Meaning of Abstract and General Terms, debated from ancient times to the present day — Different views of Plato and Aristotle upon it.
The question — What is the real and precise meaning attached to abstract and general words? — has been debated down to this day, and is still under debate. It seems to have first derived its importance, if not its origin, from Sokrates, who began the practice of inviting persons to define the familiar generalities of ethics and politics, and then tested by cross-examination the definitions given by men who thought that common sense would enable any one to define.[37] But I see no ground for believing that Sokrates ever put to himself the question — Whether that which an abstract term denotes is a mental conception, or a separate and self-existent reality. That question was raised by Plato, and first stands clearly brought to view here in the Parmenidês.
[37] Aristotel. Metaphys. A. 987, b. 3. M. 1078, b. 18-32.
If we follow up the opinion here delivered by the Platonic Sokrates, together with the first correction added to it by Parmenides, amounting to this — That the Form is a Conception of the mind with its corresponding Concept: if, besides, we dismiss the doctrine held by Plato, that the Form is a separate self-existent unchangeable Ens (ἓν παρὰ τὰ πολλὰ): there will then be no greater difficulty in understanding how it can be partaken by, or be at once in, many distinct particulars, than in understanding (what is at bottom the same question) how one and the same attribute can belong at once to many different objects: how hardness or smoothness can be at once in an indefinite number of hard and smooth bodies dispersed everywhere.[38] The object and the attribute are both of them relative to the same percipient and concipient mind: we may perceive or conceive many objects as distinct individuals — we may also conceive them all as resembling in a particular manner, making abstraction of the individuality of each: both these are psychological facts, and the latter of the two is what we mean when we say, that all of them possess or participate in one and the same attribute. The concrete term, and its corresponding abstract, stand for the same facts of sense differently conceived. Now the word one, when applied to the attribute, has a different meaning from one when applied to an individual object. Plato speaks sometimes elsewhere as if he felt this diversity of meaning: not however in the Parmenidês, though there is great demand for it. But Aristotle (in this respect far superior) takes much pains to point out that Unum Ens — and the preposition In (to be in any thing) — are among the πολλαχῶς λεγόμενα, having several different meanings derived from one primary or radical by diverse and distant ramifications.[39] The important logical distinction between Unum numero and Unum specie (or genere, &c.) belongs first to Aristotle.[40]
[38] That “the attribute is in its subject,” is explained by Aristotle only by saying That it is in its subject, not as a part in the whole, yet as that which cannot exist apart from its subject (Categor. 1, a. 30-3, a. 30). Compare Hobbes, Comput. or Logic. iii. 3, viii. 3. Respecting the number of different modes τοῦ ἔν τινι εἶναι, see Aristot. Physic. iii. p. 210, a. 18 seq., with the Scholia, p. 373 Brandis, and p. 446, 10 Brand. The commentators made out, variously, nine, eleven, sixteen distinct τρόπους τοῦ ἔν τινι εἶναι. In the language of Aristotle, genus, species, εἶδος, and even differentia are not ἐν ὑποκειμένῳ, but are predicated καθ’ ὑποκειμένου (see Cat. p. 3, a. 20). The proprium and accidens alone are ἐν ὑποκειμένῳ. Here is a difference between his language and that of Plato, according to whom τὸ εἶδος is ἐν ἑκάστῳ τῶν πολλῶν (Parmenid. 131 A). But we remark in that same dialogue, that when Parmenides questions Sokrates whether he recognises εἴδη αὐτὰ καθ’ αὐτά he first asks whether Sokrates admits δικαίου τι εἶδος αὐτὸ καθ’ αὑτό, καὶ καλοῦ, καὶ ἀγαθοῦ, καὶ πάντων τῶν τοιούτων. Sokrates answers without hesitation, Yes. Then Parmenides proceeds to ask, Do you recognise an εἶδος of man, separate and apart from all of us individual men? — or an εἶδος of fire, water, and such like? Here Sokrates hesitates: he will neither admit nor deny it (130 D). The first list, which Sokrates at once accepts, is of what Aristotle would call accidents: the second, which Sokrates doubts about, is of what Aristotle would call second substances. We thus see that the conception of a self-existent εἶδος realised itself most easily and distinctly to the mind of Plato in the case of accidents. He would, therefore, naturally conceive τὰ εἴδη as being ἐν ὑποκειμένῳ, agreeing substantially, though not in terms, with Aristotle. It is in the case of accidents or attributes that abstract names are most usually invented; and it is the abstract name, or the neuter adjective used as its equivalent, which suggests the belief in an εἶδος.
[39] Aristotel. Metaphys. Δ. 1015-1016, I. 1052, a. 29 seq. τὰ μὲν δὴ οὕτως ἓν ἢ συνεχὲς ἢ ὅλον· τὰ δὲ ὧν ἂν ὁ λόγος εἷς ᾖ· τοιαῦτα δὲ ὧν ἡ νόησις μία, &c.
About abstract names, or the names of attributes, see Mr. John Stuart Mill’s ‘System of Logic,’ i. 2, 4, p. 30, edit. 5th. “When only one attribute, neither variable in degree nor in kind, is designated by the name — as visibleness, tangibleness, equality, &c. — though it denotes an attribute of many different objects, the attribute itself is always considered as one, not as many.” Compare, also, on this point, p. 153, and a note added by Mr. Mill to the fifth edition, p. 203, in reply to Mr. Herbert Spencer. The oneness of the attribute, in different subjects, is not conceded by every one. Mr. Spencer thinks that the same abstract word denotes one attribute in Subject A, and another attribute, though exactly like it, in Subject B (Principles of Psychology, p. 126 seq.) Mr. Mill’s view appears the correct one; but the distinction (pointed out by Archbishop Whately) between undistinguishable likeness and positive identity, becomes in these cases imperceptible or forgotten.
Aristotle, however, in the beginning of the Categories ranks ἡ τίς γραμματικὴ as ἄτομον καὶ ἓν ἀριθμῷ (pp. 1, 6, 8), which I do not understand; and it seems opposed to another passage, pp. 3, 6, 15.
The argument between two such able thinkers as Mr. Mill and Mr. Spencer, illustrates forcibly the extreme nicety of this question respecting the One and the Many, under certain supposable circumstances. We cannot be surprised that it puzzled the dialecticians of the Platonic Aristotelian age, who fastened by preference on points of metaphysical difficulty.
[40] See interesting remarks on the application of this logical distinction in Galen, De Methodo Medendi, Book iii. vol. x. p. 130 seq. Aristotle and Theophrastus both dwelt upon it.