Written and collected by Zia H Shah MD

Introduction: Brian Leftow and Robert Lawrence Kuhn

Brian Leftow is a distinguished philosopher of religion known for his work in philosophical theology and metaphysics. Formerly the Nolloth Professor of the Philosophy of the Christian Religion at Oxford University, he now serves at Rutgers University. Leftow’s research delves into the nature of God, divine necessity, and the relationship between God and abstract entities like time, logic, and mathematics reasonablefaith.org. In particular, he has explored how abstract objects (such as numbers, properties, or propositions) might exist relative to an all-powerful Creator.

Robert Lawrence Kuhn, by contrast, is a public intellectual and the creator-host of the PBS television series Closer to Truth. With a PhD in brain science and a passion for life’s “big questions,” Kuhn engages leading thinkers on topics of cosmology, consciousness, theology, and philosophy. He is known for probing experts on deep issues ranging from the origin of the universe to the nature of God. In Kuhn’s interviews, he often raises thought-provoking problems in theology—questions that lie at the intersection of philosophy and faith. It is in one of these dialogues that Kuhn sat down with Brian Leftow to discuss God’s relationship to abstract objects, notably the realm of mathematics.

Mathematics and Abstract Objects: Insights from Brian Leftow (Interview Summary)

In their Closer to Truth interview, Robert Kuhn poses a fundamental question: “If God exists, did God create abstract objects such as mathematical truths and logical laws, or do these exist independently of God?” Mathematics is a prime example of abstract objects – its truths (like 2+2=4 or the properties of a triangle) seem timeless and unchanging. The conversation between Kuhn and Leftow centers on whether such eternal truths exist on their own or are grounded in the mind of God.

Leftow’s Perspective: Brian Leftow responds by first acknowledging the theological puzzle at hand. Classical theism holds that God is the creator of everything apart from Himself, the sole ultimate reality. Yet abstract objects – numbers, sets, propositions, logical principles – appear to exist necessarily and uncaused. If these exist completely independently of God, it would seem to compromise God’s status as the source of all reality. Leftow, a committed theist, finds it “theologically unacceptable” to affirm any uncreated, co-eternal entities alongside God biola.edu biola.edu. Citing the principle of “perfect being” theology, Leftow argues that God, as the greatest conceivable being, must be the self-existent ground of all else that exists biola.edu. Were there autonomous mathematical objects outside God’s creative power, God would no longer be the ultimate source. Indeed, Leftow notes, if mathematical objects existed independently of God, then God would be the source of merely an infinitesimal part of what exists biola.edu. The vast realm of eternal numbers and sets would dwarf the created physical universe in scope, meaning that God’s creative role would be marginal in the total scheme of reality biola.edu. Such a scenario conflicts with the traditional notion of divine aseity (God’s self-sufficiency and independence).

Leftow further observes that if anything exists outside God’s control – say an abstract number that God did not create – it would limit God’s omnipotence. An omnipotent creator should have the power to bring into being or annihilate all contingent things. But a truly independent abstract entity could neither be created nor destroyed by God, putting it beyond His sovereignty biola.edu biola.edu. This contradiction is unacceptable in classical theism. Pushing the logic even further, Leftow highlights a paradox identified by theologians: some of God’s own attributes (like omniscience, omnipotence – the content of “Deity”) would, under Platonism, be abstract properties existing apart from God. If “Deity” itself were an abstract object that God instantiates, then God would depend on something more fundamental than Himself – an impossible conclusion for the God of classical theism biola.edu. Taken to the extreme, pure Platonism about abstracta “undoes” theism by making God just one being among many in a universe of uncreated entities biola.edubiola.edu. Leftow agrees with earlier thinkers that this cannot be right: God, if He exists, must be absolute – the source of all else – or else “God” is not truly God biola.edu.

How, then, does Leftow resolve the tension? The interviewer Kuhn presses: Could these abstract truths perhaps be part of God or rooted in God, rather than free-floating? Here, Leftow leans on a view known as divine conceptualism. In essence, he proposes that abstract objects like mathematical truths are not external things that God finds in the universe; rather, they are contents of the divine mind thequran.love biola.edu. When asked “Did God create mathematics, or is mathematics just there?”, Leftow’s answer is that God did not create eternal truths in time (since mathematical truths are necessary and do not come into being or pass away), but neither do they exist apart from Him. Instead, such truths exist eternally as thoughts in God’s intellect. Leftow echoes a classical idea: “eternal truths require an eternal knower” thequran.love thequran.love. In other words, mathematical propositions (e.g. the law of addition, geometric axioms) are real and eternal not on their own, but because an eternal Mind is thinking them. They are grounded in God’s nature or knowledge rather than floating in a Platonic heaven. This view preserves God’s supremacy (since all truths ultimately depend on God) and simultaneously accounts for the timeless validity of mathematics and logic.

Throughout the interview, Kuhn probes practical examples to clarify Leftow’s stance. For instance, consider the statement that there are infinitely many prime numbers – was this true “before” any minds existed to consider it? Leftow responds by imagining a hypothetical: a universe with no created minds at all. In such a scenario, if even God’s mind did not hold mathematical ideas, could “prime numbers are infinite” have any truth value? Leftow argues no – truth is a property of propositions, and propositions exist as bearers of meaning only in minds thequran.love thequran.love. A statement like “2+2=4” means nothing in a world utterly devoid of intellect; it would not magically hang in space as a true fact with no thinker. “Thoughts require a thinker; an equation requires a mind that understands it,” Leftow explains thequran.love. Thus, rather than accept the baffling idea of truths with no minds, Leftow concludes that all truths – including mathematical ones – must subsist in a supreme Knower. God’s mind is the locus in which these abstract principles live. In Leftow’s own academic formulation, he seeks to “replace abstract…ontology with one of divine mental events and powers”, making God the truthmaker for all such propositions reasonablefaith.org reasonablefaith.org. For example, the laws of logic and mathematics hold because they reflect the structure of God’s rational nature, or His consistent thinking. They are not arbitrary – God cannot make 2+2 equal 5, for instance, because His own perfect intellect eternally knows 2+2=4 – but neither are they independent of Him. In Leftow’s words (as summarized by one commentator), his view is an “anti-Platonist realism” in which mathematical objects are identified with divine thoughts reasonablefaith.org biola.edu.

By the end of the interview, a thematic picture emerges. Leftow has effectively sketched the conceptualist solution: mathematics is part of the fabric of God’s eternal mind, not a rival eternal “realm” outside Him. This solution upholds both the eternity of mathematical truths and the sovereignty of God. As Kuhn notes, this idea harkens back to St. Augustine’s teaching that the Divine Mind contains the forms or eternal ideas (a view Augustine himself advanced to counter Plato’s notion of independent Forms). It also aligns with mainstream Christian theology through history biola.edu. Leftow’s stance resonates with other theologians featured on Closer to Truth – for example, William Lane Craig also affirms that “uncreated mathematical objects do not and cannot exist” apart from God biola.edu. In summary, the interview underscores a key point: while mathematical truths seem timeless and necessary, the Christian theological perspective (as championed by Leftow) is that their eternity is grounded in God’s eternal intellect rather than in a separate metaphysical plane. This preserves the doctrine that God is “the sole ultimate reality” biola.edu, even over abstract objects.

Read further in PDF file: