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Why Infinity is Not God: A Gödelian Response to Mathematical Reductionism

Author:

Al Khawaja, Sameer

Category:

Essays

Sub-Category:

Philosophy

Language:

English

Date Published:

July 6, 2026

File:

/Essays-Philosophy/Download/10593

Downloads:

Keywords:

actual infinity, mathematical reduction, Godel theorem, measurability, finitism, metaphysics

Abstract:

Gregory Barber's 2026 Quanta Magazine profile of Doron Zeilberger reports the mathematician's view that belief in mathematical infinity is analogous to belief in God: neither can be observed or finitely verified, and so neither belongs in serious mathematics. This paper argues that the analogy rests on a category mistake. Infinity is a formal concept internal to mathematical systems, while God is a metaphysical and theological reality (if God exists at all); the criteria appropriate to one domain cannot be transferred wholesale to the other. Drawing on Gödel's 1931 incompleteness theorem, the paper shows that any sufficiently powerful, consistent formal system capable of expressing arithmetic contains truths it cannot prove from its own axioms, and cannot establish its own consistency from within. This result does not settle debates over finitism or the ontological status of infinity, nor does it prove the existence of God. But it does demonstrate that mathematics cannot fully justify or exhaust itself by its own formal resources, and therefore cannot function as the ultimate arbiter of what is real or meaningful. On this basis, the paper concludes that a mathematician's rejection of actual infinity within a chosen formal system, however defensible as a position in the philosophy of mathematics, provides no warrant for dismissing questions about God.