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Finite Axiomatizability and Scientific Discovery

Published online by Cambridge University Press:  28 February 2022

Daniel N. Osherson  and
Scott Weinstein
Daniel N. Osherson
Affiliation:
Massachussetts Institute of Technology and University of Pennsylvania
Scott Weinstein
Affiliation:
Massachussetts Institute of Technology and University of Pennsylvania
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Extract

Imagine a scientist who examines an unending sequence of data about an unknown reality and responds to each datum by announcing a first-order theory in a fixed language L. The scientist hopes to determine the truth or falsity of every sentence of L, but he does not feel obliged to reach a stage in his investigation when all such questions will have been resolved. One way to represent the scientist's project is as follows. Let the unknown reality correspond to the L-structure S. Then the scientist hopes that for every sentence ϕ ∊ L, if S ╞ ϕ, then all but finitely many of the theories he emits, imply ϕ and do not imply - ϕ Following Kelly & Glymour (1987), we say in this case that the scientist “AE-identifies” S. The AE prefix signifies that for all ϕ ∊ L, there is a stage beginning at which the scientist's theories correctly decide ϕ.

Type
Part XIII. Formal Learning Theory
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 2: Volume Two: Symposia and Invited Papers 1988 , 1988 , pp. 409 - 412
Copyright
Copyright © 1989 by the Philosophy of Science Association

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Footnotes

1

Research support was provided by the Office of Naval Research under contract No. N00014-87-K-0401. Correspondence to D. Osherson, E10-006, M.I.T., Cambridge, MA 02139.

References

Kelly, K. and Glymour, C. (1987), “On convergence to the truth and nothing but the truth”, Philosophy of Science, in press.Google Scholar
Osherson, D. and Weinstein, S. (1986), “Identification in the limit of first order structures”, Journal of Philosophical Logic, 15, pp. 55–81.CrossRefGoogle Scholar
Osherson, D. and Weinstein, S. (1988), “Paradigms of truth detection”, Journal of Philosophical Logic, 18, pp. 1–42.CrossRefGoogle Scholar