As regards the ordinary usage of language there can be no doubt that we seldom do as a matter of fact make predications about non-existent subjects. For such predications would in general have little utility or interest for us. “The practical exigencies of life,” as Dr Venn remarks, “confine most of our discussions to what does exist, rather than to what might exist” (Symbolic Logic, p. 131). We must, however, consider whether there are not exceptional cases; and if we can find any in which it is clear that the speaker would not necessarily intend to imply the existence of the subject, we may draw the conclusion that the propositional form of which he makes use is not in popular usage uniformly intended to convey such an implication.
Universal Affirmatives. If a universal affirmative proposition is obtained by a process of exhaustive enumeration (e.g., All the Apostles were Jews, All the books on that shelf are bound in morocco), or if it is obtained by empirical generalisation based on the examination of individual instances (e.g., All ruminant animals are cloven-hoofed), then it is clear that the existence of the subject is a presupposition of the affirmation. We may, however, note certain other classes of cases in which such a presupposition is not necessary.
(a) We may affirm an abstract connexion of attributes, based on considerations of a deductive character or at any rate not obtained by direct generalisation from observed instances of the subject, and the existence of the subject is then not essential. For example, The impact of two perfectly elastic 236 bodies leads to no diminution of kinetic energy ; Every body, not compelled by impressed forces to change its state, continues in a state of rest or of uniform motion in a straight line.
It may perhaps be said that all propositions falling within this category will be really apodeictic, and that our present discussion has been limited to assertoric propositions. There is some force in this criticism. It is, however, to be remembered that the assertoric SaP can be inferred from the apodeictic SaP, so that if we can have the latter without any implication as to the existence of S we may have the former also, unless indeed we decide to differentiate between them in regard to their existential implication. The examples that we have given are moreover expressed in ordinary assertoric form, and not in any distinctive apodeictic form, such as S as such is P, It is inherent in the nature of S to be P.
(b) The proposition SaP may express a rule laid down, and remaining in force, without any actual instance of its application having arisen. For example, All candidates arriving five minutes late are fined one shilling, All candidates who stammer are excused reading aloud, All trespassers are prosecuted.
If it is argued that, in such cases as these,[250] the propositions ought properly to be written in the conditional and not in the categorical form (e.g., If any candidate arrives five minutes late, that candidate is fined one shilling), the reply is that this is to misunderstand the point just now at issue, which is whether we meet with propositions in ordinary discourse which are categorical in form and yet are hypothetical so far as the existence of their subjects is concerned. It is of course open to us to decide that for logical purposes we will so interpret categorical propositions that in such cases as the above the categorical form can no longer be used. But for the present we are merely discussing popular usage.
[250] This argument might be used with, reference to cases coming under (a) or (c) as well as with reference to those coming under (b).
(c) Assertions in regard to possible future events are sometimes thrown into the form SaP. For example, Who steals my purse steals trash, Those who pass this examination an 237 lucky men. The first of these propositions would not be invalidated supposing my purse never to be stolen, and the latter, as Dr Venn remarks,[251] would be tacitly supplemented by the clause “if any such there be.”
[251] Symbolic Logic, p. 132.