I have just finished reading Chris Ransford’s well-thought and well-written book God and the Mathematics of Infinity, a research concerning the most passionate and radical subject of our intellect, which is the mathematics of the Divine Infinite Being. The reading took place during my one-week holidays at the beautiful Greek island of Simi after breakfast in front of the sublime blue sea, mixed with solar fire, grey stones and pure air stimulating my spirit’s breath.

The author perfectly exposes the existential problem of Divinity. According to Ransford, it is impossible to decide whether the Divine Being exists or does not exist because by means of our infinite mind or reason we can assume and prove both alternatives or neither alternatives. It follows that the Divine Being is undecidable. If from the analytic perspective whatever is undecidable is necessarily non-existent or unobservable, then the Divine Being is an unobservable. This is a negative conception of the Divine Being defended by theistic theology, which links existence and observability with decision grounded in the analytic principle of the excluded third.

However, it is my claim that we must elevate our thought to the highest level of cognition and being and produce a positive conception of Divinity where undecidability is not synonymous to the non-existence or non-observability of the Supreme Being, but the other way around, to Its maximum existence and observability.

If we assume that the Divine Being is a complex indeterminate universe admitting simultaneously opposite determinations without contradiction or paradox, then it is the very immanent nature of the Divine Being qua  universe to be both A and not-A, existence and not- existence at the same time without absurdity.1 In this case, the undecidability of the Divine Being, the impossibility to decide one and only one alternative out of the totality of alternatives and hence the necessity of comprising (or transcending) them all, indicates Its complete and maximum existence and our infinite knowledge of Its maximum existence. Here we have a positive undecidability as the very immanent property of the Divine Being qua all-comprehensive universe.

If the Divine Being is not transcendent to the observable universe as defended by theistic theology, but is equivalent to the observable universe as defended by natural theology, then it is possible for the humans to observe and access the Divinity, as it is possible for the humans to observe and access the physical universe, that is, the universe qua physical whole, if we assume that the physical whole is observable. This means that it is possible for our finite particular senses observing only a finite part of the physical infinite whole, to eventually become infinite universal senses and observe the very physical infinite whole, which is the Divine Being, both physical and observable. We have then the case of the divinization of  humans without losing their humanity and sensibility.

The reading of this rich monograph stimulates within us a series of deep thoughts concerning the antinomies of infinity, the reality or non-reality of the hierarchy of infinities, the immanent properties of the Divine Being, the relation between infinite reason and finite senses, the corruption of all religions once they are institutionalized, the dialectics of the good and evil and how to transcend them and be free and unaffected by their dialectic game, and last but not least the relation of indefinite growth and the idea of a maximum limit, which is the Divine Being qua universe itself. 

I strongly recommend this excellent book that shakes our intellectual certitudes, energizes our imagination and refines our sensibility.


Stuttgart, Germany. ibidem –Verlag, 2017 (ISBN -13: 978-3-8382-1049-0).  

1 Aristotle, the father of analytic logic, is the first to distinguish between the individualand the universe (Metaphysics, I,10). According to Aristotle anything admitting contradictory (non-simultaneous) determinations such as either Aor not-A is an individual, and anything admitting contrary (simultaneous) determinations such as both A and not-A is a universe.

© Apeiron Centre, 2018


H. Chris Ransford

Physicist and mathematician
Karlsruhe Institute of Technology | KIT · Institute of Physical Chemistry


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