INFINITY

From Philosopedia.org

INFINITY

• Only two things are infinite, the universe and human stupidity, and I’m not sure about the former. —Albert Einstein

To most, “the infinite” refers to having no boundaries or limits, something like X to the nth degree, that which is immeasurably great, world without end. However, another kind of infinity is that of the infinitely small, the infinitesimal. Jim Holt, a writer about philosophy and science for Lingua Franca and The Wall Street Journal, has surveyed philosophers’ views about the subject and in an article (The New York Review of Books, 20 May 1999), wrote,

• In his biography of Frederick the Great, Carlyle tells us that when Leibniz offered to explain the infinitely small to Queen Sophia Charlotte of Prussia, she replied that on that subject she needed no instruction: the behavior of her courtiers made her all too familiar with it. (About the only nonpejorative use of “infinitesimal” I have come across occurs in Truman Capote’s unfinished novel Answered Prayers, when the narrator is talking about the exquisite vegetables served at the tables of the really rich: “The greenest petits pois, infinitesimal carrots. . . .”)

Holt then relates the Greek debate over the nature of being:

• On the one side of this debate stood the monists—Parmenides and his followers—who argued that being was indivisible and that all change was illusion. On the other stood the pluralists—including Democritus and his fellow Atomists, as well as the Pythagoreans—who upheld the genuineness of change, which they understood as a rearrangement of the parts of reality. . . . But when you start parsing reality, breaking up the One into the Many, where do you stop? Democritus held that matter could be analyzed into tiny units—“atoms”—that, though finite in size, could not be further cut up. But space, the theater of change, was another questions. There seemed to be no reason why the process of dividing it up into smaller and smaller bits could not be carried on forever. Therefore its ultimate parts must be smaller than any finite size.

However, to imagine that it is possible to find something smaller than the smallest quark, and that there is still something smaller than that, ad infinitum, is analgous to imagining that out of nothing something came. In his review of four current works on the subject, Holt explains the thinking of Zeno, Aristotle, Euclid, Saint Augustine, Kepler, Galileo, Fermat, Pascal, Newton, Bishop Berkeley, Voltaire, Lagrange, Laplace, d’Alembert, Hegel, Bergson, Bertrand Russell, Abraham Robinson, and others.

His general conclusion is that the last word has not yet been written about so mammoth a topic as the infinitesimal.