Abstract
The conceptualisation of movement has always been problematical for Western thought, ever since Parmenides declared our incapacity to conceptualise the plurality of change because our self-identical thought can only know an identical being. Exploiting this peculiar feature and constraint on our thought, Zeno of Elea devised his famous paradoxes of movement in which he shows that the passage from a position to movement cannot be conceptualised. In this paper, I argue that this same constraint is at the root of our incapacity to conceptualise the unseen movement at the micro-level and that the aporetic idea of super-position far from opening the gate on a deeper reality is a symptomatic word for this lack of understanding.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
We find this expression in the Sophist where Plato often refers to Parmenides’ prohibition to bridge the one and the many and the need of philosophy to overcome this prohibition.
See Andrews, God, the Evil Genius and Eternal Truths: the Structure of the Understanding in the Cartesian Philosophy.
Berkely (1734, p. 2).
Berkely (1734, p. 7).
Papa-Grimaldi (1996).
‘...but also from this, on which mortals who know nothing wander, double-headed; for helplessness guides the wandering thought in their hearts. They are carried deaf and blind at the same time, amazed, a horde incapable of judgment, by whom to be and not to be are considered the same and yet not the same, for whom the path of all things is backward turning’ (Taran 1965, p. 54).
As I have argued in A. Papa-Grimaldi, op. cit. mathematical solutions with their subtle formulas which should bridge the gap between one and many overlook this simple logical fact: the many cannot be conceptualised in its dynamic plurality, but only as repetition of a unit. This is what there is to say as far as the logical implications of movement go: it remains an unsolvable and irreducible aporia in our mind and in our epistemology, for the passage from one to many, from identity to plurality cannot be conceptualised by our self-identical thought.
It is interesting, though, to reflect on the fact that in its essence the scientific discourse is the finding of mathematical correlations that don't express as much the dynamicity and the plurality of life as the repetition of the unit embodied in the mathematical correlations themselves. So that what emerges in the highly formalised language of mathematics is not the multiform world of experience, but a sort of crystallised Parmenidean world. A one that once conceptualised in its correlations does not change anymore. Science aims to build a deterministic world where every happening is ultimately expressed by a mathematical correlation. A world, in a way, in which nothing happens because everything is and it has always been, insofar as it is implicated in the mathematical correlations.
Freeman (1946, p. 156).
Hey and Walters (1987, p. 5).
Hey and Walters (1987, p. 13).
Davies (1983, p. 107).
Davies (1983, p. 107).
Davies (1983, p. 108).
Davies (1983, pp. 108–109).
Hey and Walters (1987, p. 15).
To see how this is coherent with the nature of our epistemology, we should try and imagine what would it mean for our concepts and our logic if these entities behaved like objects in the classical sense. This is what we are going to see shortly.
On inner variables see Bohm (1980, pp. 65–110).
Also the zero time of so-called point events at the macro-level is further analysable and is only by convention a final event. Take the time a photographic device records the winning of a race. The race is said to be won at an instant, but this is so only by convention. In fact, that thousandth of a second which is, for example, the time in which the diaphragm of a sophisticated instrument of detection opens to record the winning of a race, there will be things happening, for example, whatever happens to the photographic device to allow it to operate.
Or, better, to a never accomplished movement since these sub-positions are in principle further analysable.
Certainly if we are to understand more about the nature of electrons, the discovery of their sub-events will be necessary. Maybe in time, this statement—that the electrons are final entities with no further sub-events—will be outdated. This is immaterial as far as my theory is concerned, because this would just shift the role played in my epistemology by final entities from the electrons to their sub-events. Besides, a ‘quantum object’ would still be an observational definition. To this effect I could venture that a “sub-electron” microscope or other observational tool could have the resolution to promote atoms from quantum objects to classical objects.
In their article “The Classical Limit of an Atom”, Nauenberg et al. write: (1994, p. 24)
“Atomic systems have been created which behave—for a short period of time—according to the laws of classical mechanics. Researchers fabricate such systems by exciting atoms so that they swell to 10,000 times their original size. At such a scale the position of an electron can be localised fairly closely; its orbit no longer remains a haze that represents only a probability equation. In fact, as the electron circulates around the nucleus, it traces an elliptical pattern just as the planets orbit the sun.”
Hey and Walters (1987, p. 28).
“...we have no right to talk about what that photon is doing during its long travel from the point of entry...to the point of registration. After all, no elementary quantum phenomenon is a phenomenon until it is registered. What we envisage as so definite is in fact like a Great Smokey Dragon. The tail of the Dragon is sharp and clear: that is the place where the photon enters the equipment...The mouth of the Dragon is quite clear: that is where the photon reaches one counter or the other. But in between we have no right to speak about what is present. If we’re ever going to find an element of nature that explains space and time, we surely have to find something that is deeper than space and time—something that itself has no localisation in space and time. The amazing feature of the elementary quantum phenomenon—the Great Smokey Dragon—is exactly this. It is indeed something of a pure knowledge-theoretical character, an atom of information which has no localisation in between the point of entry and the point of registration.” (Wheeler 1986).
For a concise and enlightening discussion of the historical interpretations of this paradox see also Legget (1987, pp. 85–104).
Davies (1983, pp. 112–114).
Davies (1983, p. 115).
Davies (1983, p. 116).
References
Berkely G (1734) The Analyst: A discourse addressed to an infidel mathematician. Kessinger Publishing, 2004
Bohm D (1980) Wholeness and the implicate order. Routledge, pp 65–110
Davies P (1983) God and the new physics. Penguin Books Ltd, p 107
Freeman K (1946) The pre-socratic philosophers (a companion to Diels, Fragmenteder Vorsokratiker). Basil Blackwell, Oxford
Hey and Walters (1987) The quantum universe. Cambridge University Press, p 5
Leggett AJ (1987) Reflections on the quantum measurement paradox. In: Hiley BJ, Peat FD (eds) Quantum implications, pp 85–104
Nauenberg M, Stroud C, Yeazell J (1994) The classical limit of an atom. Sci Am (June 1994)
Papa-Grimaldi A (1996) Why mathematical solutions to Zeno’s paradoxes miss the point: Zeno’s one and many relation and Parmenides’ prohibition. Rev Metaphys 50:299–314
Taran L (1965) Parmenides. Princeton University Press, Princeton, New Jersey
Wheeler J (1986) In: Davies PCW, Brown JR (eds) The ghost in the atom. Cambridge University Press, p 66
Acknowledgements
I would like to thank the anonymous reviewer of the first version of this manuscript, the reviewer’s comments and constructive criticisms were very helpful and greatly appreciated.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Papa-Grimaldi, A. The presumption of movement. Axiomathes 17, 137–154 (2007). https://doi.org/10.1007/s10516-007-9009-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10516-007-9009-9