G.H. von Wright validly remarks that Zeno’s arrow “is neither moving nor at rest”. Then he invalidly proceeds to turn this into “both moving and at rest ” eo ipso. Hegel does the exact same thing and so, it seems, does everybody else. A violat-ion of the Law of the Excluded Middle (LEM), in the form of –A and --A, is equated (eo ipso) with a violation of the Law of Non-Contradiction (LNC), as A and –A. The move is both, circular (it employs double negation) and contradictory. When it is as-serted that neither A nor –A, the last thing which follows is that both A and –A. If these two are both false, contradicting LEM, they cannot also be both true. Unexpect-edly, a violation of LEM protects LNC. In accordane [a] I argue that a system violating LEM eo ipso satisfies LNC, contrary to what von Wright, Hegel, paraconsistent logicians and everybody else seems to think. [b] Zeno’s paradoxes produce an antinomy, iff motion is continuous. (Ancient Atomists only reacted to Zeno’s infinite divisibility of processes.) [c] A comparable quantum model for discontinuous transitions, including motion, displays properties identical to those specified in [a] and [b]. If a body moves discontinuously from A to B, it is nowhere at all in-between A and B. And therefore cannot be where it is not, offerring an alternative to Zeno’s antinomies. [d] Zeno’s paradoxes, if handled by quantum discontinuity, lead to a 3-valued but consistent system. Discontinuity eliminates all possible descriptions of a system’s state. Hence, if nothing can be truthfully said about the system during a discontinuous transition, nothing self-contraditory can be said about it either. Discontinuous motion is nonbivalent but consistent.
G.H. von Wright validly remarks that Zeno’s arrow “is neither moving nor at rest”. Then he invalidly proceeds to turn this into “both moving and at rest ” eo ipso. Hegel does the exact same thing and so, it seems, does everybody else. A violat-ion of the Law of the Excluded Middle (LEM), in the form of –A and --A, is equated (eo ipso) with a violation of the Law of Non-Contradiction (LNC), as A and –A. The move is both, circular (it employs double negation) and contradictory. When it is as-serted that neither A nor –A, the last thing which follows is that both A and –A. If these two are both false, contradicting LEM, they cannot also be both true. Unexpect-edly, a violation of LEM protects LNC. In accordane [a] I argue that a system violating LEM eo ipso satisfies LNC, contrary to what von Wright, Hegel, paraconsistent logicians and everybody else seems to think. [b] Zeno’s paradoxes produce an antinomy, iff motion is continuous. (Ancient Atomists only reacted to Zeno’s infinite divisibility of processes.) [c] A comparable quantum model for discontinuous transitions, including motion, displays properties identical to those specified in [a] and [b]. If a body moves discontinuously from A to B, it is nowhere at all in-between A and B. And therefore cannot be where it is not, offerring an alternative to Zeno’s antinomies. [d] Zeno’s paradoxes, if handled by quantum discontinuity, lead to a 3-valued but consistent system. Discontinuity eliminates all possible descriptions of a system’s state. Hence, if nothing can be truthfully said about the system during a discontinuous transition, nothing self-contraditory can be said about it either. Discontinuous motion is nonbivalent but consistent.
The question whether quantum discontinuity can or cannot provide an answer to Zeno's Paradoxes is reopened. It is observed that what is usually understood by the term "discontinuity", namely, Einstein's conception of the photon as described by himself and all others, is unsuitable to the task because, essentially,it reduces to the trivial 'discontinuity' of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort of discontinuity required. Discrete quantized orbits, corresponding to eigen-frequencies, are irreducible, and nothing is allowed to stand in-between them in satisfaction of the quantum postulate, furnishing the requisite, and so far missing, immediate nextness of a point to a certain other. In this way, Zeno's Runner need not postpone his first step indefinitely, always waiting upon an infinity of preceding steps, before it can be taken. There is now a point that is next to a point and so a step on that point, which is the first step. It follows that, if one kind of discontinuity, Einstein's, is incapable of offerring an answer to Zeno, while another kind can, the two are discrepant. One of them, the former, is not a kind of discontinuity properly so called at all, though evidently the consequence of one.
Zeno of Elea's motion and infinity paradoxes, excluding the Stadium, are stated (1), commented on (2), and their historical proposed solutions then discussed (3). Their correct solution, based on recent conclusions in physics associated with time and classical and quantum mechanics, and in particular, of there being a necessary trade off of all precisely determined physical values at a time (including relative position), for their continuity through time, is then explained (4). This article follows on from another, more physics orientated and widely encompassing paper entitled "Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity" (Lynds, 2003), with its intention being to detail the correct solution to Zeno's paradoxes more fully by presently focusing on them alone. If any difficulties are encountered in understanding any aspects of the physics underpinning the following contents, it is suggested that readers refer to the original paper for a more in depth coverage.
When the concept of Zero is analyzed, it is frequently related to another equally deep and complicated concept – Nothing. If in science, Zero is closely associated with mathematics, then Nothing is primarily related to the material world. The question of whether Nothing can be found in the real physical world is often discussed in relation to the vacuum which, at some point in the history of the development of physics, is thought about as an empty space. Nevertheless, theories of modern physics have demonstrated that even in a vacuum, when all the matter is evacuated from a certain region of space, and this region is isolated from ordinary fields – gravitation field, electromagnetic fields etc – there still remain physical fields called vacuum zero fluctuations that can not be removed in principle. These vacuum fields are properties of space. In this chapter I will analyze another physics theory – namely, Quantum Physics – and will consider its less discussed relations to the concept of Nothing. One of the very first Greek philosophers, Thales (624–548 BCE) from Miletus, declared that Something can not appear from Nothing and it can not disappear, turning into Nothing. This idea, in some aspects, was further developed by Zeno from Elea (495–430 BCE) when he created his paradoxes of motion. These paradoxes can be understood as an analysis of the possibility of infinite division of time and space intervals. When we come to Quantum Physics, the very first appearance of the idea of the smallest possible portion of energy, quantum, was stimulated by the analysis of the spectrum of radiation of heated body – black-body radiation. German physicist Max Planck (1858–1947) demonstrated in 1899 that if we assume that there exists a smallest portion of radiation energy that can not be further divided into smaller parts, we arrive at the description of spectrum of the black-body radiation that perfectly matches the observable reality. In contrast, if we assume that radiation energy can be divided an infinite number of times and there does not exist the smallest possible portion, we arrive at the radiation spectrum which is in a sharp contradiction with observable reality. This contradiction is so strong that it has acquired a special term – the ultraviolet catastrophe. Certain parallels in Zeno’s reasoning and approach used in Quantum Physics can clearly be seen and will be discussed. In the conclusion, I will briefly touch on a similar situation in another field of physics when at the other extreme, departure from the idea of the possibility of the infinitely large quantities, this time velocities of motion, gave birth to another theory of modern physics – Einstein’s theory of special relativity.
During the pre-Socratic period, Parmenides created his radical idea of an eternal, unchanging, and motionless world. This was met with much doubt, contempt, and counterarguments that sought to disprove his statements claiming that the concept of past and future were false, and that both change and movement were impossible. Yet his student, Zeno, came after him and sought to further prove his teacher Parmenides' arguments, creating what are now talked about thousands of years later known as Zeno's paradoxes. This paper will specifically talk about Zeno's dichotomy paradox, claiming that movement cannot exist due to the inherent need to be capable of traversing between a theoretically infinite series of midpoints in order to reach one's destination. The infinite series of points can be overcome with the use of atomist theory to break it down into finite, indivisible points. However, the question then becomes how exactly do we move from one finite point to another? This issue can be addressed using superposition principle, a quantum theory that requires an object to be observed in order for its state to be known, and Planck time, the current smallest measurement of time. Yet even with Planck time being an incredibly small unit of time, our observation is still limited. By understanding movement as a phenomenon that occurs between these lapses of observation, the quantum particles that are resting in superposition are capable of moving from one finite point to another.
Abstract Parmenides’s insinuation of an unchanging universe is assertively supported by Zeno with various logical paradoxes that question the very nature of plurality, space, time, and the reality of apparent motion. The dichotomy is his most famous paradox. To begin a trip, say, from here to the door, a traveler must travel the first half of it, but before she does that she must travel half of the first half, and in fact half of that, ad infinitum. Since there will always exist a smaller first half to be traveled first, Zeno questions whether a traveler can ever even start a trip. Zeno’s analysis is logical; on the other hand, things everywhere appear to be moving. Hence, either Zeno’s reasoning is wrong or appearances are deceptive. Empowered by the uncertainty principle of quantum mechanics, it will be argued that, at best, the phenomenon of motion is experimentally unverifiable!
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in Tarski's hierarchy or paraconsistent logics. We propose a novel approach: a quantum circuit architecture that intrinsically enforces logical consistency during its unitary evolution. By encoding self-referential or contradictory propositions into a quantum state, the circuit uses interference effects to suppress inconsistent outcomes while preserving coherent ones. We demonstrate this with the Liar Paradox ("This statement is false"), showing that the quantum model naturally stabilizes truth values that would be paradoxical classically. The framework builds on orthomodular quantum logic treating logical propositions as subspace projectors and connects to belief revision and cognitive modeling by providing a physical mechanism for coherence restoration in epistemic states. This work bridges formal logic and quantum computation, suggesting that consistency can be embedded as a structural property of reasoning systems rather than imposed externally.