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equivalent to the original Conclusion of the Conditional Syllogism; viz. “France is likely to prosper.” As the Constructive Condition
may thus be reduced to Barbara, so may the Destructive, in like manner, to Celarent : e. g. “if the Stoics are right, pain is no evil : but pain is an evil; therefore the Stoics are not right;" is equivalent to—“ the case of the Stoics being right, is the case of pain being no evil; the present case is not the case of pain being no evil; therefore the present case is not the case of the Stoics being right.” This is Camestres, which, of course, is easily reduced to Celarent. Or, if you will, all Conditional Syllogisms may be reduced to Barbara, by considering them all as constructive; which may be done, as mentioned above, by converting by negation the major Premiss. (See
The reduction of Hypotheticals may always be effected in the manner above stated; but as it produces a circuitous awkwardness of expression, a more convenient form may in some cases be substituted : e. g. in the example above, it may be convenient to take “true" for one of the Terms : “that pain is no evil is not true; that pain is no evil is asserted by the Stoics; therefore something asserted by the Stoics is not true.” Sometimes again it may be better to unfold the
argument into two Syllogisms : e.g. in a former example; first, “ Louis is a good king; the governor of France is Louis; therefore the governor of France is a good king.” And then, second, every country governed by a good king is likely to prosper,” SC. [A Dilemma is generally to be reduced into two or more categorical Syllogisms.] And when the antecedent and consequent have each the same Subject, you may sometimes reduce the Conditional by merely substituting a categorical major Premiss for the conditional one: e.g. instead of “ if Cæsar was a tyrant, he deserved death; he was a tyrant, therefore he deserved death;” you may put for a major, “all tyrants deserve death ;" &c. But it is of no great consequence, whether Hypotheticals are reduced in the most neat and concise manner or not; since it is not intended that they should be reduced to categoricals, in ordinary practice, as the readiest way of trying their validity, (their own rules being quite sufficient for that purpose ;) but only that we should be able, if required, to subject any argument whatever to the test of Aristotle's Dictum, in order to show that all Reasoning turns upon one simple principle.
Of Enthymeme, Sorites, &c.
There are various abridged forms of Argument which may be easily expanded into regular Syllogisms : such as,
1st. The Enthymeme, which is a Syllogism Euthymeme. with one Premiss suppressed. As all the Terms will be found in the remaining Premiss and Conclusion, it will be easy to fill up the Syllogism by supplying the Premiss that is wanting, whether major or “Cæsar was a tyrant; therefore he deserved death." “ A free nation must be happy ; therefore the English are happy.”
This is the ordinary form of speaking and writing. It is evident that Enthymemes may be filled up hypothetically. *
2d. When you have a string of Syllogisms, in the first figure, in which the Conclusion of
minor: e. g.
* It is to be observed, that the Enthymeme is not strictly syllogistic; i. e. its conclusiveness is not apparent from the mere form of expression, without regard to the meaning of the Terms; because it is from that we form our judgment as to the truth of the suppressed Premiss. The expressed Premiss may be true, and yet the Conclusion false. The Sorites, on the other hand, is strictly syllogistic; as may be seen by the examples. If the Premises stated be true, the conclusion must be true.
each is made the Premiss of the next, till you arrive at the main or ultimate Conclusion of all, you may sometimes state these briefly, in a form called Sorites ; in which the Predicate of the first proposition is made the Subject of the next; and so on, to any length, till finally the Predicate of the last of the Premises is predicated (in the Conclusion) of the Subject of the first : e. g. A is B, B is C,,C is D, D is E; therefore A is E. “ The English are a brave people; a brave people are free; a free people are happy; therefore the English are happy.” A Sorites then, has as many middle Terms as there are intermediate Propositions between the first and the last; and consequently, it may be drawn out into as many separate Syllogisms; of which the first will have, for its major Premiss, the second, and for its minor, the first of the Propositions of the Sorites; as may be seen by the example. The reader will perceive also by examination of that example, and by framing others, that the first proposition in the Sorites is the only minor premiss that is expressed: when the whole is resolved into distinct syllogisms, each conclusion becomes the minor premiss of the succeeding syllogism. Hence, in a Sorites, the first proposition, and that alone, of all the premises, may be particular ; because in the first figure the minor may be particular, but
not the major; (see Chap. iii. $ 4) and all the other propositions, prior to the conclusion, are major premises. It is also evident that there may be, in a Sorites, one, and only one, negative premiss, viz. the last : for if any of the others were negative, the result would be that one of the syllogisms of the Sorites would have a negative minor premiss; which is (in the 1st Fig.) incompatible with correctness. See Chap. iii. § 4.
A string of Conditional Syllogisms may Hypothetical in like manner be abridged into a Sorites; e. g. if A is B, C is D; if C is D, E is F; if E is F, G is H; but A is B, therefore G is H. “If the Scriptures are the word of God, it is important that they should be well explained; if it is important, &c. they deserve to be diligently studied : if they deserve, &c. an order of men should be set aside for that purpose; but the Scriptures are the word, &c.; therefore an order of men should be set aside for the purpose, &c.:"* in a destructive Sorites, you, of course, go back from the denial of the last consequent to the denial of the first antecedent: “G is not H; therefore A is not B.”
* Hence it is evident how injudicious an arrangement has been adopted by former writers on Logic, who have treated of the Sorites and Enthymeme before they entered on the subject of Hypotheticals.