Divine Mathematics and the Infinite Whole

Hitoshi Ochiai is one of those rare mathematicians who have gone beyond computational mathematics to investigate the highest discipline of the field: divine mathematics. He is a professor of mathematical theology at Doshisha University, Kyoto and has published extensively.

You may order English translations of his most recent books, Cantor: Archetype of Theological Mathematics and Those Learning Mathematical Theology, by e-mailing him at hochiai@mail.doshisha.ac.jp

On July 10, 2014, Ochiai graciously talked with me in his university office.

Ion Soteropoulos. I would like to discuss with you a central idea of divine mathematics the infinite whole, or the whole of infinite space, which the mathematicians call “the infinite set”. In the “Theology of Georg Cantor” one of your excellent articles, you clearly and effectively explain why the infinite whole is rejected by Aristotelian mathematicians (because of its self-contradictory nature) but has been adopted by theologians (who consider it as the immanent nature of the Supreme Being). According to Thomas Aquinas, the divine being is not only infinite but also perfectly infinite actualized and completed in reality precisely because of its limiting boundary. But how can the unlimited have a limit?

This radical violation of the analytic principle of contradiction (to Aristotle the most certain of all principles) led Cantor to intuit the existence of the infinite whole instead of proving it analytically. This is indeed the correct approach, for a fundamental entity such as the infinite whole is by definition beyond analytic proof and therefore self-referential.

What strikes me is that on the one hand Thomas Aquinas is an Aristotelian; on the other hand, by assigning a limiting boundary to the infinite, he becomes a Pythagorean or a Platonist. Do you think that Thomas Aquinas was conscious of his platonic idea about the infinite with a limit?

Hitoshi Ochiai. Thomas Aquinas at that time had no access to platonic philosophy. He had never read Philibus. He was inspired by the Bible.

I.S. Where does the Bible mention that the perfect infinite, which is a quality of God must have a limiting boundary and therefore be actualized?

Hitoshi Ochiai. Thomas Aquinas read The Fountain of Knowledge of John of Damascus and in Expositio Fidei; De Fide Orthodoxa, John attributed God with perfect infinity, which he defined as infinity with a limiting boundary that allows infinity to be actualized.

I.S.What do you mean by “actualized”?

Hitoshi Ochiai. “Actualized” is having a boundary.

I.S. Does anything with a boundary have a place?

Hitoshi Ochiai. No, it does not, because the boundary has an infinity of points. A boundary without a place is an actualization without a place, which means that actualization is everywhere and nowhere.

I.S. You say that the infinite actualized has no place. But stoic philosophy stipulates that anything that exists has a place and that the non-existent has no place. This means that the infinite actualized everywhere has no existence. Do you agree?

Hitoshi Ochiai. Yes I agree, the infinite actualized has no existence, but it has reality this is an important distinction.

I.S What is reality?

Hitoshi Ochiai. Reality is a mathematical object; we can call it mathematical reality. It has no corporeal existence. It is a pure idea, a pure spirit.

I.S. What is the relationship between mathematical reality and corporeal existence?

Hitoshi Ochiai. There is no relationship. There is an absolute separation between spirit and corporeal existence. I am a Cartesian.

I.S.How do you accommodate your Cartesian theory about the absolute separation between the infinite whole and corporeal existence, with your belief in the incarnation of God as an infinite whole in the person of Jesus Christ?

Hitoshi Ochiai. Yes God is spirit and Jesus Christ is God incarnate.

I.S. But Christ had a physical existence in a place in a certain time.

Hitoshi Ochiai. This is not important.

I.S. So what is important for you?

Hitoshi Ochiai. Spiritual or mathematical reality reality which has no physical existence.