By thus reducing the Hypothetical Syllogism to the Categorical form, what is lost in elegance is gained in intelligibility. For, first, we may justify ourselves in speaking of the hypothetical premise as the major, and of the categorical premise as the minor; since in the categorical form they contain respectively the major and minor terms. And, secondly, we may justify ourselves in treating the Hypothetical Syllogism as a kind of Mediate Inference, in spite of the fact that it does not exhibit two terms compared by means of a third; since in the Categorical form such terms distinctly appear: a new term ('This') emerges in the position of the minor; the place of the Middle is filled by the antecedent of the major premise in the _Modus ponens_, and by the consequent in the _Modus tollens_. The mediate element of the inference in a Hypothetical Syllogism consists in asserting, or denying, the fulfilment of a given condition; just as in a Categorical syllogism to identify the minor term with the Middle is a condition of the major term's being predicated of it. In the hypothetical proposition-- If A is B, C is D-- the Antecedent, _A is B_, is the _conditio sufficiens_, or mark, of the Consequent, _C is D_; and therefore the Consequent, _C is D_, is a _conditio sine qua non_ of the antecedent, _A is B_; and it is by means of affirming the former condition, or else denying the latter, that a conclusion is rendered possible. Indeed, we need not say that the element of mediation consists in affirming, _or denying_, the fulfilment of a given condition: it is enough to say 'in affirming.' For thus to explain the _Modus tollens_, reduce it to the _Modus ponens_ (contrapositing the major premise and obverting the minor): Celarent. If A is B, C is D: The case of C being not-D is ∴ If C is not-D, A is not B; not a case of A being B; C is not-D: This is a case of C being ∴ A is not B. not-D: ∴ This is not a case of A being B. The above four forms commonly treated of as Hypothetical Syllogisms, are called by Ueberweg and Dr. Keynes 'Hypothetico-Categorical.' Ueberweg restricts the name 'Hypothetical' simply (and Dr. Keynes the name 'Conditional') to such Syllogisms as the following, having two Hypothetical Premises: If C is D, E is F; If A is B, C is D: ∴ If A is B, E is F. If we recognise particular hypothetical propositions (see chap. v. § 4), it is obvious that such Syllogisms may be constructed in all the Moods and Figures of the Categorical Syllogism; and of course they may be translated into Categoricals. We often reason in this hypothetical way. For example: