Gravity and grace (_La pesanteur et la grâce_) is a collection of aphorisms written, probably without intent of publication, by Simone Weil?, assembled by Gustav Thibon and originally published in 1947. It contains a chapter ‘Algebra’, which we reproduce below.
It is possible to read (part of) this as a criticism of formalism in mathematics, and as a musing on the importance of semantics (“the relation of the sign to the thing signified”) in the foundations of mathematics.
The following is directly quoted from Gravity and grace.
Money, mechanisation, algebra. The three monsters of contemporary civilisation. Complete analogy.
Algebra and money are essentially levellers, the first intellectually, the second effectively.
About fifty years ago the life of the Provençal peasants ceased to be like that of the Greek peasants described by Hesiod. The destruction of science as conceived by the Greeks took place at about the same period. Money and algebra triumphed simultaneously.
The relation of the sign to the thing signified is being destroyed, the game of exchanges between signs is being multiplied of itself and for itself. And the increasing complication demands that there should be signs for signs….
Among the characteristics of the modern world we must not forget the impossibility of thinking in concrete terms of the relationship between effort and the result of effort. There are too many intermediaries. As in the other cases, this relationship which does not lie in any thought, lies in a thing: money.
As collective thought cannot exist as thought, it passes into things (signs, machines…). Hence the paradox: it is the thing which thinks and the man who is reduced to the state of a thing.
There is no collective thought. On the other hand our science is collective like our technics. Specialisation. We inherit not only results but methods which we do not understand. For the matter of that the two are inseparable, for the results of algebra provide methods for the other sciences.
To make an inventory or criticism of our civilisation — what does that mean? To try to expose in precise terms the trap which has made man the slave of his own inventions. How has unconsciousness infiltrated itself into methodical thought and action? To escape by a return to the primitive state is a lazy solution. We have to rediscover the original pact between the spirit and the world in this very civilisation of which we form a part. But it is a task which is beyond our power on account of the shortness of life and the impossibility of collaboration and of succession. That is no reason for not undertaking it. The situation of all of us is comparable to that of Socrates when he was awaiting death in his prison and began to learn to play the lyre….At any rate we shall have lived….
The spirit, overcome by the weight of quantity, has no longer any other criterion than efficiency.
Modern life is given over to immoderation. Immoderation invades everything: actions and thought, public and private life.
The decadence of art is due to it. There is no more balance anywhere. The Catholic movement is to some extent in reaction against this; the Catholic ceremonies, at least, have remained intact. But then they are unrelated to the rest of existence.
Capitalism has brought about the emancipation of collective humanity with respect to nature. But this collective humanity has itself taken on with respect to the individual the oppressive function formerly exercised by nature.
This is true even with material things: fire, water etc. The community has taken possession of all these natural forces.
Question: can this emancipation, won by society, be transferred to the individual?
The text of the original French can be found in
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