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2500 years ago, Zeno of Elea destroyed the dualism separating and opposing matter and movement, space and time…

lundi 1er juin 2026, par Robert Paris

2,500 years ago, Zeno of Elea definitively destroyed the dualism that separated and opposed matter and motion, unity and divisibility, space and time, and gave victory to dialectics. At the same time, he demolished other erroneous theses such as the supremacy of mathematical logic over science, positivism, and the philosophy of dichotomy (everything is divided into equal parts).

Zeno’s paradoxes reveal several fundamental errors stemming from common, dualistic, and non-dialectical conceptions, including those of scientists, mathematicians, and philosophers, regarding matter, light, void, energy, and motion, which hinder the understanding of how the world works…

Of Zeno’s forty or so paradoxes, only nine have survived, their author having been killed by the tyrant, yet they continue to be debated today… Forty demonstrations, using reductio ad absurdum, that the world is contradictory in the dialectical sense. And what is most extraordinary is that scientists are mostly determined to demonstrate that there is no contradiction and that the paradox is resolved. Two opposing methods lead to the same result : mathematicians assert that mathematical continuity (with infinitesimals and the convergence of numerical series) has solved the problem, and physicists assert that physical discontinuity (with the absolute rejection of infinities, the so-called Planck minimum quantities, and quanta) has also solved the problem ! Unfortunately for them, Zeno actually demonstrated forty times that the world is inevitably contradictory and that the contradiction is internal, that it is profound, that it is not an error or a misinterpretation or a miscalculation, that it affects all areas of the Universe : matter, energy, light, space, time, movement…

Some have found it even easier to refute Zeno because they combat the false opinions they attribute to him. It is often claimed that Zeno and Parmenides (whose student he was) defended ridiculous opinions such as denying the existence of motion, time, space, matter, or mind. The virulent polemics against these two authors explain this type of slander. Zeno and Parmenides disturbed, and still disturb, thinkers by attacking their philosophy, or their lack thereof. Scientists and mathematicians often claim to have no need for philosophy. Zeno demonstrates that this is false, and this greatly disturbs them.

What did Zeno really mean by these paradoxes ? Well, that the world is paradoxical and not of the type of logic without contradiction… Read here :

https://www.matierevolution.fr/spip.php?article32

https://www.matierevolution.fr/spip.php?article6733

https://www.matierevolution.fr/spip.php?article7412

https://fr.wikisource.org/wiki/Les_Arguments_de_Z%C3%A9non_d%E2%80%99%C3%89l%C3%A9e_contre_le_mouvement

https://remacle.org/bloodwolf/livres/gomperz/chap8.htm

https://www.philo5.com/Textes-references/ZenonD%27Elee_LyceeInternational.htm

Another way these authors are criticized is to say that Zeno was ignorant of the mathematics of infinity and physics without infinities, otherwise he would have seen that there is no contradiction in his examples. But that is not the point, because Zeno is not asking whether, in a universe of thought (be it mathematical or mythical), the paradox could be resolved. He is asking whether, in the real world, things actually work this way, and the question, like the answer, will therefore be very different.

Of course, a real length can be written with an infinite number of digits after the decimal point, but matter, time, or space have no infinity, neither infinitely small nor infinitely large.

Beyond the manufactured controversies, there are responses to Zeno from philosophers, mathematicians, and physicists who often believe they can resolve the paradox. Consider their arguments :

https://www.youtube.com/watch?v=q_I1UPvAwxk

https://www.youtube.com/watch?v=wugLVYYxwMU

https://www.youtube.com/watch?v=whr5K3q3kF8

https://www.youtube.com/watch?v=kkgaMxz-OzI

https://www.youtube.com/watch?v=zkonP4lWopQ

https://www.youtube.com/watch?v=Gc3eJ8V-mAs

https://www.youtube.com/watch?v=s7x5ldBzorc

https://www.youtube.com/watch?v=vPTfFIN621U

https://www.youtube.com/watch?v=SMPid7Sh0EE

https://www.youtube.com/watch?v=ByBgNxK9QPk

https://www.youtube.com/watch?v=Gfci1UTuxCA

https://hal.science/hal-04866169v1/file/Zenon_La%20Recherche_M%20Mitov.pdf

The mere fact that some say, "We’ve figured out how to eliminate Zeno’s paradoxes ; the world is exclusively continuous," while others assert, "We’ve figured out how to eliminate Zeno’s paradoxes ; the world is exclusively discontinuous," clearly demonstrates the contradictory nature of the world. As for the others, generally philosophers, they say, "We understand Zeno ; he’s right. We can’t eliminate his paradoxes because the world is too difficult for the human mind to comprehend." And this is not what Zeno meant either, who asserted that dialectics can perfectly grasp the real contradictions of the world.
Zeno supports the theses of Parmenides

Let us remember that Zeno’s aim was to defend Parmenides’ conception against his detractors. And Parmenides, for his part, defended the unity of the world against all forms of dualism.

Plato attributes these words to Zeno :

“You haven’t seen,” Zeno said to Socrates, “that my work is unpretentious, that it wasn’t composed with the intention you suppose, and that I make no secret of its contents, as if they were something extraordinary. But you have clearly seen that it is a defense of Parmenides against those who attack him with jests, claiming that if Being is one, many ridiculous and contradictory consequences follow. My book answers the proponents of multiplicity : it returns the favor, with attrition, and shows that even more ridiculous consequences result from the hypothesis of multiplicity than from that of unity, if one examines it carefully. It was to support this debate that I wrote it in my youth : it was stolen from me, and I was unable to decide whether or not to publish it.” "So you are mistaken, Socrates, in believing that I did not write this work in my youth out of a love of debate, but out of ambition in my later years."

The philosophies of Zeno and Socrates :

http://www.matierevolution.fr/spip.php?article1366

Parmenides’ predecessors saw gods in the sky whose actions were supposed to explain what happens on Earth. It is to this type of conception, which he calls "opinion," that Parmenides opposes "truth," which, according to him, is both scientific and philosophical (observation and reasoning).

Maurice Sachot explains that the poem "On Nature," written by a pure "physicist," proposes a general theory that both safeguards and reconciles the permanence of the world with the equally constant change of all that exists—a problem that his predecessors and contemporaries grappled with. In the first part of the poem, he sets forth the epistemic rules to which all knowledge of reality must submit in order to claim any truth. This makes him the founder of epistemology. In the second part, the Eleatic philosopher presents his own conception of the world (his doxa), proposing a theoretical model of interpretation, which he calls diakosmos, "transworld," and whose key metaphor is sexual reproduction. This also makes him the father of science in the modern sense of the word.

Parmenides, like others before him, conceived of the universe as spherical and composed of concentric zones ; he admitted that the inner and outer spheres were formed of the same element. He defended the opinion that everything results from the mixture of two opposing elements.

Parmenides rejects dualisms such as body/soul, earth/heaven, etc.

Parmenides : “Two forms have been established for knowledge under two names : (this is one too many, and this is where the error lies) ; the bodies have been separated and opposed, the limits established and distinguished ; on the one hand, the ethereal fire, the beneficent, subtle, light flame, everywhere identical to itself, but different from the second form ; on the other hand, this latter form, opposed to the first, dark night, a dense and heavy body.”

https://fr.wikisource.org/wiki/La_Physique_de_Parm%C3%A9nide

Parmenides’ philosophy is the dialectic of the one and the many.

https://www.matierevolution.fr/spip.php?article6562

Parmenides, as told by Plato :

https://remacle.org/bloodwolf/philosophes/platon/cousin/parmenide.htm

Parmenides’ thought :

https://fr.wikipedia.org/wiki/Parm%C3%A9nide

https://www.matierevolution.fr/spip.php?article3458

http://www.matierevolution.fr/spip.php?article3653
What were Zeno’s paradoxes trying to demonstrate ?

Why are Zeno’s paradoxes a response to the criticisms against Parmenides ? Because they demonstrate the intrinsically and dialectically contradictory nature of the real world, beyond the apparent non-contradiction of the world of thought, and especially mathematics. Those who argued with Parmenides accused him of having contradictory thinking. Zeno demonstrates that contradiction is internal to reality.

Proclus in "Commentaries on the Parmenides" :

"He (Zeno) wrote a book in which he showed, in a marvelous way, that for those who suppose the plurality of things, no fewer difficulties arise than those which (it seemed to him) beset the partisans of the unity of being. And indeed he showed that the same thing would be similar and dissimilar, equal and unequal, and that there would be an absolutely complete annihilation of the order of reality and an incoherent confusion of all things."

Diogenes Laertius reminds us, in "Lives, Doctrines, and Sayings of the Philosophers," that Zeno was not content with science and philosophy alone. Like Socrates, he engaged in politics :

“Having set out to overthrow the tyrant Nearchus (some say Diomedon), he was arrested […]. When questioned about his accomplices and the weapons he had delivered to Lipara, he named all the tyrant’s friends, intending to isolate him from his own people. Then, under the pretext of confidential revelations about certain people, he cruelly bit the tyrant on the ear and only released his grip when mortally wounded […]. Finally, he cut out his own tongue with his teeth and spat it in the tyrant’s face.”

Before exploring the relationship between Zeno’s philosophy and his politics, let us recall the fundamental theses of Zeno’s paradoxes :

1) You cannot divide infinitely

Matter, time, or space cannot be divided into an infinite number of parts. Therefore, not everything is divisible. But if something is not divisible, it has no parts. Thus, not everything is made up of parts. And this applies whether we are talking about parts of matter, time, or space, or even of energy or momentum. There are no infinitesimals.

2°) The whole and its parts are inseparable and do not merge

The world (matter, time, and space) is therefore not founded on indivisible elements, but when these elements are divided, they do not cease to be part of a whole. The elements are inseparable from the whole, and the whole from its elements. They thus contradict each other while remaining inextricably united. Ultimately, the whole is neither the sum of its parts nor anything other than what is constituted by the parts.

3°) Matter and movement are in dialectical contradiction

The movement of an object (considered immobile if no energy is supplied to it) is not a diametrical contradiction, otherwise the object would never move…

4°) The transition from quantity to quality is a leap and not a continuous transition.

5) We must reject all the infinities of Physics

6°) By constantly observing, we disrupt the dynamics.

It is not possible to measure the position of a moving object at every instant, at the risk of freezing the object.

7°) Space, time, matter, and movement contain within themselves their own contradictions, without which the universe would be impossible… The paradox is irreducible because it is inherent in reality and not in our understanding of it.

8) The contradiction between the point and the continuum is irreducible, yet they are inseparable and indispensable to each other in reality. All reality must therefore be a composite of the two. Hence the wave/particle "complementarity" of quantum physics.
How quantum physics takes up Zeno’s dialectic in its own way…

What is dialectical about quantum physics ?

First of all, let’s note that physicists are often unaware of this…

https://www.matierevolution.fr/spip.php?article3819

https://www.matierevolution.fr/spip.php?article2424

https://www.matierevolution.fr/spip.php?article7629

And yet, we find dialectics everywhere in all the innovations of quantum physics compared to so-called classical physics…

Wave and particle : this is the dual image of matter and light, as well as of the void, twofold and perfectly contradictory, a wave having characteristics entirely opposite to a particle. This pair of opposites is completely inseparable since the particle is not sometimes a wave and sometimes a particle, but always both at once when its dynamics are not halted by observation, which, on the contrary, can only detect one of the two. Two incompatible yet inextricably linked worlds, indispensable to one another : this is indeed the dialectic. And this is not the only point to note. The same can be said of attraction and repulsion, or contraction and expansion, positive and negative electricity, matter and antimatter, matter and energy, matter and the void, the virtual and the real, and so on.

Are these opposites merely formal ? Is the choice to call it a dialectic truly a scientific observation ? Let’s examine the attraction between two particles. They attract each other, approach each other, and then reach a small distance where… they repel each other. Let’s examine the positive charge of a particle. It attracts a negatively charged particle until they are so close that it repels it, being negative at this point. Then, alternately, its charge layers are positive and negative. This is what quantum physics calls "charge screening" by the cloud of virtual particle-antiparticle pairs. These pairs are themselves dialectical manifestations of quantum physics. Indeed, they are opposites that remain coupled as long as they exist, that is, for a very short time. Pairs of opposites abound in quantum physics. We can also mention the boson/fermion and matter/light pairings. Two particles of matter have no contact with each other without interacting via light. Yet matter and light are opposites, like bosons and fermions. Attraction should cause fermions (matter) to collide with each other, but the repulsion of energy (bosons) prevents this (Pauli exclusion principle). Bosons and fermions obey seemingly diametrically opposed logics, and yet… Yet, fermions can only communicate with each other via emitted and absorbed photons. Yet, bosons need fermions to be emitted. And two fermions can collide to produce fermions and antifermions. Two colliding fermions can produce two bosons. Correlated fermions become a boson. Etc., etc… Bosons and fermions are inseparable and interdependent, yet they never cease to be contradictory… Dialectics, we tell you !!! Another manifestation of this dialectic : matter contracts into stars, galaxies, clusters of galaxies, etc., and it expands (expansion of the Universe). Expansion and contraction are the very essence of the universal phenomenon at all scales. On a small scale, gravitation is contraction and the Pauli exclusion principle is repulsion. On a large scale, the star is a coupling of attraction and repulsion. Attraction has provided sufficient mass to create the temperature and pressure conditions that initiate nuclear reactions and generate the energy flow, which is expansive. Hence the momentary equilibrium of the star (a dialectical compound of contraction and expansion). Time and space—yet another dialectical pair ! On a small scale, this dialectical character is perfectly described by Heisenberg’s inequalities (also called Heisenberg’s principle) which state that the more one tries to confine a particle in a restricted volume, the more energy it puts out to get out of it.Again, the dialectic of contraction/expansion and attraction/repulsion.

In the philosophy of science, we always come back to Zeno… but does the Zeno effect exist in science ?

https://www.matierevolution.fr/spip.php?article2695

Zeno’s paradoxes, Hegel’s dialectic, and quantum physics

https://www.matierevolution.fr/spip.php?article4371

The quantum Zeno effect

https://fr.wikipedia.org/wiki/Effet_Z%C3%A9non_quantique

All of Zeno’s statements are today among the universally recognized fundamental bases of Quantum Physics and Dialectical Philosophy…

The potential of the quantum particle is a wave, and the actual is a corpuscle. In reality, the two coexist contradictorily and inseparably.

Young’s double-slit experiment is one of the most striking examples of this.

Zeno didn’t foresee the quantum vacuum, but he perceived the impossibility of a material world as common sense describes it. The average person might say, "Yes, Achilles outpaces the tortoise," "Yes, a pile builds up gradually," "Yes, the arrow hits its target," and so on. Yet, Zeno is right : with a continuous, fixed, non-contradictory view of reality, it’s impossible.

Yes, the elementary particle passes through only one slit. We know this by observing its passage. Yet, it passes through both slits. We know this because its probability of presence, if we don’t perform a measurement at the exit of one slit, tells us so. And the particle is elementary, however, in the sense of being indivisible. The particle is a perfect example of Zeno’s theories : indivisible but based on a quantity of other particles (the ephemeral pairs of particles and antiparticles of the quantum vacuum that form the particle’s polarization cloud).

Yes, a particle is indeed located at a point but simultaneously extended within a space (that of the cloud). But it doesn’t travel from one point to another infinitely close one. It jumps to a distant point. Then it starts again. The "next" point is not a continuation of the previous one, like two consecutive numbers, whether integers or rational numbers. There is no trajectory for the elementary particle. And the jump seems purely random. We will see that it is not, in reality. But it is probabilistic, and it is probability that obeys a quantum law.
The material particle (the actual site) does not exist alone ; it moves while constantly surrounded by this cloud (called the polarization cloud) made up of pairs of particles and antiparticles, called virtual, which do indeed exist. These pairs are organized in such a way that a charged particle is surrounded by virtual particles forming alternating positive and negative charged layers that shield the charge of the particle with mass. The particle has mass carried by the energy of a Higgs boson that jumps from one virtual particle to another. This is why the property of a "real particle" can be carried by any of the virtual particles in the cloud. Hence, it becomes a "probability cloud." This is also how the particle, although point-like, can occupy an entire space without occupying all points in space… This is the true origin of the philosophical properties suspected and brilliantly demonstrated by Zeno 2500 years ago…

Yes indeed ! Zeno is right ! There is no particle or material object at rest that can be set in motion. Motion is inherent to matter. Furthermore, he is correct : there is no particle that exists at a single point, but rather all particles and compounds of a small number of them are located at a large number of points, forming a cloud. The particle does not move from one point to another. It is the cloud of points that moves. Continuous trajectories do not exist. Nor does continuous time or space exist. Infinitesimals, so useful in mathematics, have no physical reality. The dichotomy at infinity is not possible. Well done again, Zeno !

Conclusion : Zeno’s paradoxes demonstrate through reasoning that the world is dialectically contradictory, that negation is internal to reality and that it is this negation that drives the dynamic, with real contradiction being the driving force of nature.

2500 years ago, Zeno of Elea destroyed the dualism separating and opposing matter and movement, space and time…

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