follows that, because action is highest in real existence, its reproduction or the μos is highest in Tragedy. In the same sense Aristotle concludes negatively that the reproduction of character is not highest : Character is a quality (a Tolóv); Quality is not that in which happiness lies; that in which happiness does not lie is not the end: What is not the end is not highest. The unexpressed thought must be added : The reproduction of what is not actually highest in what is to be reproduced in Tragedy, is not highest in the work of art.

Aristotle does not, like later logicians, mean by voúμnua an abbreviated inference, but an inference of probability. He says:2 ἐνθύμημα μὲν οὖν ἐστι συλλογισμὸς ἐξ εἰκότων ἢ σηMeiwv. He classes it 3 among the rhetorical syllogisms. The Enthymeme, in the Aristotelian sense, when compared with the scientific or apodictic syllogism, is a mere previous deliberation or consideration producing only subjective conviction (and so the name signifies, although moderns have strangely made it refer to the retention of one premise in the mind, 2 Anal. Pr. ii. c. xxvii. p. 70 a, 10.

1 Poet. c. vi.

3 Anal. Post. i. 1, p. 71 a, 10.