For the operation of Formal Logic it is almost necessary to have these parts, because it is requisite to transpose the terms (as in Conversion) without changing their meaning, [1] and to get rid of tenses, which do not belong to Scientific Judgment, and are very troublesome in Formal Inference.
[1] If the “predicate” is a Substantive, this presents no difficulty; and if it is an Adjective, it can be done by a little straining of grammar, or the insertion of “thing” or “things.” With a verb it is more clumsy.
Thus in Formal Logic we prefer the shape of sentence “Gold is lustrous” to “Gold glitters,” and “The bridge is {99} cracked” to “There is a crack in the bridge.” And practically all propositions can be thrown into this shape, which is convenient for comparing them. The educational value of elementary formal logic consists chiefly, I am convinced, in the exercise of paraphrasing poetical or rhetorical assertions into this typical shape, with the least possible sacrifice of meaning. The commonest mistakes in the work of beginners, within my experience as a teacher, consist in failures to interpret rightly the sentence given for analysis.
But this type is not really ultimate. The judgment can be conveyed without a grammatical subject, and without the verb “is”—indeed without any grammatical verb at all. On the whole this agrees with Mill’s view in the chapter “Of Propositions.” [1] He points out (§ 1) that we really need nothing but the Subject and Predicate, and that the copula is a mere sign of their connection as Subject and Predicate. He does not, however, discuss the case in which the grammatical Subject is absent.
[1] Mill’s Logic, Bk. I. ch. iv.
Copula
2. In analysing the Judgment as an act of thought we may begin by dismissing the separate Copula. It has no separate existence in thought corresponding to its separate place in the typical proposition of Formal Logic. It has come to be considered separately, because the abstract verb “is” is used in our languages as a sign of the complete enunciation. But there is not in the Judgment any separate significant idea—any third idea—coming in between the Subject and Predicate of Judgment. We should try to think of the Copula not as a link, separable and always {100} intrinsically the same, [1] connecting two distinct things. We should think of it rather as the grip with which the parts of a single complex whole cohere with one another, differing according to the nature of the whole and the inter-dependence of its parts. Benno Erdmann [2] has strikingly expressed this point of view by saying, that in the Judgment, “The dead ride fast,” the Subject is “the dead,” the Predicate “fast riding,” and the Copula “the fast riding of the dead.” In other words, the Copula is simply the Judgment considered exclusively as a cohesion between parts of a complex idea, the individual connection between which can only be indicated by supplying the idea of those parts themselves.
[1] In a comic Logic, with pictures, meant to stimulate dull minds at a University, I have seen the Copula represented as the coupling-link between two railway carriages. This is an excellent type of the way in which we should not think of it.
[2] Logik, p. 189.
Are Subject and Predicate necessary?