(d) There are cases in which the intended implication of a proposition of the form All S is P is to deny that there are any S’s; for example, An honest miller has a golden thumb, All the carts that come to Crowland are shod with silver.[252]
[252] Both these propositions are naturally to be interpreted as containing an indirect denial of the existence of their subjects. “Crowland is situated in such moorish rotten ground in the Fens, that scarce a horse, much less a cart, can come to it” (Bohn’s Handbook of Proverbs, p. 211). It would appear, however, that this proverb has now lost its force, inasmuch as “since the draining, in summer time, carts may go thither.”
Universal Negatives. It is still easier to find instances from common speech in which universal negative propositions, that is, propositions of the form No S is P, are not to be regarded as necessarily implying the existence of their subjects.
(a) There are again cases in which the proposition is reached by a process of abstract reasoning about a subject the actual existence or occurrence of which is not presupposed; for example, A planet moving in a hyperbolic orbit can never return to any position it once occupied.[253]
[253] This example is taken from Dixon, Essay on Reasoning, p. 62.
(b) The import of the proposition may be distinctly to imply, if not definitely to affirm, the non-existence of the subject; for example, No ghosts have troubled me, No unicorns have ever been seen.[254]
[254] The universe of discourse must here be taken to be the material universe. With reference to this example, however, a critic writes, “But surely the universe of imagination is the only one applicable; for unicorns have long been known not to belong to the actual material universe.” The universe of imagination may be required in order to sustain the position that the subject of the proposition exists in the universe of discourse; but any person making the statement would certainly not be referring to the world of imagination or the universe of heraldry, for the simple reason that in either of these cases the proposition (which must then be interpreted elliptically) would obviously not be true. On the other hand, we can quite well suppose the statement made with reference to the material universe: “Whether unicorns exist or not, at any rate they have never been seen.” Again, to take another example of a similar kind where the reference is also to the phenomenal universe, we can quite well suppose the statement made: “Whether there are ghosts or not, at any rate none have ever troubled me.” In order to avoid misapprehension, it is important to distinguish the above examples from such (elliptical) propositions as the following: “The wrath of the Homeric gods is very terrible,” “Fairies are able to assume different forms.” In each of these cases, the subject of the proposition (properly interpreted) exists in the particular universe to which reference is made. See notes [2] and [3] on page 213.
238 (c) A denial of the conjunction ABC may be expressed in the form No AB is C without any intention of thereby affirming the conjunction AB ; for example, No satisfactory solution of the problem of squaring the circle has been published, No woman candidate for the Theological Tripos has been educated at Newnham College, No Advanced Student in Law is on the boards of Trinity College.[255]
[255] “As an instance of a possibly non-existent subject of a negative proposition, take the following: ‘No person condemned for witchcraft in the reign of Queen Anne was executed.’” (Venn, Symbolic Logic, p. 132.)
Particulars. In the case of particular propositions, it is far less easy to give examples, such as might be met with in ordinary discourse, in which there is no implication of the existence of the subjects of the propositions. There may be exceptions, but at any rate the cases are exceedingly rare in which in ordinary speech we predicate anything of a non-existent subject without doing so universally. The main reason for this is, as Dr Venn points out, that “an assertion confined to ‘some’ of a class generally rests upon observation or testimony rather than on reasoning or imagination, and therefore almost necessarily postulates existent data, though the nature of this observation and consequent existence is, as already remarked, a perfectly open question. ‘Some twining plants turn from left to right,’ ‘Some griffins have long claws,’ both imply that we have looked in the right quarters to assure ourselves of the fact. In one case I may have observed in my own garden, and in the other on crests or in the works of the poets, but according to the appropriate tests of verification, we are in each case talking of what is.”[256] If we look at the question 239 from the other side, we find that when our primary object is to affirm the existence of a class of objects, our assertion very naturally takes the form of a particular proposition. If, for example, we desire to affirm the existence of black swans, we say Some swans are black. The existential implication of a proposition of this kind in ordinary discourse is one of its most fundamental characteristics.