As her brother André was working on developing new foundations for algebraic geometry – in prison, even – Simone Weil expressed to him her philosophical excitement for Eudoxus’ solution to the problem of incommensurables because in that problem Weil found that its “essential point” for thinking was “outside geometry”. Eudoxus took the first step up Cantor’s ladder; Weil recognized the move as dialectical: by finding a way to express relations between incommensurate quantities, the real numbers include both the naturals and the incommensurates, preserving the incommensurability while also transcending the impasse of incommensurability. This discovery was “beautiful” in a precise sense for Weil:
Beauty is the manifest appearance of reality. Reality represents essentially contradiction. For reality is the obstacle, and the obstacle for a thinking being is contradiction. The beauty in mathematics lies in contradiction. Incommensurability, logoi alogoi, was the first radiance of beauty manifested in mathematics.
Although Weil seems not to have been aware of Cantor’s discoveries, like Cantor’s ladder, Weil recognized that this solution to the problem of incommensurability could not guarantee a highest unity because no matter how high we may climb, “we are denied access to the level at which [the contraries] are linked together. … Once arrived there, we can climb no further; we have only to look up, wait and love. And God descends”.
Weil’s God is necessarily a Trinitarian God, whose mystery is the ultimate incommensurability. The (Pythagorean) harmony of unity and plurality, viewed simultaneously from opposite sides,* is expressed neither in thought nor being but in love or friendship. Here theology yields to religion in the literal sense: in love we are bound to the task of producing the good and the right.
*Weil specifically uses the analogy of triangulation to describe grasping the mystery of the Trinity.
Against the more familiar ontotheologies of which philosophy is still suspicious, the Catholic mystical tradition searches not only beyond being but what lies between thought and being (always seeking the mediation, as Weil says). The metaxu is given neither in logic nor ontology, however, but in love, which is prior to the true and the good. We find God in ourselves not as an idea stamped on our minds but in our love. “The soul is united to God through love’s affection”, says Catherine of Siena, because in love the “soul becomes another [Christ]”. This love is directed neither toward ourselves nor toward God but, rather, is born from the infinite sorrow for the salvation of souls. Universality is within us through the soul’s imperfection: if our imperfection is the cause of evil, then my contrition must be for the suffering that I have caused. Conscience, not consciousness, is the indubitable fact of the mind, which is the ultimate truth of the inward journey. “In this life guilt is not atoned for by any suffering simply as suffering, but rather by suffering borne with desire, love, and contrition of the heart. … You asked for suffering, and you asked me to punish you for the sins of others. What you were not aware of was that you were, in effect, asking for love and light and knowledge of the truth.” The mind cannot resist a true idea, Spinoza says, but the truth of the mind itself is its love.
This blood [of Christ] gives you knowledge of the truth when knowledge of yourself leads you to shed the cloud of selfish love. There is no other way to know the truth. In so knowing me the soul catches fire with unspeakable love, which in turns brings continual pain. Indeed, because she has known my truth as well as her own sin and her neighbors’ ingratitude and blindness, the soul suffers intolerably.
True contrition, then, is not merely to atone for what is one’s own but the will to accept what is not. As Augustine reminds us, however, it is not by the strength of our will that we escape suffering but, as Catherine says, “by virtue of your infinite desire. For God, who is infinite, would have infinite love and infinite sorrow”.
Like the friendship between the persons of the trinity, love expresses the unity of the human and the divine in imitatio Christi. In the Itinerarium, Bonaventure describes the triplicity of being as corporeal, spiritual, and divine. The transport and unification of the mind with God is not only the understanding of the identity of being and the good in divine perfection but
this is a good of such a sort that it cannot be thought of unless it is thought of as three and one. For ‘the good is said to be self-diffusive’ [quoting Dionysius]. … In the supreme good there must be from eternity a production that is actual and consubstantial, and a hypostasis as noble as the producer, and this is the case in production by way of generation and spiration. This is understood to mean that what is of the eternal principle is of the eternal co-producer. In this way there can be both a beloved and a co-beloved, one generated and one spirated; that is, Father and Son, and Holy Spirit.
The mystery of the trinity is therefore not one of metaphysics but of love (charity) and thinking refuses ontotheology only to the extent to which it finds the identity of being and the good only in its suffering. Suffering cannot be controlled, as Heidegger warned, but perhaps it can be redeemed.