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Induction, Conceptual Spaces and Ai

Published online by Cambridge University Press:  01 April 2022

Peter Gärdenfors
Peter Gärdenfors*
Affiliation:
Department of Philosophy Lund University
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Abstract

A computational theory of induction must be able to identify the projectible predicates, that is to distinguish between which predicates can be used in inductive inferences and which cannot. The problems of projectibility are introduced by reviewing some of the stumbling blocks for the theory of induction that was developed by the logical empiricists. My diagnosis of these problems is that the traditional theory of induction, which started from a given (observational) language in relation to which all inductive rules are formulated, does not go deep enough in representing the kind of information used in inductive inferences.

As an interlude, I argue that the problem of induction, like so many other problems within AI, is a problem of knowledge representation. To the extent that AI-systems are based on linguistic representations of knowledge, these systems will face basically the same problems as did the logical empiricists over induction.

In a more constructive mode, I then outline a non-linguistic knowledge representation based on conceptual spaces. The fundamental units of these spaces are “quality dimensions”. In relation to such a representation it is possible to define “natural” properties which can be used for inductive projections. I argue that this approach evades most of the traditional problems.

Type
Research Article
Information
Philosophy of Science , Volume 57 , Issue 1 , March 1990 , pp. 78 - 95
Copyright
Copyright © 1990 by the Philosophy of Science Association

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Footnotes

†

An earlier version of this article was presented at a conference on the Philosophy of Science, Dubrovnik, April 1987, and at an AI-workshop on Inductive Reasoning, Roskilde, April 1987. I wish to thank the participants of these meetings as well as Johan van Benthem, Jens Erik Fenstad, Lars Löfgren, David Makinson, Ilkka Niiniluoto, Claudio Pizzi and two anonymous referees for helpful comments.

References

REFERENCES

Berlin, B., and Kay, P. (1969), Basic Color Terms: Their Universality and Evolution. Berkeley: University of California Press.Google Scholar
Carnap, R. (1950), Logical Foundations of Probability. Chicago: Chicago University Press.Google Scholar
Carnap, R. (1971), “A Basic System of Inductive Logic, Part I”, in R. Carnap and R. C. Jeffrey (eds.), Studies in Inductive Logic and Probability. Berkeley: University of California Press, pp. 35–165.10.1525/9780520334250CrossRefGoogle Scholar
Carnap, R. (1980), “A Basic System of Inductive Logic, Part II,” in R. Carnap and R. C. Jeffrey (eds.), Studies in Inductive Logic and Probability, Vol. II. Berkeley: University of California Press, pp. 7–156.10.1525/9780520318328-002CrossRefGoogle Scholar
Foucault, M. (1970), The Order of Things. An Archeology of the Human Sciences. New York: Random House.Google Scholar
Gärdenfors, P. (1988), “Semantics, Conceptual Spaces and the Dimensions of Music”, to appear in V. Rantala, L. Rowell and E. Tarasti (eds.), Philosophy of Music. Helsinki: Acta Philosophica Fennica. Pp. 9–27.Google Scholar
Gärdenfors, P. (1990), “Mental Representation, Conceptual Spaces, and Metaphors”, to appear in Synthese.Google Scholar
Genesereth, M. and Nilsson, N. J. (1987), Logical Foundations of Artificial Intelligence. Los Altos: Morgan Kaufmann.Google Scholar
Goodman, N. (1955), Fact, Fiction, and Forecast. Cambridge, Mass.: Harvard University Press.Google Scholar
Goodman, N. (1961), “Safety, Strength, Simplicity”, Philosophy of Science 28: 150–151.10.1086/287795CrossRefGoogle Scholar
Goodman, N. (1966), The Structure of Appearance, 2nd ed. New York: Bobbs-Merrill.Google Scholar
Hempel, C. G. (1965), Aspects of Scientific Explanation, and Other Essays in the Philosophy of Science. New York: Free Press.Google Scholar
Holland, J. H., Holyoak, K. J., Nisbett, R. E., and Thagard, P. R. (1986), Induction: Processes of Inference, Learning, and Discovery. Cambridge, Mass.: The MIT Press.Google Scholar
Johnson, W. E. (1921), Logic. Part I. Cambridge: Cambridge University Press.Google Scholar
Lewis, D. K. (1973), Counterfactuals. Oxford: Blackwell.Google Scholar
Peirce, C. S. (1931), Collected Papers, Vol. II, ed. by Hartshorne, and Weiss, . Cambridge, Mass.: Belknap Press.Google Scholar
Pizzi, C. (1983), “Il problema dei determinabili nella logica del '900”, Atti del Convegno Internazionale di Storia della Logica. Bologna: Clueb, pp. 353–358.Google Scholar
Quine, W. V. O. (1960), Word and Object. Cambridge, Mass.: MIT Press.Google Scholar
Quine, W. V. O. (1969), “Natural Kinds,” in Ontological Relativity and Other Essays. New York: Columbia University Press, pp. 114–138.10.7312/quin92204-006CrossRefGoogle Scholar
Sloman, A. (1971), “Interactions between Philosophy and A.I.—the Role of Intuition and Non-logical Reasoning in Intelligence,” Proceedings 2nd IJCAI, London, reprinted in Artificial Intelligence, Vol. 2, 1971.Google Scholar
Stalnaker, R. (1979), “Anti-Essentialism,” Midwest Studies of Philosophy IV: 343–355.10.1111/j.1475-4975.1979.tb00385.xCrossRefGoogle Scholar
Stegmüller, W. (1973), Personelle und Statistische Wahrscheinlichkeit, Erster Halbband: Personelle Wahrscheinlichkeit und Rationale Entscheidung. Berlin: Springer-Verlag.Google Scholar