Essays in Idleness

Towards the end of the Elizabeth Anscombe edition of remarks Ludwig Wittgenstein collected in a shoe-box (entitled, Zettel), there are some glorious oddments. My eye just cast upon one of my old favourites:

“Numbers are not fundamental to mathematics.”

It is a long time since I first obtained, then wrestled with this book. Yet I distinctly recall my laughter when I came to this phrase. It was not mocking laughter, of the sort cultivated in our modern academic asylums; the strange mad sarcastic laughter of dissonance. It was what I would call “the laughter of hope.” Suddenly an obstacle to understanding is removed, and one laughs in surprise at what one finds under or behind it. It is the eureka laughter.

In six words this Wittgenstein has eviscerated not only Russell, but possibly Frege. Or rather, he has exposed the mental blockage, by which “logical” and “scientific” man constructs a world, and peoples it with objects, described by their “properties” — confusing what lies glibly on the surface with what has lain profoundly, “underneath.” We think, for instance, that math is all about numbers. But no, the reverse of this is true. We only use numbers as a means to understand math. They are like tags or labels in a museum collection, things tied or pasted to the sui generis exhibits themselves.

We glimpse conceptual unities, not with numbers but through them. Yet we only begin to describe what we have seen, and can never make an end of it. There can be no analogy to an absolute; no metaphors to do it any part of justice. And this we must remember in giving it a name.

Similarly, we imagine the “infinite” from a projection of the “finite.” In fact, we can’t see it, because we have confused our multiplying counters with real things. So we become accustomed to talking nonsense. “Infinity” is a word we made up, as is “zero,” as are “one,” “two,” and “three.”

“Two and two makes four” is confidently asserted, but cannot be proved. It can only be demonstrated. “Four less two leaves two” is hardly proof. It is instead a circularity.

This is to my mind why such a concept as the Holy Trinity is lost upon the moderns. Presented as God, Christ, Spirit, it can make some sense to any peasant; but the “threeness” of it only leads us astray. It is a quality in the Divine that has nothing to do with number; it is indeed an impenetrable Mystery. Or shall I say a mystical fountain, gushing forth: “I am that I am.”

The ancient Hebrews were rightly reticent of naming what could not be named. Only, I think, in the Messiah did God, for our salvation, “name Himself.”

He would come, He has come, He will come: now there’s a trinity. But there is no three in it. Past, present, future are not three separable things. We cannot describe Time from within Time, nor understand it any better as an infinite recession in two directions from our own “fixed” point. In the moment we begin to apprehend it, it passes away.

Towards Christmas, if perhaps Advent is observed, the Gift comes irresistibly into view. It is nothing like a box with ribbons; nothing like a package with a present inside. Nothing in the womb of Our Lady is reducible to “an item” like that. It is Gift in the absolute, as our own lives are absolute Gift: a totality that cannot be reduced to pieces. It is a mysterious Event, that transcends events. We can only pretend to accept it or reject it, for it simply and immortally IS.

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POSTSCRIPTUM. … I am already in receipt of correspondence expressing alarm that I may be endorsing the view of Antonio Spadaro (the progressive Italian Jesuit), who says that in his (appalling) theology, two plus two may sometimes equal five. This is not anything like what I meant above. Some things are so absolutely [bad-word] obvious that the joke is, they cannot be proved. They can be demonstrated, however, and work every time, and must therefore be accepted by those who have not gone mad. But there is no deep philosophy here. It’s only, 2+2=4.

We might take this a little farther and assert that, by extension, all “mathematical proofs” are essentially circular, but this would require more energy than is available to me today. This does not mean the “proofs” (actually demonstrations) are wrong. Quite the opposite: a proposition is shown to be inevitable, by extension from the very first and simplest numerical postulates; i.e. it is shown to be “as true as, 2+2=4.” Thus, it must be accepted, on its own terms, by everyone who is not insane.

Of course, there is mad and mad. Some people go off their nut from biochemical causes. These can sometimes be treated with drugs. But some others go off it by choice, and meds cannot help them.