Abstract
We show the presence of genuine quantum structures in human language. The neo-Darwinian evolutionary scheme is founded on a probability structure that satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate quantum-like evolutionary change. In earlier research we revealed quantum structures in processes taking place in conceptual space. We argue that the presence of quantum structures in language and the earlier detected quantum structures in conceptual change make the neo-Darwinian evolutionary scheme strictly too limited for Evolutionary Epistemology. We sketch how we believe that evolution in a more general way should be implemented in epistemology and conceptual change, but also in biology, and how this view would lead to another relation between both biology and epistemology.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Accardi, L. 1984. “The probabilistic roots of the quantum mechanical paradoxes.” In: Diner, S.; Fargue, D.; Lochak, G., and Selleri, F. (eds.), The wave-particle dualism 47–55. Dordrecht: Kluwer Academic Publishers.
Aerts, D. 1982. “Example of a macroscopical situation that violates Bell inequalities.” Lettere al Nuovo Cimento 34: 107–111.
Aerts, D. 1986. “A possible explanation for the probabilities of quantum mechanics.” Journal of Mathematical Physics 27: 202–210.
Aerts, D. 1995. “Quantum structures: An attempt to explain their appearance in nature.” International Journal of Theoretical Physics 34: 1165–1186.
Aerts, D.; and Aerts, S. 1994. “Applications of quantum statistics in psychological studies of decision processes.” Foundations of Science 1: 85–97.
Aerts, D.; and Aerts, S. 1997. “Application of quantum statistics in psychological studies of decision processes.” In: van Fraassen, B.C. (ed.), Topics in the foundation of statistics 92–104. Dordrecht: Kluwer Academic Publishers.
Aerts, D.; Aerts, S.; Broekaert, J., et al. 2000. “The violation of Bell inequalities in the macroworld.” Foundations of Physics 30: 1387–1414.
Aerts, D.; Apostel, L.; De Moor, B., et al. 1995. Perspectives on the world, an interdisciplinary reflection. Brussels: VUBPress.
Aerts, D.; and Czachor, M. 2004. “Quantum aspects of semantic analysis and symbolic artificial intelligence.” Journal of Physics A-Mathematical and General 37: L123–L132.
Aerts, D.; Czachor, M.; Gabora, L., et al. 2003. “Quantum morphogenesis: A variation on Thom’s catastrophe theory.” Physical Review E 67: 051926-1–051926-13.
Aerts, D.; and D’Hooghe, B. 2005. “Potentiality states: Quantum versus classical emergence.” Foundations of Science, in press.
Aerts, D.; and Gabora, L. 2005a. “A theory of concepts and their combinations I: The structure of the sets of contexts and properties.” Kybernetes 34: 151–175.
Aerts, D.; and Gabora, L. 2005b. “A theory of concepts and their combinations II: A Hilbert space representation.” Kybernetes 34: 176–205.
Apostel, L. 1995. “The unfinished symphony: Positions, agreements, disagreements and gaps.” In: The worldviews group (ed.), Perspectives on the world: An interdisciplinary reflection 219–239. Brussel: VUBPress.
Aspect, A. 1999. “Bell’s inequality test: More ideal than ever.” Nature 398: 189–190.
Bell, J.S. 1964. “On the Einstein-Podolski-Rosen paradox.” Physics 1: 195–200.
Bell, J.S. 1966. “On the problem of hidden variables in quantum mechanics.” Reviews of Modern Physics 38: 447–452.
Blei, D.M.; Ng, A.Y.; and Jordan, M.I. 2003. “Latent Dirichlet allocation.” Journal of Machine Learning Research 3: 993–1022.
Clauser, J.F.; and Shimony, A. 1978. “Bell’s theorem: Experimental tests and implications.” Reports on Progress in Physics 41: 1881–1926.
Czachor, M. 1992. “On classical models of spin.” Foundations of Physics Letters 3: 249–264.
Czachor, M.; and Naudts, J. 2002. “Thermostatistics based on Kolmogorov-Nagumo averages: Unifying framework for extensive and nonextensive generalizations.” Physics Letters A 298:369–374.
Deerwester, S.; Dumais, S.T.; Furnas, G.W., et al. 1990. “Indexing by Latent Semantic Analysis.” Journal of the American Society of Information Science 41: 391–407.
Doob, J.L. 1953. Stochastic processes. New York: John Wiley and Sons.
Einstein, A.; Podolsky, B.; and Rosen, N. 1935. “Can quantum-mechanical description of physical reality be considered complete.” Physical Review 47: 777–780.
Fodor, J. 1994. “Concepts: A potboiler.” Cognition 50: 95–113.
Foulis, D.J.; and Randall, C.H. 1972. “Operational statistics I.” Journal of Mathematical Physics 13: 1667–1675.
Gabora, L.; and Aerts, D. 2002a. “Contextualizing concepts.” Proceedings of the 15th international FLAIRS conference, special track: Categorization and concept representation: Models and implications 148–152. Pensacola Florida, May 14–17, American Association for Artificial Intelligence.
Gabora, L.; and Aerts, D. 2002b. “Contextualizing concepts using a mathematical generalization of the quantum formalism.” Journal of Experimental and Theoretical Artificial Intelligence 14: 327–358.
Griffiths, T.L.; and Steyvers, M. 2004. “Finding scientific topics.” Proceedings of the National Academy of Sciences 101: 5228–5523.
Gudder, S.P. 1988. Quantum probability. San Diego: Academic Press.
Gudder, S.P. 1968. “Hidden variables in quantum mechanics reconsidered.” Reviews of Modern Physics 40: 229–231.
Hampton, J. 1997. “Conceptual combination.” In: Lamberts, K.; and Shanks, D. (eds.), Knowledge, concepts, and categories 133–159. Hove: Psychology Press.
Heit, E.; and Barsalou, L. 1996. “The instantiation principle in natural language categories.” Memory 4: 413–451.
Hofmann, T. 1999. “Probabilistic latent semantic analysis.” In: Laskey, K.B.; and Prade, H. (eds.), Proceedings of the fifteenth conference on uncertainty in artificial intelligence UAI’99 289–296. San Francisco: Morgan Kaufmann.
Hoppensteadt, F.C. 1982. Mathematical methods of population biology. Cambridge: University Press.
Jauch, J.M.; and Piron, C. 1963. “Can hidden variables be excluded in quantum mechanics.” Helvetica Physica Acta 38: 827–837.
Kamp, H.; and Partee, B. 1995. “Prototype theory and compositionality.” Cognition 57: 129–191.
Kochen, S.; and Specker, E.P. 1967. “The problem of hidden variables in quantum mechanics.” Journal of Mathematical Mechanics 17: 59–87.
Kolmogorov, A.N. 1950. Foundations of the theory of probability. New York: Chelsea.
Komatsu, L.K. 1992. “Recent views on conceptual structure.” Psychological Bulletin 112:500–526.
Landauer, T.K. 2002. “On the computational basis of learning and cognition: Arguments from LSA.” In: Ross, B.H. (ed.), Psychology of learning and motivation, vol. 41: 43–84. New York: Academic Press.
Landauer, T.K.; and Dumais, S.T. 1997. “A solution of Plato’s problem: The latent semantic analysis theory of the acquisition, induction, and representation of knowledge.” Psychological Review 104: 211–240.
Landauer, T.K.; Foltz, P.W.; and Laham, D. 1998. “Introduction to latent semantic analysis.” Discourse Processes 25: 259–284.
Landauer, T.K.; Laham, D.; and Foltz, P.W. 1998. “Learning human-like knowledge by singular value decomposition: A progress report.” Advances in Neural Information Processing Systems 10: 45–51.
Lund, K.; and Burgess, C. 1996. “Producing high-dimensional semantic spaces from lexical co-occurrence.” Behavior Research Methods, Instruments and Computers 28: 203–208.
Markov, A.A. 1906. “Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga.” Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete, 2-ya seriya 15: 135–156.
Montemurro, M.A. 2001. “Beyond Zipf-Mandelbrot law in quantitative linguistics.” Physica A 300: 563–578.
Neumann, J.V. 1932. Mathematische grundlagen der quanten-mechanik. Berlin: Springer-Verlag.
Nosofsky, R. 1988. “Exemplar-based accounts of relations between classification, recognition, and typicality.” Journal of Experimental Psychology: Learning, Memory, and Cognition 14:700–708.
Nosofsky, R. 1992. “Exemplars, prototypes, and similarity rules.” In: Healy, A.F.; Kosslyn, S.M.; and Shiffrin, R.M. (eds.), From learning theory to connectionist theory: Essays in honor of William K. Estes 149–168. Hillsdale NJ: Lawrence Erlbaum.
Osherson, D.N.; and Smith, E.E. 1981. “On the adequacy of prototype theory as a theory of concepts.” Cognition 9: 35–58.
Osherson, D.N.; and Smith, E.E. 1982. “Gradedness and conceptual combination.” Cognition 9: 35–58.
Pitowsky, I. 1989. Quantum probability—quantum logic, Lecture Notes in Physics 321. Berlin: Springer-Verlag.
Plate, T.A. 2003. Holographic reduced representation: Distributed representation for cognitive structures. Stanford: CSLI Publications.
Rips, L.J. 1995. “The current status of research on concept combination.” Mind and Language 10: 72–104.
Rosch, E. 1975. “Cognitive representations of semantic categories.” Journal of Experimental Psychology: General 104: 192–232.
Rosch, E. 1978. “Principles of categorization.” In: Rosch, E.; and Lloyd, B.B. (eds.), Cognition and categorization 27–48. Hillsdale, NJ: Lawrence Erlbaum.
Rosch, E. 1983. “Prototype classification and logical classification: The two systems.” In: Scholnick, E.K. (ed.), New trends in conceptual representation: Challenges to Piaget’s theory? 73–86. Hillsdale, NJ: Lawrence Erlbaum.
Rosch, E.; and Mervis, C.B. 1975. “Family resemblances: Studies in the internal structure of categories.” Cognitive Psychology 7: 573–605.
Smith, E.E.; and Medin, D.L. 1981. Categories and concepts. Cambridge, MA: Harvard University Press.
Smolensky, P. 1990. “Tensor product variable binding and the representation of symbolic structures in connectionist systems.” Artificial Intelligence 46: 159–216.
Widdows, D.; and Peters, S. 2003. “Word vectors and quantum logic: Experimentswith negation and disjunction.” In: Proceedings of the eighth mathematics of language conference 141–154. Bloomington, Indiana.
Zadeh, L. 1982. “A note on prototype theory and fuzzy sets.” Cognition 12: 291–297.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
Aerts, D., Czachor, M., D’Hooghe, B. (2006). Towards a quantum evolutionary scheme: Violating Bell’s inequalities in language. In: Gontier, N., Van Bendegem, J.P., Aerts, D. (eds) Evolutionary Epistemology, Language and Culture. Theory and Decision Library A:, vol 39. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3395-8_20
Download citation
DOI: https://doi.org/10.1007/1-4020-3395-8_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3394-0
Online ISBN: 978-1-4020-3395-7
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)