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A guide to truth predicates in the modern era

Published online by Cambridge University Press:  12 March 2014

Michael Sheard
Michael Sheard*
Affiliation:
Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts 01002
*
Department of Mathematics, St. Lawrence University, Canton, New York 13617, E-mail: mshe@slumus.bitnet
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Extract

A reader coming anew to the recent work on languages which contain their own truth predicates may be perplexed by the simple question of where to begin. A first approach to the literature suggests a field which is alive and busy with investigations heading in many different directions, but there is much less indication of how various pieces fit together. There are at least two sources of this confusion. First, the literature is large and diffuse (as befits a subject which goes back over 2000 years); Visser's survey [33] aptly describes the literature as “vast but scattered, repetitive, and disconnected.” Moreover, recent interest in the field has led to a proliferation of research and publication; it seems that almost any issue of any philosophical logic journal from the mid-1980s contains some article on the topic. The second reason, in part a consequence of the first, is that while a typical article in print usually presents a good internal motivation, with clear reference to its immediate intellectual antecedents, its place in the broader picture may not be so easily discerned. The problem can be especially acute in presentations of axiomatic approaches, because decisions on certain basic questions can lie hidden in the formal and notational details which abound in any axiomatization.

In fact, though, the recent research on methods for handling self-referential truth can be seen as a body of work which is very well structured, one in which a few fundamental decisions suffice to locate any particular approach in its appropriate place on the landscape. My goal is to describe this structure and in particular to stress a few critical forks in the road, which will be the recurring metaphor throughout this paper. I will also pay particular attention to pointing out where the interesting technical and mathematical questions lie.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 1032 - 1054
Copyright
Copyright © Association for Symbolic Logic 1994

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References

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