[16] Ibid. p. 17, b. 29-37. Mr. John Stuart Mill (System of Logic, Bk. I. ch. iv. s. 4) cites and approves Dr. Whately’s observation, that the recognition of a class of Propositions called indefinite “is a solecism, of the same nature as that committed by grammarians when in their list of genders they enumerate the doubtful gender. The speaker must mean to assert the proposition either as an universal or as a particular proposition, though he has failed to declare which.�
But Aristotle would not have admitted Dr. Whately’s doctrine, declaring what the speaker “must mean.� Aristotle fears that his class, indefinite, will appear impertinent, because many speakers are not conscious of any distinction or transition between the particular and the general. The looseness of ordinary speech and thought, which Logic is intended to bring to view and to guard against, was more present to his mind than to that of Dr. Whately: moreover, the forms of Greek speech favoured the ambiguity.
Aristotle’s observation illustrates the deficiencies of common speaking, as to clearness and limitation of meaning, at the time when he began to theorize on propositions.
I think that Whately’s assumption — “the speaker must mean� — is analogous to the assumption on which Sir W. Hamilton founds his proposal for explicit quantification of the predicate, viz., that the speaker must, implicitly or mentally, quantify the predicate; and that his speech ought to be such as to make such quantification explicit. Mr. Mill has shewn elsewhere that this assumption of Sir. W. Hamilton’s is incorrect.
It thus appears that there is always one negation corresponding to one and the same affirmation; making up together the Antiphasis, or pair of contradictory opposites, quite distinct from contrary opposites. By one affirmation we mean, that in which there is one predicate only, and one subject only, whether taken universally or not universally:—
| E.g. | Omnis homo est albus | … … | Non omnis homo est albus. |
| Est homo albus | … … | Non est homo albus. | |
| Nullus homo est albus | … … | Aliquis homo est albus. |
But this will only hold on the assumption that album signifies one and the same thing. If there be one name signifying two things not capable of being generalized into one nature, or not coming under the same definition, then the affirmation is no longer one.[17] Thus if any one applies the term himation to signify both horse and man, then the proposition, Est himation album, is not one affirmation, but two; it is either equivalent to Est homo albus and Est equus albus — or it means nothing at all; for this or that individual man is not a horse. Accordingly, in this case also, as well as in that mentioned above, it is not indispensable that one of the two propositions constituting the Antiphasis should be true and the other false.[18]
[17] Aristot. De Interpr. p. 18, a. 13, seq.: μία δέ ἐστι κατάφασις καὶ ἀπόφασις ἡ ἓν καθ’ ἑνὸς σημαίνουσα, ἢ καθόλου ὄντος καθόλου ἢ μὴ ὁμοίως, οἷον πᾶς ἄνθρωπος λευκός ἐστιν … εἰ τὸ λευκὸν ἓν σημαίνει. εἰ δὲ δυοῖν ἓν ὄνομα κεῖται, ἐξ ὧν μή ἐστιν ἕν, οὐ μία κατάφασις, &c., and the Scholion of Ammonius, p. 116, b. 6, seq.
[18] Aristot. De Interpr. p. 18, a. 26. The example which Aristotle here gives is one of a subject designated by an equivocal name; when he had begun with the predicate. It would have been more pertinent if he had said at first, εἰ ὁ ἄνθρωπος ἓν σημαίνει.
With these exceptions Aristotle lays it down, that, in every Antiphasis, one proposition must be true and the other must be false. But (he goes on to say) this is only true in regard to matters past or present; it is not true in regard to events particular and future. To admit it in regard to these latter, would be to affirm that the sequences of events are all necessary, and none of them casual or contingent; whereas we know, by our own personal experience, that many sequences depend upon our deliberation and volition, and are therefore not necessary. If all future sequences are necessary, deliberation on our part must be useless. We must therefore (he continues) recognize one class of sequences which are not uniform — not predetermined by antecedents; events which may happen, but which also may not happen, for they will not happen. Thus, my coat may be cut into two halves, but it never will be so cut; it will wear out without any such bisection occurring.[19]