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RESTRICTIVENESS RELATIVE TO NOTIONS OF INTERPRETATION

Published online by Cambridge University Press:  12 April 2016

LUCA INCURVATI  and
BENEDIKT LÖWE
LUCA INCURVATI*
Affiliation:
Universiteit van Amsterdam
BENEDIKT LÖWE*
Affiliation:
Universiteit van Amsterdam & Universität Hamburg
*
*INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITEIT VAN AMSTERDAM POSTBUS 94242, 1090 GE AMSTERDAM, THE NETHERLANDS E-mail: l.incurvati@uva.nl
†INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITEIT VAN AMSTERDAM POSTBUS 94242, 1090 GE AMSTERDAM, THE NETHERLANDS E-mail: b.loewe@uva.nl
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Abstract

Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy’s definition. We look at Maddy’s formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy’s original notion, but fixes the issues raised by Hamkins. Our work brings to light additional structural issues that we also discuss.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 238 - 250
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

BIBLIOGRAPHY

Aczel, P. (1988). Non-Well-Founded Sets. CSLI Lecture Notes, Vol. 14. Stanford, CA: CSLI.Google Scholar
Ahlbrandt, G., & Ziegler, M. (1986). Quasi-finitely axiomatizable totally categorical theories. Annals of Pure and Applied Logic, 30(1), 63–82.CrossRefGoogle Scholar
de Bouvère, K. L. (1965). Logical synonymity. Indagationes Mathematicae, 27, 622–629.CrossRefGoogle Scholar
Hamkins, J. D. (2013). A multiverse perspective on the axiom of constructibility. In Chong, C., Feng, Q., Slaman, T. A., and Woodin, W. H., editors. Infinity and Truth. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 25. Singapore: World Scientific, pp. 25–45.CrossRefGoogle Scholar
Kanamori, A. (2003). The Higher Infinite, Large cardinals in set theory from their beginnings (second edition). Springer Monographs in Mathematics. Berlin: Springer-Verlag.Google Scholar
Löwe, B. (2001). A first glance at non-restrictiveness. Philosophia Mathematica, 9(3), 347–354.CrossRefGoogle Scholar
Löwe, B. (2003). A second glance at non-restrictiveness. Philosophia Mathematica, 11(3), 323–331.Google Scholar
Maddy, P. (1988a). Believing the axioms. I. Journal of Symbolic Logic, 53(2), 481–511.Google Scholar
Maddy, P. (1988b). Believing the axioms. II. Journal of Symbolic Logic, 53(3), 736–764.Google Scholar
Maddy, P. (1997). Naturalism in mathematics. New York: The Clarendon Press Oxford University Press.Google Scholar
Maddy, P. (1998). V = L and MAXIMIZE. In Makowsky, J. A. and Ravve, E. V., editors. Logic Colloquium ’95, Papers from the colloquium held as part of the European Summer Meeting of the Association for Symbolic Logic in Haifa, August 9–18, 1995. Lecture Notes Logic, Vol. 11. Berlin: Springer, pp. 134–152.Google Scholar
Tarski, A., Mostowski, A., & Robinson, A. (1953). Undecidable Theories. Amsterdam: North-Holland.Google Scholar
Visser, A. (2006). Categories of theories and interpretations. In Enayat, A., Kalantari, I., and Moniri, M., editors. Logic in Tehran, Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic held in Tehran, October 18–22, 2003. Lecture Notes in Logic, Vol. 26. La Jolla, CA: Association for Symbolic Logic, pp. 284–341.Google Scholar