What are al-Ghazālī's arguments against the temporal infinity of the universe, and how did William Lane Craig develop them in contemporary debate?

Al-Ghazālī and William Lane Craig represent two interconnected links in the history of the kalām cosmological argument. Al-Ghazālī in the eleventh century formulated philosophical proofs against the temporal infinity of the universe, and Craig since the 1970s has revived them with contemporary philosophical and mathematical tools. Understanding this development is necessary for evaluating the strength of the kalām argument in contemporary debate.

Inadequate Responses to Avoid

From some defenders of theism:

"Al-Ghazālī definitively proved the impossibility of the temporal eternity of the world." An inaccurate oversimplification. Al-Ghazālī presented strong arguments, but philosophers have debated them for centuries. Ibn Rushd, for example, offered serious responses worthy of study. Claiming the matter is settled ignores the complexity of philosophical debate.

"Craig is merely a translator of al-Ghazālī." An unfair reduction. Craig built upon al-Ghazālī but added substantial developments: he used Cantorian set theory, developed the concept of "actual versus potential infinite," and dealt with contemporary objections that al-Ghazālī did not face.

"Mathematical proofs settle the matter." A confusion between mathematics and metaphysics. The infinite in mathematics has its rules, but its application to physical reality is a separate philosophical matter. Cantor himself distinguished between mathematical and metaphysical infinity.

From some naturalists:

"Al-Ghazālī was merely a theologian who rejected science." A historical distortion. Al-Ghazālī was a philosopher trained in Aristotelian logic and Islamic philosophy, and his arguments against infinity are purely philosophical, not theological. His rejection of some philosophers' views was not a rejection of reason but its application.

"Modern physics has proven the possibility of an eternal universe." A hasty claim. Cyclic or multiverse models face physical and philosophical problems. The Borde-Guth-Vilenkin (BGV) theorem indicates that even inflationary universes need a beginning. Scientific debate is open, not settled.

Why These Responses Are Inadequate

They share in oversimplifying a complex, multi-layered debate. Arguments against temporal infinity are not merely religious or scientific conclusions, but precise philosophical analyses requiring methodical evaluation.

Al-Ghazālī's Basic Arguments

In "Tahāfut al-Falāsifa," al-Ghazālī developed several proofs against the eternity of the world:

First Proof: The Impossibility of the Actual Infinite
Al-Ghazālī distinguishes between the potential infinite (what can continue without end) and the actual infinite (what has actually been realized without end). He argues that an infinite series of past events would mean an actual infinite, and this is impossible.

His example: If the universe were eternal, the number of lunar cycles around Earth would be infinite, and the number of Earth's cycles around the sun would also be infinite. But lunar cycles are more than Earth's cycles (approximately 12 times more). How can one infinite be greater than another infinite? This is a contradiction.

Second Proof: The Impossibility of Traversing the Infinite
If the past were infinite, we would never reach the present moment. Because reaching any point requires traversing what comes before it, and traversing an infinite series is impossible. Like someone wanting to reach zero by counting down from negative infinity—they would never arrive.

Third Proof: Application and Analogy
If an infinite series could exist in the past, it could exist in any context. But we see the impossibility of this in concrete examples. For instance, a library with an infinite number of books: if we removed every second book from it, an infinite number would remain. If we removed all books except three, three would remain. The same operation (removal) gives contradictory results.

Craig's Development of al-Ghazālī's Arguments

William Lane Craig, the contemporary American philosopher, began in the 1970s a project to revive the kalām argument with modern tools:

First Development: Rigorous Logical Formulation
Craig formulated the kalām argument in the form of a logical syllogism:
1. Whatever begins to exist has a cause
2. The universe began to exist
3. Therefore, the universe has a cause

He then focused on proving the second premise with developed arguments from al-Ghazālī.

Second Development: Using Set Theory
Craig benefited from developments in Cantorian mathematics. For example, in Hilbert's infinite hotel: a hotel with infinite rooms, all occupied. A new guest arrives, so every guest moves to the next room, and the new guest stays in the first room. The full hotel accommodates a new guest without removing anyone! This shows the contradictions of the actual infinite in reality.

Third Development: Responding to Contemporary Objections

The Cantorian objection: "Mathematical infinity is consistent, so why wouldn't physical infinity be so?"
Craig's response: Mathematical consistency does not mean metaphysical possibility. Mathematics deals with abstractions, but physical reality has additional constraints. For example, imaginary numbers are mathematically consistent, but there is no "imaginary meter" in reality.

The relativity objection: "Time in relativity is not absolute, so how can we speak of an absolute beginning?"
Craig's response: Even in relativity, "cosmic time" can be defined based on the expansion of the universe. More importantly, even if time is relative, the question remains: is the causal series infinite?

Fourth Development: Support from Modern Cosmology
Craig cites:
- Big Bang theory: indicates a beginning for spacetime
- The second law of thermodynamics: if the universe were eternal, it would have reached heat death
- BGV theory (2003): even inflationary or cyclic universes need a beginning

Contemporary Criticism and Craig's Responses

Graham Oppy's criticism: "The distinction between potential and actual infinite is artificial."
Craig responds that the distinction is fundamental since Aristotle and has clear applications. The future can be potentially infinite (continuing without end), but if the past were infinite, it would be actually so (fully realized).

Quentin Smith's criticism: "One can conceive of traversing the infinite if it has no starting point."
Craig responds that this assumes what it wants to prove. The question is not "can we conceive of a series without a beginning?" but "can it actually exist?" His arguments aim to prove metaphysical impossibility.

Contemporary Assessment (2018-2026)

The academic position is divided but with important developments:

Contemporary supporters: Alexander Pruss, Robert Koons, Joshua Rasmussen—they develop new formulations that respond to criticism.

Contemporary critics: Graham Oppy, Paul Draper, Walter Sinnott-Armstrong—they argue that arguments against infinity are not decisive.

Middle position: Philosophers like Timothy O'Connor see the arguments as favoring a beginning without definitive proof.

Where We Stand Today

The al-Ghazālī-Craig arguments against temporal infinity remain among the strongest arguments in contemporary philosophy of religion. They have not been refuted, but they are not unanimously accepted. The development from al-Ghazālī to Craig shows how classical philosophical arguments can be renewed with contemporary tools. The result aligns with the method of "rational probabilism" (rajḥān ʿaqlī): the arguments make the existence of a beginning for the universe more probable, without claiming absolute certainty.

For Advanced Reading

- Advanced level: Maudlin's critique of the kalām argument from the perspective of philosophy of physics
- Advanced level: Rasmussen-Pruss's new formulation of the argument from contingency
- Al-Ghazālī, Tahāfut al-Falāsifa (First Discussion)
- William Lane Craig, The Kalām Cosmological Argument (Macmillan, 1979)
- Graham Oppy, "Cosmological Arguments" (Noûs, 2009)
- Paul Copan & William Lane Craig, eds., The Kalām Cosmological Argument: Philosophical Arguments (Bloomsbury, 2018)
- "Formulation: Kalam Argument" page on the website