Analytic logic is obsessed with keeping reasoning free from error, as is seen most clearly in the developments of the philosophy of mathematics between Frege’s work in the late nineteenth century and Gödel’s second theorem: a sustained attempt at founding arithmetic on the bedrock of a logic that incorporated naïve set theory, the collapse of that attempt with the discovery of the paradoxes, Hilbert’s program of vindicating all mathematical theories by proving their consistency, and a final resolution that no such proof was possible, even for the most elementary mathematical theory. Mathematics was then going to be practiced in the context of an ineliminable risk of error—and that was understood as a limiting, negative result.
In dialectical logic, error has no currency, because everything anyone believes, at any stage of the total narrative, is dialectically justified. There is still plenty of room, however, for relative error: for something that is false with respect to a truer, later phase of the narrative. And, in this sense, dialectical logic embraces error: the starting point of every dialectical argument is a rough, or immediate, position that through the course of the argument evolves into greater and greater truth.
In oceanic logic, truth inevitably becomes error: the ordinary truth that a man is uncontroversially bald, or white, when subjected to the relentless attacks of sorites, turns out not to be true after all—the man is just as much non-bald or nonwhite. This is seen most clearly in a class of paradoxes that are not often lumped together with the sorites but in fact express the same attitude: Zeno’s paradoxes about space. There, too, uncontroversial truths about reaching a certain destination, or overcoming a contender in a race, are challenged and called in question. Ultimately, oceanic logic invites us to reject the arrogance of truth and learn to live in the territory of error.
- Aristotle, The Complete Works, in two volumes, edited by Jonathan Barnes. Princeton: Princeton University Press, 1984d.Google Scholar
- Bergson, Henri. Laughter: An Essay on the Meaning of Comic, translated by Cloudesley Brereton and Fred Rothwell. London: Macmillan, 1911e. (1911b).Google Scholar
- Bergson, Henri. Creative Evolution, translated by Arthur Mitchell. London: Macmillan, 1911d. (1911c).Google Scholar
- Croce, Benedetto. Filosofia e storiografia. Napoli: Bibliopolis, 2005.Google Scholar
- Descartes, René. Meditations on First Philosophy, with Objections and Replies. In The Philosophical Writings of Descartes, translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press, 1984b/1985, vol. II, pp. 3–62, 66–383.Google Scholar
- Descartes, René.n.d. Principles of Philosophy. In Cottingham et al. cit., vol. I, pp. 179–291.Google Scholar
- Hegel, Georg Wilhelm Friedrich. Lectures on the History of Philosophy, in three volumes, translated by Elizabeth Sanderson Haldane and Frances Helen Simson. Lincoln (NE): University of Nebraska Press, 1995.Google Scholar
- Hegel, Georg Wilhelm Friedrich. Lectures on the Philosophy of Religion, in three volumes, translated by Robert F. Brown, Peter Crafts Hodgson, and J. Michael Stewart, with the assistance of Henry Silton Harris. Berkeley (CA), University of California Press, 1984b/1988.Google Scholar
- Heidegger, Martin. Being and Time, translated by John Macquarrie and Edward Robinson. New York: Harper & Row, 1962.Google Scholar
- Hilbert, David. “On the Infinite,” translated by Stefan Bauer-Mengelberg. In From Frege to Gödel: A Source Book in Mathematical Logic, 1879– 1931, edited by Jean van Heijenoort. Cambridge (MA): Harvard UniversitPress, 1967, pp. 369–392.Google Scholar
- Kirk, Geoffrey Stephen, John Earle Raven, and Malcolm Schofield. The Presocratic Philosophers. Cambridge: Cambridge University Press, 1983.Google Scholar
- Plato. Republic, translated by Robin Waterfield. Oxford: Oxford University Press, 1993a.Google Scholar
- Sartre, Jean-Paul. Being and Nothingness, translated by Hazel Estella Barnes. New York: Washington Square Press, 1992.Google Scholar