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Gold's Theorem and Cognitive Science

Published online by Cambridge University Press:  01 January 2022

Kent Johnson
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Abstract

A variety of inaccurate claims about Gold's Theorem have appeared in the cognitive science literature. I begin by characterizing the logic of this theorem and its proof. I then examine several claims about Gold's Theorem, and I show why they are false. Finally, I assess the significance of Gold's Theorem for cognitive science.

Type
Research Article
Information
Philosophy of Science , Volume 71 , Issue 4 , October 2004 , pp. 571 - 592
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

I am grateful to Robert Matthews for stimulating my thinking about learnability; his positive influence can be seen throughout this paper. I am also grateful to Brian Skyrms, Geoffrey Pullum, and two anonymous reviewers for much useful feedback. All errors are mine.

References

Angluin, Dana (1980), “Inductive Inference of Formal Languages from Positive Data”, Inductive Inference of Formal Languages from Positive Data 45:117–135.Google Scholar
Bertolo, Stefano (ed.) (2001), Language Acquisition and Learnability. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Chomsky, Noam (1986), Knowledge of Language. Westport, CT: Praeger.Google ScholarPubMed
Cowie, Fiona (1997), “The Logical Problem of Language Acquisition”, The Logical Problem of Language Acquisition 111:17–51.Google Scholar
Cowie, Fiona (1999), What’s Within? Oxford: Oxford University Press.Google Scholar
Deacon, Terrence W. (1997), The Symbolic Species. New York: W. W. Norton.Google Scholar
Demopoulos, William (1989), “On Applying Learnability Theory to the Rationalism-Empiricism Controversy”, in Matthews, Robert and Demopoulos, William (eds.) Learnability and Linguistic Theory. Dordrecht: Kluwer, 77–88.10.1007/978-94-009-0955-7_4CrossRefGoogle Scholar
Elman, Jeffrey, Bates, Elizabeth, Johnson, Mark, Karmiloff-Smith, Annette, Parisi, Domenico, and Plunkett, Kim (1996), Rethinking Innateness. Cambridge, MA: MIT Press.Google Scholar
Feldman, Jerome (1972), “Some Decidability Results on Grammatical Inference and Complexity”, Some Decidability Results on Grammatical Inference and Complexity 20:244–262.Google Scholar
Gibson, Edward, and Wexler, Kenneth (1994), “Triggers”, Triggers 25:407–454.Google Scholar
Gold, E. Mark (1965), “Limiting Recursion”, Limiting Recursion 30:28–48.Google Scholar
Gold, E. Mark (1967), “Language Identification in the Limit”, Language Identification in the Limit 10:447–474.Google Scholar
Higginbotham, James (1984), “English Is Not a Context-Free Language”, English Is Not a Context-Free Language 15:225–234.Google Scholar
Hirsh-Pasek, Kathy, and Golinkoff, Roberta Michnick (1996), The Origins of Grammar: Evidence from Early Language Comprehension. Cambridge, MA: MIT Press.Google Scholar
Howe, Christine J (1993), Language Learning: a Special Case for Developmental Psychology? Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Jain, Sanjay, Osherson, Daniel, Royer, James S., and Sharma, Arun Kumar (1999), Systems That Learn, 2d ed. Cambridge, MA: MIT Press.10.7551/mitpress/6610.001.0001CrossRefGoogle Scholar
Kelly, Kevin (1996), The Logic of Reliable Inquiry. Oxford: Oxford University Press.Google Scholar
Marcus, Gary (1993), “Negative Evidence in Language Acquisition”, Negative Evidence in Language Acquisition 46:53–85.Google ScholarPubMed
Matthews, Robert J. (1984), “The Plausibility of Rationalism”, The Plausibility of Rationalism 81:492–515.Google Scholar
Matthews, Robert J. (2001), “Cowie”s Anti-Nativism”, Cowie”s Anti-Nativism 16:215–230.Google Scholar
Morgan, J. L. (1989), “Learnability Considerations and the Nature of Trigger Experiences in Language Acquisition”, Learnability Considerations and the Nature of Trigger Experiences in Language Acquisition 12:352–353.Google Scholar
Niyogi, Partha, and Berwick, Robert C. (1996), “A Language Learning Model for Finite Parameter Spaces”, A Language Learning Model for Finite Parameter Spaces 61:161–193.Google ScholarPubMed
Nowak, Martin A, Komarova, Natalia, and Niyogi, Partha (2001), “Evolution of Universal Grammar”, Evolution of Universal Grammar 291:114–118.Google ScholarPubMed
Osherson, Daniel, Stob, Michael, and Weinstein, Scott (1984), “Learning Theory and Natural Language”, Learning Theory and Natural Language 17:1–28.Google ScholarPubMed
Osherson, Daniel, Stob, Michael, and Weinstein, Scott (1986), Systems That Learn. Cambridge, MA: MIT Press.Google Scholar
Pinker, Steven (1989), Learnability and Cognition. Cambridge, MA: MIT Press.Google Scholar
Prinz, Jesse (2002), Furnishing the Mind. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Pullum, Geoffrey K., and Scholz, Barbara C. (2003), “Linguistic Models”, in Banich, Marie T. and Mack, Molly (eds.), Mind, Brain, and Language. Mahwah, NJ: Lawrence Erlbaum Associates, 113–141.Google Scholar
Shoenfield, Joseph (1993), Recursion Theory. New York: Springer-Verlag.10.1007/978-3-662-22378-9CrossRefGoogle Scholar
Valiant, L. G. (1984), “A Theory of the Learnable”, A Theory of the Learnable 27:1134–1142.Google Scholar
Wexler, Kenneth, and Culicover, Peter W. (1980), Formal Principles of Language Acquisition. Cambridge, MA: MIT Press.Google Scholar
Williams, Edwin (1987), “Introduction”, in Roeper, T. and Williams, E. (eds.) Parameter Setting. Dordrecht: Kluwer, vii–xix.Google Scholar