Can the existence of God be proven using the logic of mathematics?

Can the existence of God be proven using the logic of mathematics?
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In short: Samuel Clarke, the preeminent English metaphysician of the early 18th century, believed that logical reasoning could mirror mathematical precision. By applying Newtonian physics to theology, he attempted to prove the necessity of an intelligent designer, sparking intense debates that challenged the boundaries of faith, science, and the nature of reality.

Born in 1675, Samuel Clarke was a clergyman and intellectual who sought to bridge the gap between divinity and the emerging scientific rigor of his age. A dedicated disciple of Isaac Newton, Clarke famously translated Newtonian works into Latin, including the Opticks, and used his annotated translation of Jacques Rohault’s physics text to promote Newtonian perspectives over Cartesian ones. His intellectual ambition was to span all fields of knowledge, treating mathematical argument as the supreme form of logical reasoning.

Clarke’s reputation as a philosopher was cemented by his Boyle lectures in 1704 and 1705. In these, he argued that religious belief could be demonstrated with a validity approaching mathematical certainty. He posited that the universe required a self-existent, intelligent designer to both create and maintain it. This physico-theological system suggested that God was not merely a distant creator but a Supreme Governor who continually directed the world, a view he staunchly defended against Gottfried Wilhelm Leibniz. In their famous correspondence of 1715–16, Clarke argued that space and time were attributes of God, rejecting Leibniz's claim that such a view made God part of his own creation.

Despite his influence, Clarke’s career was marked by persistent religious controversy. His 1712 work, The Scripture Doctrine of the Trinity, openly questioned mainstream orthodoxy by arguing that the Son derived his attributes from the Father, a position that led many to accuse him of Arianism. This stance effectively stalled his advancement within the Church. Furthermore, his efforts to prove God’s existence through reason faced criticism from thinkers like David Hume, who remained dissatisfied with Clarke’s logical framework. By the time of his death in 1729, Clarke had established himself as a pivotal, if polarizing, figure whose work defined the intersection of 18th-century theology and natural philosophy.

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