Perceptual axioms are irreconcilable with Euclidean geometry.
cognition
illusions
perception
priors
Journal
The European journal of neuroscience
ISSN: 1460-9568
Titre abrégé: Eur J Neurosci
Pays: France
ID NLM: 8918110
Informations de publication
Date de publication:
27 May 2024
27 May 2024
Historique:
revised:
12
04
2024
received:
27
10
2023
accepted:
15
05
2024
medline:
28
5
2024
pubmed:
28
5
2024
entrez:
28
5
2024
Statut:
aheadofprint
Résumé
There are different definitions of axioms, but the one that seems to have general approval is that axioms are statements whose truths are universally accepted but cannot be proven; they are the foundation from which further propositional truths are derived. Previous attempts, led by David Hilbert, to show that all of mathematics can be built into an axiomatic system that is complete and consistent failed when Kurt Gödel proved that there will always be statements which are known to be true but can never be proven within the same axiomatic system. But Gödel and his followers took no account of brain mechanisms that generate and mediate logic. In this largely theoretical paper, but backed by previous experiments and our new ones reported below, we show that in the case of so-called 'optical illusions', there exists a significant and irreconcilable difference between their visual perception and their description according to Euclidean geometry; when participants are asked to adjust, from an initial randomised state, the perceptual geometric axioms to conform to the Euclidean description, the two never match, although the degree of mismatch varies between individuals. These results provide evidence that perceptual axioms, or statements known to be perceptually true, cannot be described mathematically. Thus, the logic of the visual perceptual system is irreconcilable with the cognitive (mathematical) system and cannot be updated even when knowledge of the difference between the two is available. Hence, no one brain reality is more 'objective' than any other.
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Subventions
Organisme : Leverhulme Trust
ID : RPG-2020-022
Informations de copyright
© 2024 The Author(s). European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd.
Références
Brainard, D. H. (1997). The psychophysics toolbox. Spatial Vision, 10(4), 433–436. https://doi.org/10.1163/156856897X00357
Brown, H., & Friston, K. J. (2012). Free‐energy and illusions: The Cornsweet effect. Frontiers in Psychology, 3, 43. https://doi.org/10.3389/FPSYG.2012.00043/BIBTEX
Casey, J. (1885). The first six books of the elements of Euclid (third). Ponsonby and Weldrick.
Filippov, M., & Zeki, S. (2022). On the necessity of importing neurobiology into mathematics. PsyCh Journal, 11, 755–756. https://doi.org/10.1002/PCHJ.524
Geisler, W. S., & Kersten, D. (2002). Illusions, perception and Bayes. Nature Neuroscience, 5, 508–510. https://doi.org/10.1038/nn0602-508
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte Für Mathematik Und Physik, 38, 173–198. https://doi.org/10.1007/BF01700692/METRICS
Gray, J., & Ferreirós, J. (2022). Epistemology of geometry. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall’21). Metaphysics Research Lab, Stanford University.
Hilbert, D. (1930). David Hilbert's radio address. https://www.maa.org/book/export/html/326610
Holt‐Hansen, K. (1961). Hering's illusion. British Journal of Psychology, 52(4), 317–321. https://doi.org/10.1111/j.2044-8295.1961.tb00796.x
Knol, H., Huys, R., Sarrazin, J.‐C., & Jirsa, V. K. (2015). Quantifying the Ebbinghaus figure effect: Target size, context size, and target‐context distance determine the presence and direction of the illusion. Frontiers in Psychology, 6, 1679. https://doi.org/10.3389/fpsyg.2015.01679
Lee, J. M. (1997). Riemannian manifolds. Springer. https://doi.org/10.1007/b98852
Mamassian, P., & de Montalembert, M. (2010). A simple model of the vertical–horizontal illusion. Vision Research, 50(10), 956–962. https://doi.org/10.1016/j.visres.2010.03.005
Notomi, N. (1999). The unity of Plato's sophist: Between the sophist and the philosopher. Cambridge University Press. https://doi.org/10.1017/CBO9781107297968
Prinzmetal, W., Shimamura, A. P., & Mikolinski, M. (2001). The Ponzo illusion and the perception of orientation. Perception & Psychophysics, 63(1), 99–114. https://doi.org/10.3758/BF03200506
Raatikainen, P. (2022). Gödel's incompleteness theorems. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Spring’22). Metaphysics Research Lab, Stanford University.
Restle, F., & Decker, J. (1977). Size of the Mueller‐Lyer illusion as a function of its dimensions: Theory and data. Perception & Psychophysics, 21(6), 489–503. https://doi.org/10.3758/BF03198729
Roberts, B., Harris, M. G., & Yates, T. A. (2005). The roles of inducer size and distance in the Ebbinghaus illusion (Titchener circles). Perception, 34(7), 847–856. https://doi.org/10.1068/p5273
Vitruvius. (20 B.C.E.). (n.d.). De Architectura.
Weiss, Y., Simoncelli, E. P., & Adelson, E. H. (2002). Motion illusions as optimal percepts. Nature Neuroscience, 5, 598–604. https://doi.org/10.1038/nn0602-858
Westheimer, G. (2008). Illusions in the spatial sense of the eye: Geometrical–optical illusions and the neural representation of space. Vision Research, 48(20), 2128–2142. https://doi.org/10.1016/j.visres.2008.05.016
Yang, S., Bill, J., Drugowitsch, J., & Gershman, S. J. (2021). Human visual motion perception shows hallmarks of Bayesian structural inference. Scientific Reports, 11, 3714. https://doi.org/10.1038/s41598-021-82175-7
Zeki, S., & Chén, O. Y. (2020). The Bayesian‐Laplacian brain. European Journal of Neuroscience, 51(6), 1441–1462. https://doi.org/10.1111/ejn.14540