Vagueness and mass nouns have been unconquerable land for the logic founded by Aristotle, mathematized by Boole, and developed by Frege and others since the end of the nineteenth century—a logic I call analytic. Which is unfortunate and perplexing, since vague predicates and mass nouns constitute the overwhelming majority of the terms used in ordinary conversation and reasoning, on which analytic logic offers then no clue: qualities like yellow or smooth don’t have precise boundaries, nor do materials like flour or gold, nor do objects like Socrates or this table, liable as the latter are to constant changes in their makeup. It seems that only ideal entities like numbers, Platonic forms, and theoretical constructs offer no intractable difficulties to the application of this logic. A different logic, which I call oceanic, successfully addresses such anomalies. Of oceanic logic I have spoken before—in most detail in Theories of the Logos and The Logic of Mysticism—; here I give a more succinct and abstract presentation.
The basic semantic unit of oceanic logic is an expanse. Think of it as a continuous stretch, in any kind of environment. A line, in physical space; a stream of thought or a melody, in time; a life, in time and space; a spectrum of colors, in perceptual space; a proof,1 in logical space. There is a tendency, in this logic, to stress the continuity of any expanse with any other, and end up with a universal expanse in which everything is continuous with everything else—with universal monism. I have explored this tendency in specific connection with the work of various mystics; but here I bracket it, to provide the reader with a more pliable, more conventional tool.
There is an expanse in the background—or, sometimes, the foreground—of all the recalcitrant entities mentioned above. The spectrum of colors hovers over the vagueness of yellow and its fuzzy relation with orange; the spectrum of textures over the vagueness of smooth and its fuzzy relation with rough; flour and gold are, of course, their own expanse; Socrates and this table are, on any occasion, phases of an expanse (a life) whose every phase merges continuously with the previous and with the next ones.2
Expanses have modes or manifestations (these are different names of the same things).3 Yellow and orange are modes of the spectrum of colors; smooth and rough modes of the spectrum of textures; lumps of flour and lumps of gold modes of flour and gold; child Socrates and old Socrates modes of Socrates; this table as new and this table as decrepit modes of this table. Crucially, modes are not individual objects, distinct from each other: as they are modes of one and the same expanse, they are also, all of them, one and the same—each of them is nothing other than the expanse in one of its modes. To bring up the metaphor that made me give this logic its name, all waves are modes of the same ocean, and the same with each other: the only identity in question is that of the ocean with itself. And, to get a glimpse of the most ambitious extension of the metaphor, all objects taken to be distinct from each other could be seen instead as modes of the One, as waves in the ocean of being—hence also as identical with each other.
Oceanic logic does not operate in a vacuum. Its point of view is constantly intruded upon by analytic logic, which projects into any situation its own standards and demands. Take for example the expanse sand. Its modes will be heaps of sand, all identical with each other, however large or small they might be. But analytic logic is based on contraries: predicates that cannot be true together, objects that are “what they are and not another thing.”4 Therefore, when analytic logic intrudes, it will want to distinguish between the objects this heap of sand and that heap of sand, or between the predicates heap of sand and non-heap of sand. And, by doing this, it will reveal its limitations: prove incapable to distinguish between heaps and non-heaps. (This failure is the basis of Eubulides’ paradox of The Heap, which not accidentally he conceived as a weapon against Aristotle’s analytic logic.)5
To introduce additional terminology, the objects analytic logic intrudes upon an expanse are types, and, true to the logic they belong to, they are precisely identified and distinct from each other. The type which is a specific shade of yellow—call it shade A of yellow—will be precisely identified and distinct from another similarly identified shade (another type), which we can call shade B of yellow. And there will be precisely identified levels of smoothness (this one, not that one, nor anything else however similar), precisely identified grains of sand and particles of gold, precisely identified instants of Socrates’ life and instants of the life of this table. There will be precisely identified points or locations along a linear path. All of these types are as much amenable to applications of analytic logic as numbers, Platonic forms, or theoretical constructs, because all of them, in fact, are just as much ideal objects as those others—and just as foreign to ordinary experience and ordinary conversation or reasoning. What matters most here: all of them are constitutionally unable to capture the relevant modes. No amount of shades of yellow will be able to capture the mode yellow as distinct from the mode orange; no amount of levels of smoothness will be able to capture the mode smooth as distinct from the mode rough; no amount of grains of sand or particles of gold will be able to capture the modes heap of sand or lump of gold as distinct from non-heap of sand or non-lump of gold; no amount of instants of Socrates’ life will be able to capture the mode phase A of Socrates’s life as distinct from phase B of Socrates’ life; no amount of points will be able to capture the mode stretch A of a linear path as distinct from stretch B of the same linear path (here Zeno is a source as much as Eubulides).
A logic is a comprehensive strategy of reasoning. So, when analytic logic intrudes upon contexts within which oceanic logic is at home, two different strategies of reasoning come in conflict. One party will insist on wanting exact definitions of all the terms involved; the other will insist that those terms have no exact confines, hence cannot be defined, and no exactness of the sort required holds for them. As they reason differently, hence have no principles in common, they will be in no position to build any arguments to make their point that would be acceptable, or even intelligible, to the other party; all they can do is throw paradoxes (supposed refutations) at each other. Eubulides’ The Bald or The Heap, say, or something like Aristotle’s defense of the Principle of Non-Contradiction in Book IV of the Metaphysics, according to which, if you don’t make clear distinctions, you end up making no sense.6 But these are all petitio principii: nothing other than turning one’s own lack of understanding into an objective impossibility. A much more fruitful attitude, I suggested in Theories of the Logos, is to become aware that there are different tools in play, that they apply naturally to different fields, and to switch from one to the other (to, indeed, play with them) as different needs and opportunities arise.
How ineffective it is, on the other hand, to force a purely analytic reading outside the realm of ideal objects, hence in particular when handling vagueness, mass nouns, and the like, can be instructively illustrated by perusing one significant case. Mereology is the study of the relations between parts and wholes: practiced since Aristotle, it was formalized in the twentieth century starting with Stanisław Leśniewski, some variants of it have been used to address the semantics of mass nouns, and part is an obvious case of a vague predicate. In his entry on mereology of the Stanford Encyclopedia of Philosophy, Achille Varzi gives a highly competent and remarkably lucid survey of the field, impressive mostly for how impotent it (unwittingly, I am sure) makes it look. An unsympathetic recap of it is: the only formal elements of an axiomatization of mereology on which there is substantial (though not complete) agreement do not characterize uniquely the part/whole relation; they reduce to the axioms of a partial order (reflexivity, transitivity, and antisymmetry) that are also true of countless other relations. As soon as we go beyond this rough, inadequate sketch, and make an effort to be talking about the part/whole relation as opposed to any other, every proposal is met with a number of counterexamples, resulting in total (not partial) inconclusiveness. What those examples direct our attention to (if only we paid proper attention to them, and drew the correct moral from them) is that there is no hope of seizing the meaning of part by treating it as a predicate with clear, definite boundaries, to be exhaustively described by a set of axioms; whenever we try that, slippery slopes loom menacing from all corners. Oceanic logic is where part belongs; sorites, not syllogisms, are the arguments appropriate to it.
Notes
1 This must not be a proof in the post-Fregean sense of the word, where intuition is ruled out and the proof consists of a number of individual, separate steps resulting from the application of rules, but a proof in the sense of Descartes’ VII rule in Rules for the Direction of the Mind: “If we wish our science to be complete, those matters which promote the end we have in view must one and all be scrutinized by a movement of thought which is continuous and nowhere interrupted” (p. 19; all italicized in the text).
2 Socrates and this table are also primary targets of dialectical logic (for which see my Hegel’s Dialectical Logic). But the emphasis is different; here we care about the indistinguishability of all phases of these lives; there about the narrative necessity that connects them.
3 The terminology of modes is homage to Spinoza, the one of manifestations to various mystic authors, for whom creatures are manifestations of God (conceived as a universal expanse). All of whom are crucially relevant to the development of oceanic logic.
4 This is borrowed from a celebrated saying by Joseph Butler, to be found in his Fifteen Sermons Preached at the Rolls Chapel, p. 28.
5 The Heap, and The Bald mentioned later, are examples of a class of arguments called sorites, or in colloquial discourse slippery slopes, which point to the impossibility of making precise distinctions within an expanse. They are the most powerful argumentative tool of oceanic logic.
6 See The Complete Works of Aristotle, pp. 1588-1593 (1005b-1009a).
References
Aristotle, The Complete Works of Aristotle, Princeton: Princeton University Press, 1984.
Bencivenga, E. Hegel’s Dialectical Logic, New York: Oxford University Press, 2000.
Bencivenga, E. Theories of the Logos, Berlin: Springer, 2017.
Bencivenga, E. The Logic of Mysticism, Berlin: Springer, 2025.
Butler, J. Fifteen Sermons Preached at the Rolls Chapel, Cambridge: Hilliard and Brown, 1827.
Descartes, R. Rules for the Direction of the Mind, in The Philosophical Works of Descartes, vol. I, Cambridge: Cambridge University Press, 1979.
Varzi, A. Mereology, Stanford Encyclopedia of Philosophy, 2016.
Ermanno Bencivenga is a Distinguished Professor of Philosophy and the Humanities, Emeritus, at the University of California. The author of seventy books in three languages and one hundred scholarly articles, he was the founding editor of the international philosophy journal Topoi (Springer) for thirty years, as well as of the Topoi Library. Among his books in English are Kant’s Copernican Revolution (New York: Oxford University Press, 1987); The Discipline of Subjectivity: An Essay on Montaigne (Princeton NJ: Princeton University Press, 1990); Logic and Other Nonsense: The Case of Anselm and His God (Princeton NJ: Princeton University Press, 1993); A Theory of Language and Mind (Berkeley and Los Angeles: University of California Press, 1997); Hegel’s Dialectical Logic (New York: Oxford University Press, 2000); Ethics Vindicated: Kant’s Transcendental Legitimation of Moral Discourse (New York: Oxford University Press, 2007); Theories of the Logos (Berlin: Springer, 2017); Understanding Edgar Allan Poe: They Who Dream by Day (Newcastle upon Tyne UK: Cambridge Scholars, 2023); The Logic of Mysticism (Berlin: Springer, 2025).
Blue Labyrinths 