←IndexThe Reconstruction of Religious Thought in Islam

Lecture 2: The Philosophical Test of the Revelations of Religious Experience

Section 3 of 10

Space, Movement, and Zeno

Section summary

In brief

Working through Zeno's paradoxes and the modern responses of Russell and Cantor, Iqbal lands on a master distinction: movement-as-observed versus movement-as-lived. Mathematical descriptions of motion are valid but not exhaustive — the act of movement, like the self, is indivisible, and 'in partition lies its destruction.'

Section 2 closed on an unanswered question: is space an independent void in which things are situated, or is it constituted by the relations between events? Section 3 takes up that question by reaching back to its oldest and most rigorous formulation — the paradoxes of Zeno of Elea. This is not a detour into ancient philosophy. Zeno's arguments were weapons designed to defend his teacher Parmenides' thesis that Reality is one, unchanging, and indivisible, and that all apparent motion is illusion. The Eleatic denial of change is therefore the deepest philosophical opponent of everything the Reconstruction wants to affirm: a metaphysics of creative becoming, dynamic selfhood, and purposive change. Before Iqbal can build his theology of the Ultimate Ego, he must show that movement is real — and the section is a staged contest in which four responses to Zeno are tested in turn until Iqbal reaches the one he can accept.

The section advances through four connected moves. First, Iqbal considers the Ash'arite response: deny infinite divisibility, treat space and time as composed of discrete atoms (jawāhir) and instants that God re-creates at every moment, and the paradox dissolves because the arrow traverses a finite number of positions. The solution is logically coherent on its own terms, but Iqbal is wary of its theological cost — Ash'arite occasionalism, by denying that created things have any genuine causal power, ultimately denies that they have any genuine agency, and the denial of creaturely agency is the denial of khudī. Second, he closes off this escape route by citing Ibn Ḥazm — the eleventh-century Andalusian polymath who rejected the Ash'arite doctrine of infinitesimals on logical grounds and was vindicated, nearly a millennium later, by Weierstrass, Dedekind, and Cantor. Third, he turns to the most sophisticated modern defence of motion's reality: Bertrand Russell's deployment of Cantor's theory of mathematical continuity. On this view, between any two points there is always another, no two points are 'next' to each other, and motion just is the one-to-one correspondence between the infinite series of positions and the infinite series of instants. The paradox dissolves because Zeno assumed discreteness where there is in fact dense continuity. Fourth, Iqbal delivers his own verdict: Russell's mathematics is not wrong, but it answers the wrong question. The mathematical description of continuity applies to movement as 'viewed from the outside' — to the trajectory plotted on a graph, the flight reconstructed in retrospect — but not to movement as an act. The act of movement, lived rather than described, does not admit of any divisibility. 'The flight of the arrow observed as a passage in space is divisible, but its flight regarded as an act, apart from its realization in space, is one and incapable of partition into a multiplicity. In partition lies its destruction.'

This is the master distinction of the section, and one of the most important in the entire Reconstruction: movement-as-observed versus movement-as-lived, the picture versus the act, the map versus the territory. Iqbal is not making an anti-scientific argument. He does not reject Cantor's mathematics or Russell's logic; he rejects the philosophical claim that mathematical description exhausts what is described. The flight of the arrow has a mathematical structure, but it also has a character as a living act, and that character is annihilated the moment one translates it entirely into spatial terms. The theological stakes of this distinction are immense. If the reality of movement lies in the indivisible act rather than the divisible trajectory, then reality itself is closer to agency than to geometry. The universe is fundamentally more like a deed than like a diagram. And a universe of deeds requires a Doer. The principle 'in partition lies its destruction' applies far beyond the arrow: it applies to the self, which can be described from outside as a sequence of brain events but is, as lived, indivisible; and it applies to acts of insight and judgement, which can be reconstructed afterwards as a series of logical steps but are, as performed, leaps. Iqbal's resonance here is partly Bergsonian, but it is also deeply Islamic — Ghazālī's Tahāfut made a structurally similar charge against the philosophers, and the Sufi tradition from Rūmī to Ibn 'Arabī insisted that the deepest realities are accessed through an immediate taste (dhawq) that analysis cannot replicate. The crucial difference is that Iqbal does not conclude from this that analysis should be abandoned; he concludes that it must be supplemented by a mode of knowing that grasps reality as a living whole.

For the Tadreej project, this section delivers two lessons of foundational importance. The first concerns intellectual posture. Iqbal's citation of Ibn Ḥazm against the Ash'arite mainstream is a model of exactly what Tadreej means by ijtihād: a deeply committed Muslim who refused to defer to the dominant theological school, reasoned independently from logical premises, and reached a conclusion that contradicted the prevailing Muslim position — and happened to be confirmed by centuries of subsequent mathematical development. Independent reasoning is not a Western import. It is an Islamic inheritance that Muslims have been practising — and periodically abandoning — for a thousand years. The second concerns the refusal to mistake descriptions of life for life itself. Pakistan's technocratic discourse routinely treats measurable proxies as exhaustive accounts of the realities they map: GDP growth as a proxy for national wellbeing, exam scores as a proxy for education, citation counts as a proxy for intellectual contribution. These measurements are not wrong — they capture something real — but they are pictures of movement viewed from the outside, and no amount of data points, however precisely mapped, can substitute for the act they describe. Tadreej's Seven Capacities framework is an attempt to cultivate the act, not merely to chart its external markers: epistemic confidence, for example, is not measured by the count of correct answers a person produces but by the quality of reasoning as a living performance — the capacity to think under uncertainty, to hold positions provisionally, to revise without collapse. This is movement-as-act, not movement-as-trajectory, and the entire educational vision rests on the distinction this section first articulates.

Original text

The ancient Greek philosopher Zeno approached the problem of space through the question of movement in space. His arguments for the unreality of movement are well known to the students of philosophy, and ever since his days the problem has persisted in the history of thought and received the keenest attention from successive generations of thinkers.

Two of these arguments may be noted here.⁹ Zeno, who took space to be infinitely divisible, argued that movement in space is impossible. Before the moving body can reach the point of its destination it must pass through half the space intervening between the point of start and the point of destination; and before it can pass through that half it must travel through the half of the half, and so on to infinity. We cannot move from one point of space to another without passing through an infinite number of points in the intervening space. But it is impossible to pass through an infinity of points in a finite time. He further argued that the flying arrow does not move, because at any time during the course of its flight it is at rest in some point of space.

Thus Zeno held that movement is only a deceptive appearance and that Reality is one and immutable. The unreality of movement means the unreality of an independent space.

Muslim thinkers of the school of al-Ash'arí did not believe in the infinite divisibility of space and time. With them space, time, and motion are made up of points and instants which cannot be further subdivided. Thus they proved the possibility of movement on the assumption that infinitesimals do exist; for if there is a limit to the divisibility of space and time, movement from one point of space to another point is possible in a finite time.¹⁰

Ibn \u1e24azm, however, rejected the Ash'arite notion of infinitesimals,¹¹ and modern mathematics has confirmed his view. The Ash'arite argument, therefore, cannot logically resolve the paradox of Zeno.

Of modern thinkers the French philosopher Bergson and the British mathematician Bertrand Russell have tried to refute Zeno's arguments from their respective standpoints. To Bergson movement, as true change, is the fundamental Reality. The paradox of Zeno is due to a wrong apprehension of space and time which are regarded by Bergson only as intellectual views of movement. It is not possible to develop here the argument of Bergson without a fuller treatment of the metaphysical concept of life on which the whole argument is based.¹²

Bertrand Russell's argument proceeds on Cantor's theory of mathematical continuity¹³ which he looks upon as one of the most important discoveries of modern mathematics.¹⁴

Zeno's argument is obviously based on the assumption that space and time consist of infinite number of points and instants. On this assumption it is easy to argue that since between two points the moving body will be out of place, motion is impossible, for there is no place for it to take place. Cantor's discovery shows that space and time are continuous. Between any two points in space there is an infinite number of points, and in an infinite series no two points are next to each other. The infinite divisibility of space and time means the compactness of the points in the series; it does not mean that points are mutually isolated in the sense of having a gap between one another.

Russell's answer to Zeno, then, is as follows:

‘Zeno asks how can you go from one position at one moment to the next position at the next moment without in the transition being at no position at no moment? The answer is that there is no next position to any position, no next moment to any moment because between any two there is always another. If there were infinitesimals movement would be impossible, but there are none. Zeno therefore is right in saying that the arrow is at rest at every moment of its flight, wrong in inferring that therefore it does not move, for there is a one-one correspondence in a movement between the infinite series of positions and the infinite series of instants. According to this doctrine, then it is possible to affirm the reality of space, time, and movement, and yet avoid the paradox in Zeno's arguments.’ ¹⁵

Thus Bertrand Russell proves the reality of movement on the basis of Cantor's theory of continuity. The reality of movement means the independent reality of space and the objectivity of Nature. But the identity of continuity and the infinite divisibility of space is no solution of the difficulty. Assuming that there is a one-one correspondence between the infinite multiplicity of instants in a finite interval of time and an infinite multiplicity of points in a finite portion of space, the difficulty arising from the divisibility remains the same. The mathematical conception of continuity as infinite series applies not to movement regarded as an act, but rather to the picture of movement as viewed from the outside.

The act of movement, i.e. movement as lived and not as thought, does not admit of any divisibility. The flight of the arrow observed as a passage in space is divisible, but its flight regarded as an act, apart from its realization in space, is one and incapable of partition into a multiplicity. In partition lies its destruction.

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2. The Nature of Matter

4. Einstein, Relativity, and Time

Original text

Thus Zeno held that movement is only a deceptive appearance and that Reality is one and immutable. The unreality of movement means the unreality of an independent space.

Bertrand Russell's argument proceeds on Cantor's theory of mathematical continuity¹³ which he looks upon as one of the most important discoveries of modern mathematics.¹⁴

Russell's answer to Zeno, then, is as follows:

‘Zeno asks how can you go from one position at one moment to the next position at the next moment without in the transition being at no position at no moment? The answer is that there is no next position to any position, no next moment to any moment because between any two there is always another. If there were infinitesimals movement would be impossible, but there are none. Zeno therefore is right in saying that the arrow is at rest at every moment of its flight, wrong in inferring that therefore it does not move, for there is a one-one correspondence in a movement between the infinite series of positions and the infinite series of instants. According to this doctrine, then it is possible to affirm the reality of space, time, and movement, and yet avoid the paradox in Zeno's arguments.’ ¹⁵