Jeffrey Ketland

Research

If you would be interested to read one of these papers, contact me by e-mail ( jeffrey.ketland (at) ed.ac.uk ) and I will send you a copy.

Journal Publications

[1] 1999: Deflationism and Tarski’s Paradise, Mind 108, 69-94.

This paper notes a conflict between the deflationary conception of truth and Gödel’s incompleteness results. Another paper presenting (independently) a very similar argument is Stewart Shapiro 1998, “Proof and Truth – Through Thick and Thin”, Journal of Philosophy 95. I wrote this paper when I was a graduate student at LSE in 1997. It contains some mistakes and unclarities. In particular, Theorem 1 is not quite correct as stated and the proof is a bit muddled. A corrigendum for Theorem 1 is here. The proof of Theorem 2, though correct, is also stated badly.

[2] 2000a: A Proof of the (Strengthened) Liar Formula in a Semantical Extension of Peano Arithmetic, Analysis 60/1, 1-4.

In the Tarskian theory of truth, the strengthened liar sentence is a theorem. More generally, any formalized truth theory which proves the full scheme Tr(<f>) ® f will prove the strengthened liar sentence. (This scheme is sometimes called (T-Out).)

[3] 2000b: Conservativeness and Translation-Dependent T-Schemes, Analysis 60/4, 319-328.

Certain translational T-schemes of the form Tr(<f>) « f(f), where f(f) can be almost any translation you like of f, will be a conservative extension of Peano arithmetic.

[4] 2002: Hume = Small Hume, Analysis 62/1, 92-3.

One page! We can modify Hume’s Principle in the same manner that George Boolos suggested for modifying Frege’s Basic Law V. This leads to the principle Small Hume. Then, we can show that Small Hume is interderivable with Hume’s Principle.

[5] 2003a: On Wright’s Inductive Definition of Coherence Truth for Arithmetic, Analysis 63/1, 6-15.

In “Truth – A Traditional Debate Reviewed” (1999), Crispin Wright proposed an inductive definition of “coherence truth” for arithmetic relative to an arithmetic base theory B. Wright’s definition is a notational variant of the usual Tarskian inductive definition, except for the basis clause for atomic sentences. This paper provides a model-theoretic characterization of the resulting sets of sentences “cohering” with a given base theory B.

[6] 2003b: Can a Many-Valued Language Functionally Represent its own Semantics?, Analysis 63/4, 292-297.

Tarski’s Indefinability Theorem can be generalized so that it applies to many-valued languages. This is relevant to the so-called “Revenge Problem”.

[7] 2004a: Bueno and Colyvan on Yablo’s Paradox, Analysis 64/2, 165-72.

This is a response to a paper “Paradox without satisfaction”, Analysis 63, 152-6 (2003) by Otavio Bueno and Mark Colyvan on Yablo’s paradox. I argue that this paper makes a number of errors which vitiate the paper. (For the technical details, see [12] below.)

[8] 2004b: Empirical Adequacy and Ramsification, BJPS 55, 287-300.

This paper gives a reasonably precise formulation of the Newman Problem for structural realism.

[9] 2005a: Some More Curious Inferences, Analysis 65/1, 18-24.

There are rather simple inferences which are valid, but whose formal proof requires rather a large number of symbols. This article mentions some simple examples using “cardinality quantifiers” (i.e., “there are exactly n Fs”). This might be a problem for nominalism.

[10] 2005b: Deflationism and the Gödelian Phenomena—Reply to Tennant, Mind 114, 75-88.

This is a reply to Neil Tennant’s “Deflationism and the Gödel Phenomena” (Mind 2002), itself a response to Shapiro 1998 and [1] above. Torkel Franzén also mentioned objections to Tennant 2002 on the Foundations of Mathematics discussion list (FOM). Tennant claims that someone who accepts a theory like PA may also prove Gödel sentences for PA, but Tennant gives no serious indication how this “proof” proceeds.

[11] 2005c : Jacquette on Grelling’s Paradox, Analysis 65/3, 258-60.

This is discussion of Dale Jacquette’s “Grelling’s Revenge”, Analysis 64, 251-6 (2004), where it is claimed that the simple theory of types is inconsistent. The error is pointed out.

[12] 2005d: Yablo’s Paradox and w-Inconsistency, Synthese 145, 295-307.

This paper gives a formalization of Yablo’s paradox (see Stephen Yablo 1993, “Paradox without self-reference”, Analysis). A certain formalization of the Yablo paradox, using merely the T-scheme, rather than the uniform version, leads to w-inconsistency rather than inconsistency.

[13] 2006: Structuralism and the Identity of Indiscernibles. Analysis 66/4, 303-15.

This is a contribution to the debate concerning the question whether a structuralist must provide a definition of identity. I provide some results concerning the definability of the identity relation in a structure.

[14] 2007: A Comment on Bermúdez Concerning the Definability of Identity. Analysis 67/4, 315-18.

This is reply to José Luis Bermúdez, who disputed (in Analysis 67, pp 112-6) a result mentioned in [13] above. A proof of the result is given.

[15] (Forthcoming): Identity and Indiscernibility. Review of Symbolic Logic.

This is a largely technical article setting out some results concerning the Quine indiscernbility formula and the definability of identity in relational structures.

[16] (Forthcoming): Truth. To appear in John Shand (ed.), Central Issues of Philosophy, Blackwell.

This is an introductory piece, surveying the main attempts to analyse the concept of truth, set at roughly first-year or second-year undergraduate philosophy level (requires a small level of logic).

Encyclopedia Articles

[1] 2005: Second-Order Logic, in D. Borchert (ed.), Macmillan Encyclopedia of Philosophy. 2^nd Revised Edition.

[2] 2005: Craig’s Theorem, in D. Borchert (ed.), Macmillan Encyclopedia of Philosophy. 2^nd Revised Edition.

Reviews

[1] 2000: Review of Geoffrey Stokes (1998), Popper: Philosophy, Politics and Scientific Method. In BJPS 51, 363-369.

A valuable book on Popper, but marred by social constructivist confusions about the notion of truth.

[2] 2001: Review of Stephen G. Simpson (1999), Subsystems of Second-Order Arithmetic. In BJPS 52, 191-195.

An excellent and comprehensive book, detailing a very important line of foundational research: Reverse Mathematics.

[3] 2005: Review of Paul Horwich (2005), From a Deflationary Point of View (Oxford). In Notre Dame Philosophical Reviews 2005.12.13.

A valuable collection of papers, with many of Horwich’s previous articles on deflationism and related topics.

Unpublished paper:

1996-2008: The Model-Theoretic Conception of Scientific Theories.

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Revised 4 October 2008.