Philosophy · Contested
The Actual Infinite in the Kalam Argument
The kalam argument claims a beginningless chain of past events is impossible because an actual infinite cannot exist, a premise widely disputed by mathematicians and philosophers.
The evidence explained
Medieval thinkers such as al-Ghazali and Bonaventure argued against an infinite past; William Lane Craig revived the case, using illustrations like Hilbert's Hotel to suggest absurdities in an actual infinite collection.
Critics reply that Hilbert's Hotel is counterintuitive but consistent, and that Cantorian set theory treats actual infinites coherently. Alex Malpass and Wes Morriston argue that the argument conflates mathematical possibility with physical instantiation, and that the past may be infinite without having traversed an infinite series from a start.
Defenders respond that the issue is not mathematics but the real existence of an infinite collection of concrete events. Whatever the verdict, the dispute shows that the kalam's first premise about a beginning needs more than set theory to be settled.
What it does show
- • The kalam's strength depends on a contested metaphysical premise.
- • The debate engages real mathematics and philosophy.
- • Both sides have articulate scholarly defenders.
What it does not show
- • It does not show that the universe began.
- • It does not prove God exists.
- • It does not decide the A-theory versus B-theory of time question on which it depends.
Primary sources and literature
- William Lane Craig, The Kalam Cosmological Argument (1979)Classic defense.
- Wes Morriston, 'Must the Past Have a Beginning?' (various papers)Critical reply.
- Alex Malpass and Wes Morriston, 'Endless and Infinite', Philosophical Quarterly (2020)Recent analysis.
Where scholars disagree
Philosophers divide over whether actual infinites can exist in reality, and whether traversal arguments hold.
For further study
Primary and secondary sources on both sides of this question. Reading the strongest opposing case is part of the work, not a concession.
The Blackwell Companion to Natural Theology — William Lane Craig and J. P. Moreland (eds.)
The reference volume: long, technical chapters defending each major theistic argument, with the best statements of the cosmological, fine-tuning, moral, and ontological arguments.
Five Proofs of the Existence of God — Edward Feser
Classical (Aristotelian, Neo-Platonic, Thomistic) arguments defended in analytic form, with sustained attention to what the conclusions do and do not establish.
The Miracle of Theism — J. L. Mackie
The best twentieth-century atheist engagement with the theistic arguments; read it to see which objections actually bite.
Arguing About Gods — Graham Oppy
A rigorous skeptical assessment arguing that no theistic argument succeeds as a proof; the standard opposing benchmark.
The Existence of God — Richard Swinburne
Builds a cumulative probabilistic case rather than a single deductive proof — useful for seeing how arguments combine.