If the margin of cultivation be extended, rents will rise; If prices of produce rise, the margin of cultivation will be extended: ∴ If prices of produce rise, rents will rise. But the function of the Hypothetical Syllogism (commonly so called), as also of the Disjunctive Syllogism (to be discussed in the next section) is to get rid of the conditional element of the premises, to pass from suspense to certainty, and obtain a decisive categorical conclusion; whereas these Syllogisms with two hypothetical premises leave us still with a hypothetical conclusion. This circumstance seems to ally them more closely with Categorical Syllogisms than with those that are discussed in the present chapter. That they are Categoricals in disguise may be seen by considering that the above syllogism is not materially significant, unless in each proposition the word 'If' is equivalent to 'Whenever.' Accordingly, the name 'Hypothetical Syllogism,' is here employed in the older usage. § 2. A Disjunctive Syllogism consists of a Disjunctive Major Premise, a Categorical Minor Premise, and a Categorical Conclusion. How many Moods are to be recognised in this kind of argument depends on whether the alternatives of the Disjunctive Premise are regarded as mutually exclusive or possibly coincident. In saying '_Either_ A is B, _or_ C is D,' do we mean 'either, but not both,' or 'either, it may be both'? (See chap. v. § 4.) When the alternatives of the Disjunctive are not exclusive, we have only the _Modus tollendo ponens._ Either A is B, or C is D; A is not B (or C is not D): ∴ C is D (or A is B). Either wages fall, or the weaker hands are dismissed; Wages do not fall: ∴ The weaker hands are dismissed. But we cannot argue-- Wages fall: ∴ The weaker hands are not dismissed; since in 'hard times' both events may happen together. Rule of the _Modus tollendo ponens_: If one alternative be denied, the other is affirmed. When, however, the alternatives of the Disjunctive are mutually exclusive, we have also the _Modus ponendo tollens._ Either A is B, or C is D; A is B (or C is D): ∴ C is not D (or A is not B). Either the Tories or the Whigs win the election; The Tories win: ∴ The Whigs do not win. We may also, of course, argue as above in the _Modus tollendo ponens_-- The Tories do not win: ∴ The Whigs do. But in this example, to make the _Modus tollendo ponens_ materially valid, it must be impossible that the election should result in a tie. The danger of the Disjunctive Proposition is that the alternatives may not, between them, exhaust the possible cases. Only contradictory alternatives are sure to cover the whole ground. Rule of the _Modus ponendo tollens:_ If one alternative be affirmed, the other is denied.