The establishment of the God and Mathematics research group is based on the belief that mathematics is useful for thinking about God. This thinking about God relates primarily to two questions: What is God like? and Are there good reasons to believe that God exists? The answer to the first question takes us into the study of God’s attributes (of God’s nature). The easiest way to answer the second question would be to point out the arguments (proofs) for or against the existence of God. The trouble is that although the arguments for and against the existence of God have been discussed since ancient times, there is no consensus today as to the assessment of their value.

The establishment of the God and Mathematics research group  is based on the belief that mathematics is useful for thinking about God.  This thinking about God relates primarily to two questions: What is God like?  and  Are there  good reasons to believe that God exists?  The answer to the first question takes us into the study of God’s attributes (of God’s nature). The easiest way to answer the second question would be to point out the arguments (proofs) for or against the existence of God. The trouble is that although the arguments for and against the existence of God have been discussed since ancient times, there is no consensus   today as to the assessment of their value. The correctness of the arguments for the existence of God is determined, on the one hand, by the formal criteria, and on the other hand, by the ontological theories encoded in these arguments. Two behaviors seem to be most appropriate:

(i). One should aim at a formal improvement of the arguments for the existence of God   —  functioning in philosophical literature — and revise their ontological assumptions; and/or
(ii). Attempts should be made to construct new arguments for the existence of God that would be formally correct  and with unquestionable ontological assumptions.

Of course,  questions  concerning God’s existence come after questions regarding what would be God’s nature. The problem of how mathematics relates to God is very fascinating. Many  results obtained in logic, foundations of mathematics and metamathematics can and should be used in the research works regarding the attributes and existence of God.  For  example,

• There is a similarity between the role that the ineffability of Absolute Infinity  plays in relation to God and in set theory.
• A concept of God as the being with the  maximal consistent set of knowledge, power and benevolence, etc., is based on the concept of set-theoretical maximality. Set theorists and philosophers of mathematics have formulated a variety of maximality principles. The question is how these relate to the concept of God.
• Omniscience is one of the central divine attributes. Omniscience presupposes the existence of a set of all truths.   According to Patrick Grim, it follows by Cantor’s power set theorem that there can be no set of all truths, hence there can be no omniscient being.  So,  it is important to trace the arguments for or against the existence of such a set.
• The concept of God is bedevilled by a plethora of logical and metaphysical paradoxes. Similarly, truth – which is a central notion in philosophy, mathematical logic and computer science – is inconsistent. In the philosophical-mathematical literature there is a bewildering variety of (purported) solutions to the inconsistency of truth. Utilizing these solutions to avoid the paradoxes produced by the concept of God seems to be a natural endeavor.
• There is an analogy between relationships: God-created beings, on the one hand, and the universe of sets – countable models, on the other hand.
• A. Wronski’s idea is very inspiring:

“Proving the existence of God seems to be similar to proving the non-contradiction of arithmetic. We believe that arithmetic is non-contradictory. Yet, as it constitutes the foundation of our entire knowledge, we would also like to have a convincing proof in addition to the belief. It is known (Godel’s 2nd incompletness theorem) that the proof for the non-contradiction of arithmetic cannot be successful without referring to external means (not formalized in arithmetic). Hence, the non-contradiction of the theory which “is able” to prove the non-contradiction of arithmetic is as problematic as the noncontradiction of arithmetic itself. But for any pre-determined natural number n, the fact that there is no contradiction among arithmetic statements whose formal proofs’ length is ≤ n can be easily proved by means formalized in arithmetic (reflection principle). Is there any theological counterpart of the reflection principle? It may be useful to differentiate between  global and local proofs for the existence of God, show the possibility of local proof, impossibility of global proof, etc. ”

The God and Mathematics research group is open to acquiring new members. Only by collective effort can be achieved great scientific results.

Neil Barton ⁞ University of Konstanz, Germany
neilalexanderbarton@gmail.com

Jc Beall ⁞ University of Connecticut, USA
jcbeall@gmail.com

Simon Hewitt ⁞ University of Leeds, UK
sublimeobject@gmail.com

Jan Heylen ⁞ Centre for Logic and Philosophy of Science, University of Leuven, Belgium
jan.heylen@kuleuven.be

Leon Horsten ⁞ University of Konstanz, Germany
leon.horsten@uni-konstanz.de

Tatiana Levina ⁞ Higher School of Economics in Moscow, Russia
TatianaLevina@hse.ru

Mirosław Szatkowski ⁞ University of Munich, Germany
misza@gmx.de

Claudio Ternullo ⁞ University of Barcelona, Spain
claudio.ternullo@ub.edu
ternoa@hotmail.com