Skip to main content
SpringerLink
Log in

Computational Complexity and Cognitive Science: How the Body and the World Help the Mind be Efficient

  • Chapter
  • First Online:
Johan van Benthem on Logic and Information Dynamics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 5))

  • 1231 Accesses

Abstract

Computational complexity has been developed under the assumption that thinking can be modelled by a Turing machine. This view of cognition has more recently been complemented with situated and embodied cognition where the key idea is that cognition consists of an interaction between the brain, the body and the surrounding world. This chapter deals with the meaning of complexity from a situated and embodied perspective. The main claim is that if the structure of the world is taken into account in problem solving, the complexity of certain problems will be reduced in relation to Turing machine complexity. For example, search algorithms can be simplified if the visual structure of the world is exploited. Another case is the logical problem of language acquisition, claiming that children cannot learn language simply by considering the input. It is argued that this problem will not arise if it is taken into account that children’s learning of grammatical features often exploits world knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For example, it is surprising that Marr [22] did not at all mention computational complexity in his description of the three levels of computation.

  2. 2.

    There are attempts, however, in the work on adaptive Turing machines.

  3. 3.

    This assumption is the basis for all sci-fi novels about a brain in the vat.

  4. 4.

    In contrast to [2], the position does not deny, however, that the brain employs some detached representations, for example, when it is planning [13].

  5. 5.

    In the terminology of Barwise and Shimojima’s [1] “surrogate reasoning”, this example is a “free ride” provided by the geometric constraints. However, the authors do not consider the reduction in complexity provided by “free rides”.

  6. 6.

    Several researchers have used Gold’s [16] theorem to support this argument, but, as Johnson [17] shows, this result has little bearing on how people actually learn languages.

  7. 7.

    Chomsky’s early work concerned the relations between different kinds of formal automata and the (formal) languages they could identify. This is a typical problem of computationalism that builds on Assumptions (1) and (2). Chomsky seems, more or less, to have stuck to these assumptions throughout his career.

References

  1. Barwise J, Shimojima A (1995) Surrogate reasoning. Cogn Stud Bull Japan Cogn Sci Soc 2(4):7–27

    Google Scholar 

  2. Brooks R (1991) Intelligence without representation. Artif Intell 47:139–159

    Article  Google Scholar 

  3. Carnap R (1928) Der logische Aubau der Welt. Felix Meiner Verlag, Hamburg

    Google Scholar 

  4. Chella A, Frixione M, Gaglio S (1997) A cognitive architecture for artificial vision. Artif Intell 89:73–111

    Article  Google Scholar 

  5. Chomsky N (1980) Rules and representations. Basil Blackwell, Oxford

    Google Scholar 

  6. Clark A (1997) Being there: putting brain body and world together again. MIT Press, Cambridge

    Google Scholar 

  7. Dennett DC (1984) Cognitive wheels: the frame problem of AI. In: Hookway C (ed) Minds, machines and evolution: philosophical studies. Cambridge University Press, Cambridge, pp 129–151

    Google Scholar 

  8. Fodor JA (1975) The language of thought. Harvard University Press, Cambridge

    Google Scholar 

  9. Fodor JA, Pylyshyn ZW (1988) Connectionism and cognitive architecture: a critical analysis. Cognition 28:3–71

    Article  Google Scholar 

  10. Foraker S, Regier T, Khetarpal N, Perfors A, Tenenbaum J (2009) Indirect evidence and the poverty of the stimulus: the case of anaphoric “one”. Cogn Sci 33:287–300

    Article  Google Scholar 

  11. Gärdenfors P (1999) Cognitive science: from computers to anthills as models of human thought. World Social Science Report, UNESCO Publishing, Paris, pp 316–327

    Google Scholar 

  12. Gärdenfors P (2000) Conceptual spaces: the geometry of thought. MIT Press, Cambridge

    Google Scholar 

  13. Gärdenfors P (2004) Cooperation and the evolution of symbolic communication. In: Oller K, Griebel U (eds) The evolution of communication systems. MIT Press, Cambridge, pp 237–256

    Google Scholar 

  14. Gärdenfors P (2012) The cognitive and communicative demands of cooperation. In: van Eijck J, Verbrugge R (eds) Games, actions and social software, LNCS 7010. Springer, Berlin, pp 164–183

    Google Scholar 

  15. Gibson JJ (1979) The ecological approach to visual perception. Houghton Mifflin, Boston

    Google Scholar 

  16. Gold E (1967) Language identification in the limit. Inf Control 10:447–474

    Article  Google Scholar 

  17. Johnson K (2004) Gold’s theorem and cognitive science. Philos Sci 71:571–592

    Article  Google Scholar 

  18. Kirsh D (1991) Today the earwig, tomorrow man? Artif Intell 47:161–184

    Article  Google Scholar 

  19. Kirsh D, Maglio P (1994) On distinguishing epistemic from pragmatic action. Cogn Sci 18:513–549

    Article  Google Scholar 

  20. Leitgeb H (2001) Nonmonotonic reasoning by inhibition nets. Artif Intell 128:161–201

    Article  Google Scholar 

  21. Leitgeb H (2003) Nonmonotonic reasoning by inhibition nets II. Int J Uncertainty Fuzziness Knowl Based Syst 11:105–135

    Article  Google Scholar 

  22. Marr D (1982) Vision: a computational investigation into the human representation and processing visual information. Freeman, San Francisco

    Google Scholar 

  23. McCarthy J, Hayes PJ (1969) Some philosophical problems from the standpoint of artificial intelligence. In: Michie D, Meltzer B (eds) Machine intelligence, vol 4. Edinburgh University Press, Edinburgh, pp 164–183

    Google Scholar 

  24. Ramscar M, Yarlett D (2007) Linguistic self-correction in the absence of feedback: a new approach to the logical problem of language acquisition. Cogn Sci 31:927–960

    Article  Google Scholar 

  25. Rumelhart DE, McClelland JL (1986) Parallel distributed processing: explorations in the microstructure of cognition. MIT Press, Cambridge

    Google Scholar 

  26. Sima J, Orponen P (2003) General purpose computation with neural networks: a survey of complexity theoretic results. Neural Comput 15:2727–2778

    Article  Google Scholar 

  27. Smolensky P (1988) On the proper treatment of connectionism. Behav Brain Sci 11:1–23

    Article  Google Scholar 

  28. Treisman A (1988) Features and objects: the fourteenth Bartlett memorial lecture. Q J Exp Psychol Sect A: Hum Exp Psychol 40:201–237

    Article  Google Scholar 

  29. Triantafyllou MS, Triantafyllou GS (1995) An efficient swimming machine. Sci Am 272:64–70

    Article  Google Scholar 

  30. Tsotsos J (1990) Analyzing vision at the complexity level. Behav Brain Sci 13:423–469

    Article  Google Scholar 

  31. Wiener N (1948) Cybernetics: or control and communication in the animal and the machine. Hermann and Cie, Paris

    Google Scholar 

  32. Williams MA (2008) Representation = grounded information. In: Proceedings of the 10th Pacific Rim international conference on artificial intelligence, Hanoi, pp 473–484

    Google Scholar 

Download references

Acknowledgments

I gratefully acknowledge support from the Swedish Research Council for the Linnaeus environment Thinking in Time: Cognition, Communication and Learning. Thanks to Holger Andreas, Johan van Benthem, Alistair Isaac, Giovanni Pezzulo and Jakub Szymanik for helpful comments on an earlier version of the paper.

Author information

Authors and Affiliations

  1. Cognitive Science, Lund University, Lund, Sweden

    Peter Gärdenfors

Authors
  1. Peter Gärdenfors
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Gärdenfors .

Editor information

Editors and Affiliations

  1. University of Amsterdam Inst Logic,Language & Computation, Amsterdam, The Netherlands

    Alexandru Baltag

  2. Amsterdam, The Netherlands

    Sonja Smets

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Gärdenfors, P. (2014). Computational Complexity and Cognitive Science: How the Body and the World Help the Mind be Efficient. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_31

Download citation

Publish with us

Policies and ethics

Search

Navigation