Monographs
- ** Spandrels of Truth, OUP 2009 [Abstract] This book presents a fairly conservative dialetheic truth theory within a broader `transparent' conception of truth.
- Logical Pluralism, OUP 2005 (with Greg Restall). [Abstract] This is our manifesto on logical pluralism. We argue that the notion of logical consequence doesn't pin down a unique deductive consequence relation; rather, it yields many of them. In particular, we argue that broadly classical, intuitionistic and relevant accounts of deductive logic are genuine logical consequence relations. We should not search for One True Logic, since there are many.
Textbooks
- ** Logic: The Basics (LTB), Routledge 2010. [Abstract] This is a very gentle introduction to some common elementary logics from a wholly 'semantic' (more accurately: model-theoretic) perspective. This book takes you from step zero up through classical first-order logic (semantically construed) and a few of its well-known (non-classical) sublogics, and also presents basics of free logic and a bit of modal logic (all, again, semantically construed).
- ** LTB Supplement, Routledge 2011 (with Dave Ripley). [Abstract] This is a supplement to Logic: The Basics that contains answers to exercises and a short presentation of adequate tableau systems for the canvassed logics.
- Possibilities and Paradox, OUP 2003 (with Bas C. van Fraassen). [Abstract] This is a gentle-but-rigorous (or rigorous enough) introduction to some basic philosophical logics (i.e., formal logics motivated by philosophical problems). The main aim is to show you how to construct philosophically useful 'model languages', which is a chief aim in philosophical logic.
Edited Collections
- Revenge of the Liar, OUP 2007. [Abstract] This volume focuses on paradoxes and the notorious phenomenon of 'revenge' for would-be solutions to paradox.
- The Law of Non-Contradiction, OUP 2004/6. [Abstract] This volume, jointly edited with Graham Priest and Brad Armour-Garb, focuses on general (e.g., logical, metaphysical, epistemological) issues concerning 'true falsehoods' or, equivalently, 'true contradictions' or, equivalently, 'truths with a true negation'. There's a broad introductory essay that sets things up. (Hbk 2004; pbk 2006.)
- The Monist: Truth 89:1 January 2006. [Abstract] I was the (advisory) editor for this volume. There's a fairly even balance between 'nature' and 'logic' issues surrounding truth.
- Deflationism and Paradox, OUP 2005. [Abstract] This volume, edited with B. Armour-Garb, focuses on deflationary options for dealing with semantic paradox (however 'deflated' the 'semantics' may be).
- Deflationary Truth, OUP 2005 (with B. Armour-Garb). [Abstract] This volume, edited with Brad Armour-Garb, collects classic essays on deflationary truth, and contains additional 'afterthoughts' by authors. There's a fairly useful introductory essay.
- Liars and Heaps, OUP 2004. [Abstract] This volume focuses on both semantic and soritical paradoxes.
Work in progress (or talk-based notes)
- LP, K3, and their 'classical collapse'. [Abstract] Under review. Comments welcome!
This paper generalizes the propositional 'collapse results' given in my 2011 Review of Symbolic Logic paper on multiple-conclusion LP. (This is part of a larger project that makes philosophical use of such collapse results.) - Truth without detachment (Beamer). [Abstract] These are Beamer slides from a recent MCMP talk in Munich. (nb: there are a few minor errors which I haven't corrected.)
This talk presents one way of thinking about my current 'truth without detachment' project. - Time for curry (with Dave Ripley). [Abstract] This paper presents a novel (temporal) version of curry paradox, which, we argue, raises an apparent dilemma for certain (explanatory-non-normal-worlds) contraction-free responses to Curry's paradox.
- 'B+ tableau' (with Dave Ripley). [Abstract] Draft posted soon. We explore a novel semantics (in the family of star-simplified semantics) for an extension of the basic relevant logic B. We give a sound and complete tableau system for the semantics. What we really want to establish is whether the resulting logic is so-called depth-relevant.
- Necessity, Normality, and Contraction. [Abstract] This is a Beamer presentation from 2009 AAP and 2009 Logica in which I discuss how necessity behaves in certain semantic settings suitable for so-called dialetheic truth theories. (The results are implied by the 'overspill' result at the end of the 'Talk about normality' handout below.)
- Talk about normality: an 'overspill' result. [Abstract] (These notes are not self-contained. The main 'overspill' result, written up in a soon-to-be-posted paper, is at the very end.
Logics useful for unrestricted semantic theories (truth theories, semantical property theories, etc.) are robustly contraction-free. Natural semantics for such logics are so-called non-normal-world semantics. This paper notes that one cannot add anything to the logic that, in effect, would pick out only normal worlds. The paper closes with questions about the philosophical import of this result. - Duo Worlds. [Abstract] These notes sketch a way of looking at the so-called ternary semantics that highlights the similarities with standard binary-access worlds semantics. (This might just get gobbled up in the 'Ternary Relation' paper below.)
These are just notes from a recent departmental brown-bag talk.
Papers
- A note on detachment-freedom in LP (w/ Forster and Seligman). [Abstract] Final version forthcoming in Notre Dame Journal of Formal Logic.
One approach to paradox (which I now favor!) rejects the existence of any detachable connective (in any non-trivial sense). In this short paper, we don't concern ourselves with the attractions (or otherwise) of such detachment-free approaches to paradox. Instead, we give a simple proof that the logic LP is suitable for such an approach (i.e., that it is detachment-free). We do this via a nice variable-sharing result. - Why Priest's reassurance is not reassuring. [Abstract] Forthcoming in Analysis July 72:3 (cite only published version!).
Priest has long advocated his minimally inconsistent LP (viz., MiLP) as the 'universal logic' (for standard extensional connectives), which enjoys LP as its weaker (monotonic) core. In this paper, I show that MiLP faces a dilemma: either it is (plainly) unsuitable as a universal logic or its role as a 'universal logic' (indeed, its role full stop) is a mystery. - Finding tolerance without gluts. [Abstract] The final version of this paper is forthcomiing in Mind. This is not the final version.
Zach Weber (Mind, 2010) has recently advanced a glutty (dialetheic) approach to the sorites: the truth about the penumbral region of a soritical series is inconsistent. Joining Weber, advocating essentially the same approach, are Mark Colyvan (Dyke, 2009) and Graham Priest (NDJFL, 2010). The major benefit of such a glut-based approach is preserving the truth of all sorites premises while nonetheless avoiding, in a principled fashion, the absurdity of the sorites conclusion(s). I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, this result weighs heavily against the proposed glutty approach, at least given the default-consistency principle that all target glutty philosophers accept: posit gluts only if there's no consistent theory that enjoys the same virtues as the would-be glutty solution. - Two flavors of Curry's paradox (with Julien Murzi). [Abstract] A final version is forthcoming in The Journal of Philosophy. This is not the final version.
This is a paper that goes beyond the difficulties involved in truth-preservation claims about validity; it discusses 'validity curry' and its apparent upshot for recent theories (e.g., Beall, Brady, Field, Priest). More details to be posted soon, including a draft. - Future contradictions. [Abstract] This paper, forcoming in final form in Australasian Journal of Philosophy, sketches a novel view of the future and future-contingent claims: the future contains gluts, but the present `filters' them out.
- Non-classical truth theories (with Dave Ripley). [Abstract] This is a paper for the Oxford Handbook of Truth, edited by Michael Glanzberg. (This is not the final version.) We aim to concisely present, in a user-friendly fashion, the basic ideas behind four prominent avenues for non-classical truth theories (glutty, gappy, contraction-free, and non-transitive). We'd be delighted to get feedback on this one.
- Dialetheists against Pinocchio. [Abstract] This paper, forthcoming in final form in Analysis, responds to Eldridge-Smith's Analysis paper called 'Pinocchio against the dialetheists' (Analysis 71(2):306–308, 2011).
- Multiple-conclusion LP and default classicality. [Abstract] NB: This is NOT the final, published version, which is forthcoming in Review of Symbolic Logic.
Non-classical truth (etc) theorists tend reflect a default-classicality assumption. In this paper (the first in a series) I advance a simple new (monotonic) way in which to understand such 'default classicality' by first presenting a multiple-conclusion version of LP (what I call 'LP+') and, in turn, sketching a perspective on the use of multiple-conclusion logics that reflects a natural sort of 'defeasibility of inference'. - A neglected reply to Prior's dilemma. [Abstract] This paper, forthcoming in James MacLauren, ed., Rationis Defensor (Springer, 2012) offers a novel reply to Prior's dilemma (for the Is/Ought principle), advocating a so-called Weak Kleene framework motivated by two not uncommon thoughts in the debate, namely, that ought statements are identified as those that use `ought', and that ought statements are `funny' in ways that is statements aren't (e.g., perhaps sometimes being `gappy' with respect to truth and falsity).
- Adding to relevant restricted quantification. [Abstract] This paper follows up on (and presupposes) a joint paper called 'Relevant Restricted Quantification' (JPL, 2006). (See below.)
In my Spandrels of Truth book, I take on an objection by Vann McGee to the truth theory advanced in the book. The objection, in the end, points to problems involving restricted generalizations (problems that are particularly bad for the philosophical position I advance in the book). In the paper here, I present one reply to McGee, but do so in a much more theory-neutral fashion than in the book (and, in fact, present the matter independently of McGee's objection, focusing on a different objection due to David Ripley). - Can u do that? (with G. Priest and Z. Weber). [Abstract] This paper, now available in final form in Analysis, responds to Greg Restall's forthcoming Analysis paper called 'On t and u and what they can do'.
- On the ternary relation and conditionality (with 10 others). [Abstract] This paper, forthcoming in Journal of Philosophical Logic, tackles the problem of putting (intuitive, familiar-ish) philosophical flesh on the ternary relation invoked in various relevant logics. We offer discussion and at least three novel accounts. [The we is a genuine us -- 11 authors (!), notably, Beall, Brady, Dunn, Hazen, Mares, Meyer, Priest, Restall, Ripley, Slaney, and Sylvan (formerly Routley).]
- Deflated truth pluralism. [Abstract] This paper (possibly with some revisions) is forthcoming in Truth Pluralism (OUP), ed. N. Pedersen and Cory Wright. I simply sketch one sort of 'deflated' pluralism about truth.
- Truth, necessity, and abnormal worlds. [Abstract] In Pelis, ed., Logica Yearbook09 (from the Logica-09 conference).
This paper discusses an issue that arises when adding standard philosophical modalities (like necessity) into so-called depth-relevant truth or property theories. (There's a more general result that I will publish soon.) This paper is based on the Beamer slides available in the in-progress section above. - Prolegomenon to future revenge. [Abstract] In Jc Beall, ed., Revenge of the Liar OUP 2007.
This paper attempts to set up issues of the Liar's revenge in a new light, while also setting the stage for chapters in the given volume. - Vague intensions. [Abstract] In Dietz and Moruzzi, eds., Cuts and Clouds (OUP, 2009), pp. 187-199.
This paper offers a (non-profound) proposal on reframing how we look at the apparent 'full tolerance' (no cutoffs) and 'utility' (some cutoffs) of vague predicates.
(NB: these are obviously proofs, and not the final copy.) - Knowability and odd epistemic possibilities. [Abstract] In Joe Salerno, ed., New Essays on Knowability OUP 2009.
[NB: this pdf is not the final version.]
This paper carries on an earlier paraconsistent idea that was published in the AJP (see bib for details). Here, I introduce a paraconsistent, non-normal worlds approach to knowability and the given 'paradox'. - Where the paths meet (w/ Michael Glanzberg). [Abstract] The study of truth is often seen as running on two separate paths: the nature path and the logic path. The former concerns metaphysical questions about the `nature', if any, of truth. The latter concerns logic and the paradoxes. It is often assumed that these two paths do not meet, and the two concerns are independent of each-other. In this paper, we argue that the paths do in fact meet; in particular, that the nature path impacts the logic path. We argue that what one can and must say about the logic of truth and the Liar paradox is influenced, or even in some cases determined, by what one says about the metaphysical nature of truth.
- Truth and paradox: a philosophical sketch. [Abstract] In D. Jacquette, ed., Philosophy of Logic (Oxford: Elsevier), 2007. (This is part of the Woods et al. Handbook of Phil. Science series.)
I give a narrow, transparent-truth-related discussion of truth and paradox. This essay was largely taken from early drafts of my Spandrels of Truth (OUP, 2009). - Not so deep inconsistency (with Graham Priest). [Abstract] This is a discussion, from a heavily dialetheic perspective, of Matti Eklund's pioneering 'inconsistency view'. (Matti has a reply in the Australasian Journal of Logic.)
- Relevant restricted quantification (with 4 authors). [Abstract] This is joint with Ross Brady, Allen Hazen, Graham Priest, and Greg Restall.
We review a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional. (NB: a newer idea is in Ch. 5 of Spandrels of Truth, and under the ms 'Adding to relevant restricted quantification' (see Work In Progress).) - 'Unsettledness' in a bivalent language. [Abstract] In In Heather Dyke, ed., From Truth to Reality: Essays on the Logic and Nature of Truth, Routledge 2008.
This paper suggests a way of accommodating the appearance of ‘gaps’ or ‘unsettledness’ in a language in which we have bivalence or LEM (with transparent truth). [NB: I now see that the core of this idea goes back a long, long way to so-called predicate-negation phenomena. It is not clear to me that current theories – particularly, theories of the logic – are worked out in ways that are compatible with 'transparent truth' (for which notion see my Spandrels of Truth), but I hope to look at this in the future if time reveals itself... - Modeling the 'ordinary view'. [Abstract] In Greenough and Lynch, eds., Truth and Realism (Oxford 2006).
This paper discusses what Crispin Wright (same volume) calls 'the ordinary view' of taste and similar matters. - At the intersection of truth and falsity. [Abstract] In Priest et al., eds., The Law of Non-Contradiction (Oxford 2007).
This paper very gently and broadly sets up issues concerning non-contradiction and so-called dialetheism. It can be used as a sort of 'first step' into such issues. - True and false -- as if. [Abstract] In Priest et al., eds., The Law of Non-Contradiction (Oxford 2007).
This paper advocates a sort of 'as-if' attitude towards truth and true falsehoods. (These ideas have been superseded by those in Spandrels of Truth, but there's still a few interesting things here.) - True, false, and paranormal. [Abstract] This paper, reprinted (with changes for the better) as the final appendix in Spandrels of Truth, advocates a non-dialetheic transparent truth theory. In some respects, the paper serves as an argument against dialetheism: it agrees that our 'semantic categories' must overlap, but disagrees with the idea that the truth and falsity need overlap.
- Analehteism and Dialetheism (with Dave Ripley). [Abstract] We explore a non-dialetheic but paraconsistent truth theory (a sort of dual of standard LP account).
- Transparent disquotationalism. [Abstract] In Beall and Armour-Garb, eds., Deflationism and Paradox (OUP, 2008).
I advocate a dialetheic theory of transparent truth. This paracomplete (but with an exhaustive negation-like device) approach has since collapsed into a non-paracomplete theory spelled out in Spandrels of Truth. (The collapse emerged because the only models wound up being so-called LP/BX-ish models.) - Minimalism, epistemicism, and paradox (w/ B. Armour-Garb). [Abstract]In Beall and Armour-Garb, eds., Deflationism and Paradox (OUP, 2008).
We discuss Paul Horwich's views on paradox. (For a very good response of sorts to this paper, see Greg Restall's paper in the same volume.) - Should Deflationists Be Dialetheists? (w/ B. Armour-Garb). [Abstract] Noûs Volume 37, Issue 2 , Pages 303-324, 2003 Blackwell Publishing Inc.
- Can deflationists be dialetheists? (w/ B. Armour-Garb). [Abstract] We respond to Keith Simmons' JPL claims to the contrary.
- Further remarks on truth and contradiction (w/ Armour-Garb). [Abstract] We extend Graham Priest's discussion (same journal) by giving some further considerations on truth and contradiction.
- On the singularity theory of denotation. [Abstract] In Beall, ed., Liars and Heaps (OUP, 2003).
I point to what I think are fairly major problems concerning Keith Simmons' singularity theory of denotation. - On the identity theory of truth. [Abstract] This paper notes that an apparent difficulty, raised by Stewart Candlish, for the identity theory of truth is not a difficulty. Whether one should actually endorse the identity theory along Candlish lines is something I do not touch. (I have firm views, but they're not discussed here.)
- Logical Pluralism (with Greg Restall). [Abstract] This is our manifesto on logical pluralism. Our book Logical Pluralism expands on this paper.
- On mixed inferences and pluralism about truth predicates. [Abstract] I point out that the problem of mixed inferences for 'truth pluralism' seems not to be a problem. (I regret not discussing the role of a transparent truth predicate.)
- On truthmakers for negative truths. [Abstract] I respond, on behalf of truthmaker theorists, to an objection based on 'negative truthmakers'.
- Negation's holiday: aspectival dialetheism. [Abstract] In D. DeVidi and T. Kenyon, eds., A Logical Approach to Philosophy: Essays in Honour of Graham Solomon (Springer 2006).
This advocates a certain theory of negation for certain theories of truth. The key idea was independently (and previously) discovered by the so-called adaptive logicians, who have explored the target (non-monotonic) ideas in great detail. One value of this paper, perhaps, is that it lends a fairly natural philosophical story about such 'adaptive' behavior. - Simple liar without bivalence? (with Otavio Bueno). [Abstract] We discuss whether, as some have claimed, the so-called simple-liar derivation goes through without bivalence. (I'm no longer sure that I agree with the conclusion.)
- Defending Logical Pluralism (with Greg Restall). [Abstract] Appears on pages 1–22 in Logical Consequence: Rival Approaches, Proceedings of the 1999 Conference of the Society of Exact Philosophy (Stanmore: Hermes, 2001), John Woods and Bryson Brown (editors), ISBN 1-903398-17-5.
This paper is a defence of logical pluralism against a number of objections, primarily from Graham Priest in his article 'Logic: One or Many' in the same volume. - Looking for contradictions (with Mark Colyvan). [Abstract] We (further) explore the issue of vagueness and contradictions in the world. (I've since become much more conservative, as witnessed in Spandrels of Truth.)
- Existential claims and Platonism. [Abstract] This paper responds to Colin Cheyne's new anti-platonist argument according to which knowledge of existential claims -- claims of the form such-and-so exist -- requires a caused connection with the given such-and-so. If his arguments succeed then nobody can know, or even justifiably believe, that acausal entities exist, in which case (standard) platonism is untenable. I argue that Cheyne's anti-platonist argument fails.
- Heaps of gluts and Hyde-ing the sorites (with Mark Colvan). [Abstract] We raise questions about Dom Hyde's paper 'Heaps of Gluts' (Mind).
- Deflationism and gaps: untying 'not's in the debate. [Abstract] This paper, while ignoring paradoxes, points out that, contrary to debates, deflationists can be 'gap theorists' by simply acknowledging additional negation-like devices. (An unmentioned alternative: add an additional notion of truth, definable in terms of negation and deflationary truth. As it turns out, this is not far from the route that Hartry Field takes, though avoiding paradox-driven triviality requires more to the story!)
- Is Yablo's paradox non-circular? [Abstract] This paper raises questions about whether Yablo's paradox -- or yabloesque paradoxes in general -- are really non-circular as advertised. (I think that there are some interesting things here, but I think that Roy Cook does a nice job getting to the heart of the matter. See his paper in the Monist volume that I edited on truth.)
- A neglected deflationist approach to the liar. [Abstract] This paper, motivated by brief discussion with Kim Sterelny back in 1999, suggests that deflationists might appear to be tailor-made for the notorious 'meaningless' reply. (I think that when details of our vaguely stated 'deflationist' are made clearer, this sort of line is not viable.)
- Completing Sorensen's menu: a yabloesque curry. [Abstract] Roy Sorensen's discussion of Yablo's paradox failed to note one of the (if not the) most difficult paradoxes: Curry's. I give a yabloesque Curry paradox.
- From full-blooded platonism to really full-blooded platonism. [Abstract] I argue that if you're going to follow Mark Balaguer into 'full-blooded platonism', you ought to go all the way.
- Minimalism, gaps, and the Holton conditional. [Abstract] Richard Holton opens an avenue for minimalists to embrace gaps. I argue that, for logical-cum-paradoxical reasons (viz., Curry!), his proposal won't work.
- A neglected response to the Grim result. [Abstract] Patrick Grim argues that there's no set of all truths. Grim may be (in fact, I think is) right, but his 'proof' fails to cover a not implausible reply. This paper gives the reply.
Stanford Encyclopedia Entries
- Curry's Paradox
- Liar Paradox (with Michael Glanzberg)
- Logical Consequence (with Greg Restall)
NDPR Reviews
- Modal Logic for Philosophers by James Garson
- Towards Non-Being by Graham Priest
- Oxford Handbook of Phil Maths and Logic ed. Stewart Shaprio.
- Paraconsistency and Paradox by John Woods (reviewed with Dave Ripley).
- Vagueness and Contradiction by Roy Sorensen
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