Abstract
One of the perennial questions of philosophy concerns the simple statements which say that an object is so and so or that such and such objects are so and so related: simple predicative statements. Do such statements have an ontological basis, and if so, what is that basis? The answer to this question determines—or in any case, is expressive of—a specific fundamental outlook on the world. In the course of the history of Western philosophy, various philosophers have given various answers to the question of predication. This essay presents the main, crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. In addition, the essay follows (to some extent) the most influential—the Aristotelian or mereological—paradigm of predication in its continuity and modification through the many centuries of its reign. However, the essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, there was no philosophically adequate theory of predication, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication theory considered in it. Frege, in the nineteenth century, brought the philosophy of predication on the right track, but his own theory of predication has its own deficits. The essay ends with the presentation of a theory of predication that the author himself considers adequate.
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Notes
In his Philosophical Investigations, Wittgenstein, significantly, says the following (PI, § 381): “How do I know that this colour is red?—It would be an answer to say: ‘I have learnt English’.”
For example (and paradigmatically), Judith Butler.
See (Kutschera 1998).
For an explicit statement of Aristotle’s acceptance of universals in contrast to Plato’s separate forms, see An. Post. 77 a 5–9; that passage also contains Aristotle’s definition of universal; it is this: one which can be truthfully said of many.
See Cat. 1 a 24–25, where Aristotle defines—or rather: gives a partial explication of—being in a subject: “In a subject I call that which exists in something, but not as a [literal] part, and cannot be separate from that in which it is.” [Translation U.M.] Note that the “cannot be separate from” is not meant by Aristotle to express a symmetrical relationship: “x cannot be separate from y” does not entail, for Aristotle, “y cannot be separate from x.” For he understands “x cannot be separate from y” in the sense of “x cannot exist apart from y,” and “y cannot be separate from x” in the sense of “y cannot exist apart from x,” and of course it can be—and sometimes is—the case that x cannot exist apart from y, while y can very well exist apart from x.
That this is the correct diagnosis is strongly suggested by Cat. 3 a 7–15. Regarding Aristotle’s asserting separability—the ability to exist apart from any supposed subject—of substances, see Met. Z, 1029 a 27–28. But note that in the same short passage Aristotle also asserts particularity of substances.
See Met. B 1003 a 8–10; Met. Z, 1038 b 8–12, 34–37, 1041 a 3; Met. I 1053 b 16–20; Met. M 1087 a 2.
Note that for Aristotle any universal is said truthfully of some subject (because it is by definition truthfully said of many subjects; cf. note 4).
Regarding Husserl, the following passage from his lecture Phenomenological Psychology [Phänomenologische Psychologie] of 1925 rather strongly suggests his being ready to uphold the two classical quasi-mereological predication-theories simultaneously, the universalistic one standing, as it were, on top of the particularistic one: “One must not believe that the identity of the eidos [which for Husserl merely amounts to the universal] is just an exaggerating way of speaking. … [It is not merely the case that] every object has its in-being moment, for example, of redness, and [that] each of the many objects, all of which are red, has its individually own moment, but in sameness. One must see that the sameness is only a correlate of the identity of something that is general and in common [eines Allgemeinen], that can, in truth, be intuited as one and the same out of—and as a ‘counterpart’ of—what is individual. This identical something ‘particularizes’ itself in many ways and can, in an open infinity, be considered arbitrarily particularized. All of these particularizations are, in virtue of their relationship to what is identical, related to each other, and are accordingly called ‘each the same as the other’. In an extended, non-literal way of speaking, the concrete objects themselves are, in virtue of having eidetic particularizations in them, each called ‘the same as the other with respect to the red’, and are themselves, in a non-literal sense, particularizations of the something that is general and in common [des Allgemeinen].” (Phän. Psych., p. 80; translation and italics U.M.)
R. E. Allen writes (Allen 1973, p. 367): “If Socrates is just, there is, according to the Categories, an instance of justice in him, an instance which is individual, numerically one, and inseparable from Socrates in the sense that it cannot exist apart from him.” In other words: If Socrates is just, there is a particularization of the form of being just (“an individual instance of justice”) in him—and, clearly, that particularization is the Socrates-particular form of being just. In general we have: (a) If a particularization of the form of being Φ is in α, then the α-particular form of being Φ is in α (for every particularization of the form of being Φ that is in α is identical with the α-particular form of being Φ). And we also have the converse: (b) If the α-particular form of being Φ is in α, then a particularization of the form of being Φ is in α (for the α-particular form of being Φ is, if in α, a particularization of the form of being Φ). One can derive both (a) and (b) on the basis of the following definition: the α-particular form of being Φ = Def the particularization of the form of being Φ that is in α—presupposing, for all cases of α and Φ, that there is no more than one particularization of the form of being Φ that is in α and that there is a particularization of the form of being Φ that is in α if the particularization of the form of being Φ that is in α is in α. One might object that there could be more than one particularization of the form of being red (for example) in a subject: if a table has a red area here and a red area there. But one can stipulate that the phrase “[there is] a particularization of the form of being Φ [that] is in α” is understood to refer, if true, to the (relatively to α) entire particularization of the form of being Φ in α.
From the sixteenth to the nineteenth century, the emphasis on the mind-affinity, the conceptualness of universals remained present, but, progressively, it took on decidedly human proportions; for the initially co-present Platonic/Plotinic absoluteness of universals progressively disappeared—until it triumphantly re-appeared in the work of Frege.
For the history of in-being between concepts and its relationship to predicative in-being, see (Meixner 1998).
For concluding that the concept of once crossing the Rubicon is necessarily contained in the concept of Caesar, the reason given is, in fact, not in itself sufficient: “the concept of Caesar” and “the concept of once crossing the Rubicon” must also each refer to one and the same (respective) concept in every possible world (compare the situation regarding the necessity or contingency of true identity statements). Leibniz certainly assumed the rigidity of the mentioned designators, but in the case of “the concept of Caesar” rigidity is, as a matter of fact, doubtful (the reason being this: if the concept of Caesar is the sum of all concepts that apply to Caesar, then that sum seems to be different in different possible worlds, since, apparently, in different possible worlds different concepts apply to Caesar).
Frege’s concepts (“Begriffe”) are extensional concepts (that is: they are identical if, and only if, they have the same extension); therefore they are one-to-one correlates of sets. Extensionality is not the only feature of Fregean concepts that fits ill with the normal concept of a concept: another is lack of mind-affinity (which in part is a consequence of their extensionality). Thus: Frege’s use of the word “concept” (“Begriff”)—for what is really intended by him—still bears witness to the (above-described) emphasis on the conceptualness of universals after the Middle Ages, but it does so on the linguistic surface only.
If one leaves out Leibniz’s assumption of the rigidity of the designator “the concept of α” (for example, “the concept of Caesar”; see note 13), then Leibniz’s predication theory turns out to be adequate even with respect to our normal modal expectations. But what it offers is merely a true logical rationalization of non-relational predication; it has no belief-foundational value.
The full theory is presented non-metaphorically in Meixner (2006).
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Meixner, U. From Plato to Frege: Paradigms of Predication in the History of Ideas. Int Ontology Metaphysics 10, 199–214 (2009). https://doi.org/10.1007/s12133-009-0051-5
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DOI: https://doi.org/10.1007/s12133-009-0051-5