Argument from mathematics

Further information: Philosophy of mathematics and Mathematics and God

The argument from mathematics is presented by American philosopher William Lane Craig. In the philosophy of mathematics, the ontological status of mathematical entities, such as numbers, sets, and functions is debated. Within this philosophical context, two primary positions emerge: mathematical realism and mathematical anti-realism. Realists argue that mathematical objects exist independently of human thought as abstract, non-causal entities. In contrast, anti-realists deny the independent existence of these mathematical objects. A pivotal issue in this debate is the phenomenon that physicist Eugene Wigner termed "the unreasonable effectiveness of mathematics." This refers to the ability of mathematics to describe and predict phenomena in the natural world, exemplified by theoretical physicist Peter Higgs' use of mathematical equations to predict the existence of a fundamental particle, which was verified experimentally decades later.

Craig posits that this effectiveness presents a significant philosophical question about the applicability of mathematics, regardless of one's stance on the existence of mathematical entities. He argues that theism provides a more compelling framework for understanding this phenomenon than metaphysical naturalism. Under realism, non-theistic perspectives might view the alignment of mathematical abstractions with physical reality as a mere coincidence. However, a theistic realist might argue that this alignment is intentional, as a Supreme Being created the world based on these abstract mathematical structures. On the other hand, anti-realists, particularly those of a naturalistic persuasion, see mathematical relationships as reflections of real-world interactions, without necessitating abstract entities. Yet, Craig challenges this view by questioning why the physical world inherently exhibits such complex mathematical patterns without an intentional design. In contrast, the theistic anti-realist has a straightforward explanation: the world reflects a complex mathematical structure because it was created by God following an abstract model. Thus, Craig concludes that theism offers a superior explanation for why mathematics applies so effectively to understanding and predicting the physical world.^[113]