Abstract
Clearly we can solve problems by thinking about them. Sometimes we have the impression that in doing so we use words, at other times diagrams or images. Often we use both. What is going on when we use mental diagrams or images? This question is addressed in relation to the more general multi-pronged question: what are representations, what are they for, how many different types are they, in how many different ways can they be used, and what difference does it make whether they are in the mind or on paper? The question is related to deep problems about how vision and spatial manipulation work. It is suggested that we are far from understanding what is going on. In particular we need to explain how people understand spatial structure and motion, and how we can think about objects in terms of a basic topological structure with more or less additional metrical information. I shall try to explain why this is a problem with hidden depths, since our grasp of spatial structure is inherently a grasp of a complex range of possibilities and their implications. Two classes of examples discussed at length illustrate requirements for human visualisation capabilities. One is the problem of removing undergarments without removing outer garments. The other is thinking about infinite discrete mathematical structures, such as infinite ordinals. More questions are asked than answered.
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References
Brachman, R. and Levesque, H. (Eds) (1985). Readings in knowledge representation. Los Altos, CA: Morgan Kaufmann.
Chalmers, D.J. (1996). The conscious mind: In search of a fundamental theory. Oxford: Oxford University Press.
Glasgow, J., Narayanan, H. and Chandrasekaran (Eds) (1995). Diagrammatic reasoning: Computational and cognitive perspectives. Cambridge, MA: MIT Press.
Hayes, P. (1985). The second naive physics manifesto. In J.R. Hobbs and R.C. Moore (Eds), Formal theories of the commonsense world. Norwood, NJ: Ablex, pp. 1–36. Also in [1], pp. 1–36.
Kant, I. (1781). Critique of pure reason. London: Macmillan. Translated (1929) by N. Kemp Smith.
Karmiloff-Smith, A. (1996). Internal representations and external notations: A developmental perspective. In D.M. Peterson (Ed.), Forms of representation: An interdisciplinary theme for cognitive science. Exeter: Intellect Books, pp. 141–151.
Kohler, W. (1927). The mentality of apes (2nd edn). London: Routledge & Kegan Paul.
Nelsen, R. (1993). Proofs without words: Exercises in visual thinking. Washingon, DC: Mathematical Association of America.
Peterson, D.M. (Ed.) (1996). Forms of representation: An interdisciplinary theme for cognitive science. Exeter: Intellect Books.
Sloman, A. (1971). Interactions between philosophy and AI: The role of intuition and non-logical reasoning in intelligence. In Proceedings of the 2nd IJCAI, London. Reprinted in Artificial Intelligence 1971, 209–225, and in J.M. Nicholas (Ed.) Images, perception, and knowledge. Dordrecht: Reidel, 1977.
Sloman, A. (1975). Afterthoughts on analogical representation. In R. Schank and B. Nash-Webber (Eds), Theoretical issues in natural language processing (TINLAP). Cambridge, MA: MIT Press, pp. 431–439. Reprinted in [1].
Sloman, A. (1978). The computer revolution in philosophy: Philosophy, science and models of mind. Hassocks, UK: Harvester Press.
Sloman, A. (1985). Why we need many knowledge representation formalisms. In M. Bramer (Ed.), Research and development in expert systems. Cambridge, UK: Cambridge University Press, pp. 163–183.
Sloman, A. (1989). On designing a visual system (towards a Gibsonian computational model of vision). Journal of Experimental and Theoretical AI 1(4):289–337.
Sloman, A. (1992). The emperor’s real mind. Artificial Intelligence 56:355–396. Review of Roger Penrose’s The emperor’s new mind: Concerning computers minds and the laws of physics.
Sloman, A. (1993a). The mind as a control system. In C. Hookway and D.M. Peterson (Eds), Philosophy and the cognitive sciences. Cambridge, UK: Cambridge University Press, pp. 69–110.
Sloman, A. (1993b). Varieties of formalisms for knowledge representation. Computational Intelligence 9(4):413–423 (special issue on computational imagery).
Sloman, A. (1996a). Actual possibilities. In L.C. Aiello and S.C. Shapiro (Eds), Principles of knowledge representation and reasoning: Proceedings of the fifth international conference (KR `96). Los Altos, CA: Morgan Kaufmann, pp. 627–638.
Sloman, A. (1996b). Towards a general theory of representations. In D.M. Peterson (Ed.), Forms of representation: An interdisciplinary theme for cognitive science. Exeter: Intellect Books, pp. 118–140.
Sloman, A. (2000a). Architectural requirements for human-like agents both natural and artificial. (What sorts of machines can love?). In K. Dautenhahn (Ed.), Human cognition and social agent technology. Advances in consciousness research. Amsterdam: John Benjamins, pp. 163–195.
Sloman, A. (2000b). Models of models of mind. In Proceedings of the symposium on how to design a functioning mind, AISB’00, Birmingham, UK.
Sloman, A. and Logan, B. (2000). Evolvable architectures for human-like minds. In G. Hatano, N. Okada and H. Tanabe (Eds), Affective minds. Amsterdam: Elsevier, pp. 169–181.
Sussman, G. (1975). A computational model of skill acquisition. New York: American Elsevier.
Wittgenstein, L. (1953). Philosophical investigations (2nd edn 1958). Oxford: Blackwell.
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Sloman, A. (2002). Diagrams in the Mind?. In: Anderson, M., Meyer, B., Olivier, P. (eds) Diagrammatic Representation and Reasoning. Springer, London. https://doi.org/10.1007/978-1-4471-0109-3_1
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DOI: https://doi.org/10.1007/978-1-4471-0109-3_1
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