ategorical 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. Sec. 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:

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