Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T07:26:32.706Z Has data issue: false hasContentIssue false

Disquotational truth and analyticity

Published online by Cambridge University Press:  12 March 2014

Volker Halbach*
Affiliation:
Universität Konstanz, Fachgruppe Philosophie, Postfach 5560 D 21, 78434 Konstanz, Germany, E-Mail: [email protected]

Abstract.

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences. yet not in the scope of negation, the system with the reflection schema for these T-sentences assumes the strength of the Kripke-Feferman theory KF. and thus of ramified analysis up to ε0.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Cantini, Andrea, Notes on formal theories of truth, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 35 (1989), pp. 97130.CrossRefGoogle Scholar
[2]Cantini, Andrea, A theory of truth formally equivalent to ID1, this Journal, vol. 55 (1990), pp. 244259.Google Scholar
[3]Cantini, Andrea, Logical frameworks for truth and abstraction. An axiomatic study, Studies in Logic and the Foundations of Mathematics, vol. 135, Elsevier, Amsterdam, 1996.Google Scholar
[4]Carnap, Rudolf, Meaning and necessity, University of Chicago Press, Chicago, 1947.Google Scholar
[5]Feferman, Solomon, Transfinite recursive progressions of axiomatic theories, this Journal, vol. 27 (1962), pp. 259316.Google Scholar
[6]Feferman, Solomon, Reflecting on incompleteness, this Journal, vol. 56 (1991), pp. 149.Google Scholar
[7]Field, Hartry, The deflationary conception of truth, Fact, science and morality (MacDonald, G. and Wright, C., editors), Blackwell, Oxford, 1986, pp. 55117.Google Scholar
[8]Field, Hartry, Deflationist views of meaning und content, Mind, vol. 103 (1994), pp. 247285.CrossRefGoogle Scholar
[9]Field, Hartry, Disquotational truth and factually defective discourse, The Philosophical Review, vol. 103 (1994), pp. 405452.CrossRefGoogle Scholar
[10]Field, Hartry, Deflating the conservativeness argument, Journal of Philosophy, vol. 96 (1999), pp. 533540.CrossRefGoogle Scholar
[11]Friedman, Harvey and Sheard, Michael, An axiomatic approach to self-referential truth, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 121.CrossRefGoogle Scholar
[12]George, Alexander, On washing the fur without wetting it: Quine, Carnap, and analyticity, Mind, vol. 109 (2000), pp. 124.CrossRefGoogle Scholar
[13]Halbach, Volker, A system of complete and consistent truth, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 311327.CrossRefGoogle Scholar
[14]Halbach, Volker, Axiomatische Wahrheitstheorien, Akademie Verlag, Berlin, 1996.CrossRefGoogle Scholar
[15]Halbach, Volker, Conservative theories of classical truth, Studia Logica, vol. 62 (1999), pp. 353370.CrossRefGoogle Scholar
[16]Halbach, Volker, Disauotationalism fortified, Circularity, definitions, and truth (Chapuis, André and Gupta, Anil, editors), Journal of the Indian Council of Philosophical Research, New Delhi, 2000, pp. 155176.Google Scholar
[17]Halbach, Volker, How innocent is deflationism?, Synthese, vol. 126 (2000), pp. 167194.CrossRefGoogle Scholar
[18]Halbach, Volker, Truth and reduction, Erkenntnis, vol. 53 (2000), pp. 97126.CrossRefGoogle Scholar
[19]Ketland, Jeffrey, Deflationism and Tarski's paradise, Mind, vol. 108 (1999), pp. 6994.CrossRefGoogle Scholar
[20]Kotlarski, Henryk, Full satisfaction classes: a survey, Notre Dame Journal of Formal Logic, vol. 32 (1991), pp. 573579.CrossRefGoogle Scholar
[21]Kripke, Saul, Outline of a theory of truth, Journal of Philosophy, vol. 72 (1975), pp. 690712.CrossRefGoogle Scholar
[22]Lachlan, Alistair, Full satisfaction classes and recursive saturation, Canadian Mathematical Bulletin, vol. 24 (1981), pp. 295297.CrossRefGoogle Scholar
[23]McGee, Vann, Truth, vagueness and paradox, Hackett Publishing, Indianapolis, 1991.Google Scholar
[24]McGrath, Matthew, Weak deflationism, Mind vol. 106 (1997), pp. 6998.CrossRefGoogle Scholar
[25]Quine, Willard van Orman, Two dogmas of empiricism, From a logical point of view, Harvard University Press, Cambridge, Massachusetts, 1964, second edition, pp. 2046.Google Scholar
[26]Reinhardt, William, Some remarks on extending and interpreting theories with a partial predicate for truth, Journal of Philosophical Logic, vol. 15 (1986), pp. 219251.CrossRefGoogle Scholar
[27]Shapiro, Stewart, Proof and truth: Through thick and thin, Journal of Philosophy, vol. 95 (1998), pp. 493521.Google Scholar
[28]Sosa, Ernest, The truth of modest realism, Philosophical Issues, vol. 3, Science and Knowledge (1993), pp. 7795.Google Scholar
[29]Takeuti, Gaisi, Proof theory, North Holland, Amsterdam, 1987, second edition.Google Scholar
[30]Tarski, Alfred, The concept of truth in formalized languages, Logic, semantics, metamathematics, Clarendon Press, Oxford, 1956, pp. 152278.Google Scholar
[31]Visser, Albert, Four-valued semantics and the liar, Journal of Philosophical Logic, vol. 13 (1984), pp. 181212.CrossRefGoogle Scholar