Light Upon Light

By Matt McKeown

Differential calculus may not be for everyone, but, in some branch or other, the mind of Leibniz is.

Gottfried Wilhelm Leibniz is a difficult figure to profile concisely. He was a polymath (like Benjamin Franklin): Leibniz studied, and in many cases revolutionized, fields from logic to theology to higher mathematics to linguistics to library science. He is also a little difficult to keep track of here and there; honesty was not the most conspicuous of his virtues. But his scholarly output, though much of it remained unpublished at his death in 1716, was prodigious, and foreshadowed a number of later developments in science and philosophy—even the relativity theory of Albert Einstein.

One of Leibniz’s most famous, and controversial, discoveries was calculus. The discovery proved controversial due to the fact that Sir Isaac Newton, around the same time (or rather, a few years earlier) but quite independently, also discovered calculus—and both men then waited several years to make any formal publication about, or even including, their discovery. However, the methods the two men used were markedly different, as were their methods of notation—fluxional notation in Newton’s case, while Leibniz devised differential notation. (Unluckily, the present author is a classicist who cannot tell fluxional from differential notation any more than he can tell one individual drop of water from another, and so shall write no more about that!)

Another invention of Leibniz’s, this time in the field of logic, was his slightly confusingly named calculus rationcinator. This was an attempt to devise a form of symbolic logic, allowing extensive and involved chains of reasoning to be notated in a much briefer series of simple glyphs. The nature of its construction has led some academics to consider the calculus ratiocinator system a forerunner of computer programming; it is also worth noting that Leibniz invented a mechanical calculator that he called a “stepped reckoner,” and of which one prototype is still preserved in the National Library of Lower Saxony in Germany.

I do not believe that a world without evil, preferable in order to ours, is possible; otherwise it would have been preferred.

But besides his contributions to mathematics and technology (though of these we have scarcely scratched the surface), Leibniz is widely known for his philosophical influence as one of the great figures of Enlightenment thought, alongside Baruch de Spinoza and René Descartes. Like them, he was a rationalist, and laid down several first principles of reasoning that remain influential, and in some cases debated, to this day. A particularly contentious example is his rule of the “identity of indiscernibles,” which states that two discrete objects cannot have all of the same qualities, or they are simply the same object. This seems intuitively accurate, but is also open to a multitude of objections—for instance, aren’t two visibly identical plastic buttons distinct only in number? Does Leibniz’s law imply that “where something is located” is one of its qualities, for instance? Or do modern ideas about quantum mechanics imply that the law is valid, because the two buttons’ subatomic structure effectively could not be identical, statistically speaking?

Besides concerns of this type, Leibniz also took an interest in theodicy, or the problem of evil. The problem arises from the classical theist assertion that there is an all-good, all-knowing, and all-powerful being (normally called “God”), which in turn implies that any and all bad things could in principle be stopped by this being; hence, either the existence of such a being or the nature of good and bad must be called into question.

Leibniz propounded the “best of all possible worlds” solution, on the basis of a presumption of philosophical optimism rooted in the premises of classical theism. This explains evil as arising entirely from creatures rather than God: their limited goodness, knowledge, and powers all dispose creatures to make mistakes (and, unlike the perfect goodness of God, even allow them to do deliberate evil). God does not prevent these mistakes because this potential for moral evil is an unavoidable consequence of the metaphysical imperfection of creatures—imperfection not in the sense that they are flawed, but in the sense that they are finite; the only way God could “solve” the problem of evil would therefore be not to create at all. Nonetheless, this must be the best possible world, because God, being God, would not create an inferior world if he knew of a better one that he could have made instead (and, being all-knowing, he would assuredly know of any and all possible worlds and their relative goodness or badness). Not everyone finds this argument equally persuasive, but interestingly, its adherents can be found in multiple traditions, and across a wide span of time: Leibniz’s argument is akin to one of the points St. Thomas himself makes in the “five ways” proofs for the existence of God.


Every week, we publish a profile of one of the figures from the CLT author bank. For an introduction to classic authors, see our guest post from Keith Nix, founder of the Veritas School in Richmond, VA.

If you enjoyed this piece and would like to read more from the Journal, take a look at these profiles of Kierkegaard and Pascal, or these “Great Conversation” posts on democracy and the one and the many. And be sure to check out our podcast, Anchored, hosted by our founder Jeremy Tate.

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