175. Conditional Propositions and Categorical Propositions.—We may go on to consider what is the essential nature of the distinction between conditional propositions and 254 categorical propositions, and in particular whether the distinction is one of verbal form only or one that corresponds to a real distinction between judgments.
If a vital distinction is to be drawn between the two forms, it must be on one or other of the two following grounds, namely, either (i) that the categorical is to be interpreted assertorically while the conditional is to be interpreted modally, or (ii) that the categorical is to be interpreted as implying the existence of its subject while the conditional is not to be interpreted as implying the occurrence of its antecedent.
(i) There is much to be said for adopting a convention by which the categorical form would be interpreted assertorically and the conditional form modally. The adoption of this convention would, however, necessitate some modification of the forms of ordinary speech, for, as we have already seen, the proposition All S is P is in current use sometimes apodeictic, while the proposition If any S is P then it is Q may (though perhaps rarely) be merely assertoric. Whether the one form or the other is used really depends a good deal on linguistic considerations. Consider, for instance, the propositions, All isosceles triangles have the angles at their base equal to one another, If the angles at the base of a triangle are equal to one another, that triangle is isosceles. These propositions fall naturally into the categorical and conditional forms respectively, simply because there happens to be no single adjective (like “isosceles”) which connotes “having two equal angles.” It is clear, however, that the use of the one form rather than the other is not intended to imply any fundamental difference in the character of the relation asserted. If either of the propositions in its ordinary use is apodeictic, so is the other; if either is merely assertoric, so is the other.
It is to be added that if we adopt the convention under consideration then the universal categorical is inferable from the universal conditional, but not vice versâ ; while, on the other hand, the problematic conditional (which corresponds to the particular) is inferable from the particular categorical, but not vice versâ. Thus, All PQ is R is subaltern to If any P is Q it 255 is R, while If any P is Q it may be R is subaltern to Some PQ is R.
(ii) We may pass on to consider whether categoricals and conditionals are to be differentiated in respect of their existential import.
We have seen in section [163] that if categoricals are interpreted modally they are not to be regarded as necessarily implying the existence of their subjects; and certainly conditionals, interpreted modally, are not to be regarded as necessarily implying the occurrence of their antecedents. Hence if both propositional forms are interpreted modally, we have no differentiation as regards their existential import.
It further seems clear that, so far as universal are concerned, a conditional proposition—even though interpreted as merely assertoric—is not to be regarded as necessarily implying the actual occurrence of its antecedent. Hence, whether, on the assertoric interpretation of both, the two forms are to be existentially differentiated depends upon our existential interpretation of the categorical.
(a) If a universal categorical is interpreted as necessarily implying the actual existence of its subject, then we have a marked distinction between the two forms.[273] If any P is Q then it is also R cannot be resolved into All PQ is R, since the latter implies the existence of PQ, while the former does not.
[273] This is Ueberweg’s view, “The categorical judgment, in distinction from the hypothetical, always includes the pre-supposition of the existence of the subject” (Logic, § 122).
(b) If, on the other hand, universal categoricals are not interpreted as necessarily implying the existence of their subjects, then universal conditionals and universal categoricals (both being interpreted assertorically) may be resolved into one another. We may say indifferently All S is P or If anything is S it is P ; If ever A is B then on all such occasions C is B or All occasions of A being B are occasions of C being D.