Guenon: The Infinite and the Indefinite

If there is but one pearl to be gleaned from Rene Guenon’s peculiarly precise use of words and terms, it is the distinction he insists upon between the infinite and the indefinite. Confusion on this terminology is rife in our own times, a fact which signals the malady at the core of our problems: we live in an age that is metaphysically illiterate. For Guenon, the infinite is, by definition, a metaphysical notion, and the modern misuse of the term is symptomatic.

 

Monsieur Guenon, let us recall, was himself a mathematician. But he was also, arguably, the most realized metaphysician in Western civilization in recent centuries. He has been described as a “pure pneumatic,” a man of pneuma. After dabbling, without satisfaction, in various esoteric fringe fraternities in Europe, he eventually went into exile in Cairo, married the daughter of a Sufi Sheihk, and lived an inconspicuous life there happily disguised as a Muslim family man for the rest of his days. His magnus opus, The Reign of Quantity, is among the most scathing and surgical critiques of modernity ever written.

 

Guenon’s view on this terminological matter is simple: what is truly infinite is beyond all limitations whatsoever, else it would be limited by some finitude, whereas what is indefinite pertains to things which are necessarily limited by being one thing and not another. So, for Guenon, it is an appalling category error to say, for example, that the series of integers (numbers) is “infinite”. No. It is indefinite. It extends without any definite end. But it is not infinite. It is not infinite because the set of integers is itself a finite thing among the set of all things. It is limited by the fact that it is the set of numbers and not the set of something else. Whereas the infinite has no limitations whatsoever. It encompasses and is greater than the set of all things. In order to be infinite, it must be.

 

The place where one hears abuses of these terms most often is in popular astrophysics. People in that field throw the word “infinite” around willy nilly. Thus we might be told that “space is infinite”. No. Space might extend indefinitely in all directions, but it is not “infinite” because it is one thing (space) and not another. (The same goes for Einstein's 'Space-Time') For Guenon, you cannot have an infinite anything, except infinity itself. You cannot qualify infinity. It's the biggest, most all-encompassing - also the simplest - idea you can think. The universe is not infinite – but it might go on indefinitely. Time is not infinite - but it might go on indefinitely. All physical things are finite. Infinity is, by definition, meta-physical, an inherently transcendent notion.

 

There is a Platonic point to be made here. The universe may be within the infinite – it must be – but it is itself not infinite but merely indefinite. Now, this indefinitude is, as it were, a copy of the model. Among created things the infinite is expressed as indefinitude – as Plato would have it, a sort of lesser or counterfeit version of the original. The indefinite is a manifest copy of the infinite, which is the principle. Why is it that created things and qualities of the created realm, such as number, say, can extend indefinitely? It is because they are nested within, or created from, and bear the imprint of, the Infinite with an upper case I.

 

On the face of it, these abuses are simply sloppiness and laziness. Lazily, we use “infinite” and “indefinite” as synonyms. “Infinite” is preferred in general currency because it sounds better and bigger. “Indefinite” has dropped out of common use, except among the pretentious. But it is more than a linguistic fashion. It is a crucial laziness about an all-important pivot. Guenon was unusually precise in his terms for good reason. He wasn’t just being pedantic. (Actually, he was a humorless pedant by all accounts, but that’s not the point.) A loss of any true sense of the infinite – while befuddled by things that are indefinite – is exactly the modern condition. We are agog at the vast vistas of telescopic space, or the ever-receding dimensions of the quantum realm, or the mind-boggling forces within the so-called Big Bang, we are bewitched by these vastnesses. But as Goethe said, ‘The telescope will make us blind.’ Immersed in the indefinite, we are blind to the infinite.

 

This clarification of the notion of the infinite has many important ramifications. For a start, it provides an immediate and satisfactory answer to the question – so beloved of modern existentialists – ‘Why is there anything at all and not nothing?’ The short answer is: there must be something in order for the infinite to be infinite. The infinite – in order to be infinite – must include all possibilities, and a physical universe is one of them. It could not not be if the infinite is truly infinite. The question of why there need be anything at all is only a conundrum to those without a robust and thoroughgoing grasp of the infinite.

 

In traditional cosmologies, the Guenonian infinite is rather like the Pleroma. In the Platonic emanationist cosmology it is like the creative principle in which “there is no envy” (because it is subject to no limitations) but which is “overflowing” with perfect generosity (it is absolutely fecund, because limitless.) Again: you cannot have an infinite number of apples. Indeed, you cannot have an infinite number of anything. The term “infinite number” makes no sense. You can have an indefinite number of apples (in a good year), but apples, by being apples, aren’t infinite.