What If Infinity Did Not Exist? From Al-Kindi to the Big Bang

More than a thousand years before anyone spoke of expanding galaxies, cosmic microwave background radiation, or the Big Bang, a philosopher living in the ninth-century Islamic world asked a remarkably modern question: Can the universe really be infinite and eternal?

It is, after all, a question many children ask: How can the universe be infinite if everything else we know seems to have a limit?

His name was Al-Kindi, and his answer was unequivocal: no.

In his view, the universe could not be infinite, nor could it have existed forever. It must have had a beginning.

Of course, Al-Kindi did not anticipate the Big Bang in the scientific sense. He had no telescopes, knew nothing of general relativity, and could have known nothing about cosmic expansion. Yet he had identified a problem that, in radically different forms, continues to accompany modern cosmology: What does it actually mean to say that the universe had a beginning?

A Philosopher Between Athens and Baghdad

Al-Kindi was born around the year 800 and lived during one of the most intellectually fertile periods of Islamic civilisation.

Baghdad was then one of the great centres of learning in the world. Works of Greek philosophy and science were being translated, studied, and debated. Aristotle, Plato, Euclid, Ptolemy, and many others thus entered the great philosophical conversation taking place in Arabic.

Al-Kindi was one of the leading figures of this extraordinary period, but he did not simply repeat the Greeks. He was one of the earliest major philosophers of the Islamic tradition and is often remembered as the “Philosopher of the Arabs.”

He sought to use the tools of philosophy to address some of the great questions raised by his own faith as well: God, creation, the soul, time, and the origin of the world.

And it was precisely over the eternity of the universe that he found himself confronting a formidable opponent: Aristotle.

Aristotle and a Universe Without a Beginning

For Aristotle, the world had never had a first day: the cosmos was eternal.

Generations of living beings succeeded one another, the celestial bodies continued their motions, and time did not lead back to some primordial moment in which everything had suddenly begun.

From this perspective, asking for the first instant of the universe would be almost like asking for the first point on a circle.

Al-Kindi rejected this conclusion. To challenge it, he drew not only on theology but also on philosophy and mathematics.

At the heart of the problem was infinity.

Can an Actual Infinity Exist?

Imagine an infinite physical magnitude. Now remove a finite part from it.

If the original magnitude were truly infinite, what remained should still be infinite.

We might write:

∞ − 1 = ∞

Now put back what we removed:

∞ + 1 = ∞

And here lies the problem that concerned Al-Kindi: how can a magnitude to which something has been added remain equal to what it was before?

If the two magnitudes are equal, then adding something appears to have produced no increase at all.

If one is greater than the other, however, we seem to have two infinities of different magnitudes.

For Al-Kindi, consequences of this kind showed that an actually infinite physical body could not exist.

Infinity could be conceived as something that continues indefinitely, but not as a physical quantity already completed in its entirety.

And it is here that the problem of space also becomes a problem of time.

Can There Be an Infinite Past Behind Us?

Imagine that the universe has always existed. There would then have been no first day.

Before today there was yesterday; before yesterday another day; before that another, and so on:

… → past → past → past → today

No matter how far back we go, there will always be an earlier event.

The history of the universe would therefore contain an infinite succession of events that have already occurred.

But Al-Kindi believed that an infinity could not be completed through a succession of finite elements.

Each day adds another element to history.

If we have reached the present, he reasoned, then the sequence of events preceding us cannot constitute an actually completed infinity.

The past must therefore be finite. And if the past is finite, there must have been a beginning.

When Does Time Begin?

Here Al-Kindi’s thought becomes even more intriguing.

We should not necessarily imagine creation as an event that occurred inside some enormous temporal container that was already there, because time itself is bound up with the world and with motion.

If the world has a beginning, then time has a beginning as well.

And this gives rise to a dizzying question:

What was there before the beginning of time?

The question itself may contain a mistake.

To say “before” is already to invoke a temporal relationship. But if time itself has an origin, asking what happened before time existed may be rather like asking what lies north of the North Pole.

Not because we necessarily know the answer, but because we may be applying a category beyond the domain in which it has any meaning.

Modern Cosmology

For many centuries, the idea of an eternal universe remained philosophically powerful.

In the twentieth century, however, the picture changed dramatically.

General relativity showed that space and time were not merely an immutable stage upon which cosmic events unfolded. The geometry of the universe itself could evolve. Astronomical observations then revealed that the universe is expanding.

If we conceptually trace this expansion backwards, we arrive at an extremely hot and dense primordial state.

This is what, with some simplification, we call the Big Bang.

Modern cosmological observations indicate that the universe is approximately 13.8 billion years old.

At first glance, this might seem like an extraordinary vindication of Al-Kindi over Aristotle.

The universe would not be eternal: its known cosmic history can be traced back to an extraordinarily remote primordial state.

But the matter is more complicated.

Al-Kindi Did Not Discover the Big Bang

It would be fascinating to claim that a ninth-century philosopher had predicted a twentieth-century scientific theory.

It would also be historically wrong.

The Big Bang theory did not arise from a philosophical demonstration of the impossibility of infinity. It emerged from physics, general relativity, and astronomical observation.

Moreover, the Big Bang model does not automatically answer the metaphysical question of creation.

Describing the universe in its earliest stages is not the same as explaining why there is something rather than nothing.

Even the word “beginning” requires caution.

Modern physics can describe the primordial universe back to extraordinarily early epochs, but as we approach the earliest conditions, our theories become incomplete. A satisfactory theory of quantum gravity may profoundly alter what we mean by cosmic origins.

The Big Bang, therefore, should not simply be imagined as a bomb exploding into nothingness.

It describes the evolution of the universe from primordial conditions radically different from those we observe today.

A Young Universe Can Still Be Infinite

There is another apparent paradox that Al-Kindi would probably have found fascinating.

A universe can have a finite age and yet be spatially infinite.

These are two different questions. We can ask:

How long has the universe existed?

And we can ask:

How large is the entire universe?

They are not the same question.

We can observe only a finite region of the cosmos because light has had only a finite amount of time to reach us. This region is known as the observable universe.

But we do not know with certainty what lies beyond our cosmic horizon.

Space as a whole may be finite, or it may extend indefinitely.

The fact that the observable universe is finite does not prove that the universe as a whole is finite.

And so infinity, driven out through the door by Al-Kindi, returns through the window of cosmology.

Cantor Changes the Rules of Infinity

There is also something Al-Kindi could not have known: many centuries later, mathematics would develop a far more sophisticated understanding of infinity.

Consider the natural numbers:

1, 2, 3, 4, 5, 6…

Now consider only the even numbers:

2, 4, 6, 8, 10, 12…

The second set appears to be smaller than the first.

And yet every natural number can be paired with an even number:

1 ↔ 2

2 ↔ 4

3 ↔ 6

4 ↔ 8

and so on without end.

Modern mathematics therefore teaches us that some properties of infinity that seem absurd to ordinary intuition are perfectly coherent.

In this respect, some of Al-Kindi’s arguments against infinity can no longer be accepted in the form in which he presented them.

But one fundamental distinction remains.

It is one thing to ask whether infinity is mathematically possible; it is another to ask whether anything physically infinite actually exists.

Mathematics can describe infinite structures without contradiction. But that does not prove that the physical universe itself is infinite.

What Remains?

It is precisely here that Al-Kindi becomes particularly interesting to us.

Not because he predicted the Big Bang, nor because modern cosmology has proved his theology, but because he understood that when we think about the origin of the universe, we very quickly reach the limits of our everyday intuitions.

And the questions return: What does a “first moment” mean? Can the past be infinite? Can an infinite amount of space physically exist? Why does the universe exist at all?

Al-Kindi sought the ultimate answer in God.

For him, a universe that does not contain within itself the reason for its own existence points towards a first cause, eternal and uncaused: the One.

Modern cosmology, as a science, cannot simply confirm or deny this metaphysical conclusion. It can reconstruct cosmic history, formulate models, and compare them with observation.

The question of the ultimate ground of existence also belongs to philosophy. For this reason, philosophy and religion need not necessarily be regarded as competitors. They can be understood as two paths arising from the same human need to understand reality and its ultimate principle.

In the case of the Qur’an, this convergence takes on a particular significance. Philosophy seeks truth through reason, argument, and demonstration; revelation communicates it through a different language, one that also makes use of images, narratives, symbols, and precepts, and can therefore address a far wider audience than philosophy alone.

The point, then, is not to oppose a philosophy intended for an intellectual elite to a religion intended for the “foolish.” It is rather to recognise different languages addressed to different capacities and sensibilities.

From this perspective, at least within a philosophical reading of the Qur’an, reason and revelation can point towards the same fundamental truth. What changes is the language through which that truth is expressed, not necessarily the reality towards which it leads.

The message, ultimately, is one; what differs are the paths through which human beings seek to understand it.

And it is here that, more than a thousand years later, Al-Kindi can still take a seat, metaphorically, at our table.

He had no telescopes. He knew nothing of galaxies or Einstein, and of course he had not discovered the Big Bang. Yet he understood that behind an apparently simple word — infinity — lies one of the most difficult questions the human mind can formulate.

The most fascinating question, then, is not whether Al-Kindi anticipated the Big Bang.

It is whether, after more than a thousand years of philosophy, mathematics, and cosmology, we have finally managed to answer the question that troubled him:

Does infinity exist only in our minds, or does it truly exist in the universe?

Perhaps infinity does not belong to the universe at all, but to the mind that contemplates it.

We live immersed in a reality that appears finite: everything has a form, a boundary, a duration. And yet, within this finitude, there exists a mind capable of performing an extraordinary act: it can conceptually transcend every boundary. We can imagine a number and always add one more; we can conceive of a boundary and immediately ask what lies beyond it. Whenever reality seems to close in upon itself, thought can open it again.

Perhaps infinity arises precisely within this gap between what exists and what we are capable of thinking.

If that is so, we would not need a materially infinite universe to account for the idea of infinity. Infinity might instead be a possibility inherent in consciousness: not something we encounter in the world as we encounter a mountain or a star, but a horizon that recedes every time we attempt to reach it.

Yet an even more radical question remains: How can something finite contain the thought of that which has no limit?

It is here that Al-Kindi’s One returns.

If the human mind were not an isolated reality, but rather the finite expression of an order that precedes it and makes it possible, then our ability to conceive of infinity might take on a different meaning. The brain would remain finite, biological, subject to time and matter; yet what becomes thinkable through it would seem continually to exceed those limits.

This does not necessarily mean that something infinite is literally “contained” within our brains. Perhaps it means something subtler: the finite can be open to what transcends it without having to contain it.

From this perspective, the One would not simply be a being located somewhere beyond the universe, but the principle through which multiplicity, limitation, and even thought itself can exist. The infinity we conceive might then be not a measure of space, but the intellectual sign of this openness towards the ultimate principle.

Perhaps we have been looking for infinity in the wrong place.

We have searched for it beyond the galaxies, asking whether space continues forever. But perhaps its deepest mystery lies much closer to us: a finite being, within a perhaps finite universe, possesses a mind capable of conceiving that which never ends.

And then the question would no longer simply be: Is the universe infinite?

It would become something even more difficult:

Why is the finite capable of thinking the infinite?