Jc Beall

[2045 Future Action Photo] 2025 ChatGPT4.0 Image of Jc Beall working in 2045

Philosophy, University of Notre Dame.

Philosophy Monographs

Formal Theories of Truth, OUP 2018 (w/ M. Glanzberg and E. Ripley). [Abstract] We present a user-friendly walk through some very simplified representatives of leading approaches in so-called formal truth theories.
Spandrels of Truth, OUP 2009 [Abstract] This book presents a fairly conservative glut-theoretic 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.

Philosophical Theology Monographs

The Contradictory Christ, OUP 2022. [Abstract] Advances a contradictory (glut-theoretic) account of the core christian doctrine of divine incarnation.
Divine Incarnation, OUP 2023 [Abstract] Sequel to The Contradictory Christ, this work advances a contradictory (glut-theoretic) account of trinitarian reality in christian theology.

Textbooks

2nd Edition Logic: The Basics, Routledge (with Shay Logan). [Abstract] This is a completely new edition of Logic: The Basics.
Logic: The Basics, 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 Ellie 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.

Articles: philosophy/logic

A note on FDE 'all the way up' (w/ C. Camrud).
Transparent truth as a logical property.
The simple argument for subclassical logic (and final online here).
Logic (w/ John P. Burgess).
God of the gaps (w/ A. J. Cotnoir).
There is no logical negation: true, false, both, neither.
Off-topic: a new interpretation of Weak Kleene logic.
Trivializing sentences and the promise of semantic completeness.
Non-detachable validity and deflationism.
Glutty theories and the logic of antinomies.
Philosophy of logic: 5 questions.
End of inclosure.
A simple approach for recapturing consistent theories in a paraconsistent setting.
Free of detachment: logic, rationality, and gluts.
Shrieking against gluts: the solution to the 'just true' problem.
LP+, K3+, FDE+, and their 'classical collapse'.
A note on detachment-freedom in LP (w/ Forster and Seligman).
Why Priest's reassurance is not reassuring.
Finding tolerance without gluts.
Two flavors of Curry's paradox (with Julien Murzi).
Future contradictions.
Non-classical truth theories (with Dave Ripley).
Dialetheists against Pinocchio.
Multiple-conclusion LP and default classicality.
A neglected reply to Prior's dilemma.
Adding to relevant restricted quantification.
Can u do that? (with G. Priest and Z. Weber).
On the ternary relation and conditionality (with 10 others).
Deflated truth pluralism.
Truth, necessity, and abnormal worlds.
Prolegomenon to future revenge.
Vague intensions.
Knowability and odd epistemic possibilities.
Where the paths meet (w/ Michael Glanzberg).
Truth and paradox: a philosophical sketch.
Not so deep inconsistency (with Graham Priest).
Relevant restricted quantification (with 4 authors).
'Unsettledness' in a bivalent language.
Modeling the 'ordinary view'.
At the intersection of truth and falsity.
True and false -- as if.
True, false, and paranormal.
Analehteism and Dialetheism (with Dave Ripley).
Transparent disquotationalism.
Minimalism, epistemicism, and paradox (w/ B. Armour-Garb).
Should Deflationists Be Dialetheists? (w/ B. Armour-Garb).
Can deflationists be dialetheists? (w/ B. Armour-Garb).
Further remarks on truth and contradiction (w/ Armour-Garb).
On the singularity theory of denotation.
On the identity theory of truth.
Logical Pluralism (with Greg Restall).
On mixed inferences and pluralism about truth predicates.
On truthmakers for negative truths.
Negation's holiday: aspectival dialetheism.
Simple liar without bivalence? (with Otavio Bueno).
Defending Logical Pluralism (with Greg Restall).
Looking for contradictions (with Mark Colyvan).
Existential claims and Platonism.
Heaps of gluts and Hyde-ing the sorites (with Mark Colvan).
Deflationism and gaps: untying 'not's in the debate.
Is Yablo's paradox non-circular?
A neglected deflationist approach to the liar.
Completing Sorensen's menu: a yabloesque curry.
From full-blooded platonism to really full-blooded platonism.
Minimalism, gaps, and the Holton conditional.
A neglected response to the Grim result.

A Different Project: Analytic Theology

Christ -- A Contradiction. [Abstract] Forthcoming in the Journal of Analytic Theology

This paper advances and defends a `Contradictory Christology'.
A neglected QUA solution (w/ J. Henderson). [Abstract] Forthcoming in Faith and Philosophy

NB: this is not the final version!!!

We advance a neglected QUA solution to the fundamental problem of Christology. Our chief aim is to put the view on the theological table, leaving future debate to tell its ultimate fate. After presenting the view we measure it against standard problems that confront extant QUA views and also against objections peculiar to the proposed view.
God of the gaps (w/ A. J. Cotnoir). [Abstract] Forthcoming: Analysis, Comments still welcome!

Traditional monotheism has long faced logical puzzles (omniscience, omnipotence, and more). We present a simple but plausible `gappy' framework for addressing these puzzles. By way of illustration we focus on God's alleged stone problem. What we say about the stone problem generalizes to other familiar `paradoxes of omni- properties', though we leave the generalization implicit.

Work (once) in progress (or talk-based notes)

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 Ellie 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 Ellie 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.

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 Ellie Ripley).
Vagueness and Contradiction by Roy Sorensen

General-Public Lectures

Logic, paradox, and truth
[Abstract] These are Beamer notes from a 30-minute-ish public (i.e., general-public) lecture in Dunedin, New Zealand. The aim was to give a broad (if misleading) sketch of logic, broadly construed, and the impact that paradoxes can have on logical theories.

3-16AM Magazine

In-Sight PUblishing Magazine

Interview

Night of Philosophy

Neat NYC Evening

Exact Philosophy

Society for Exact Philosophy

Former Students

Recent Teaching

S25: /From a subclassical point of view/
F24: Intro to logical tools in philosophy

Some Teaching

F17: Philosophical theology
F17: 5307: Intro to logical tools in philosophy

Some Teaching

F13: Philosophical Logic
F12: Detachment freedom!
F12: Philosophical Logic
S12: Philosophy of Time
F11: Philosophical logic
S11: Introductory Logic (UG)
F10: Philosophical logic
S10: Introductory Logic (UG)
F09: Truth and Paradox
F09: Introductory Logic (UG)
S09: Diagonalization
F08: Philosophical logic
S08: Logic of truth
S07: Metalogic non-classical
S06: Computability
F05: Language, truth, and meaning
F05: History of analytic philosophy

* Lifted Site Design

Cribbed from: Ted Sider
[More on this:] Ted's site structure is too useful not to use. I hope to add a bit of novelty eventually. For now, see source and style files for more information.

* Lifted Site Ideas

Antony Eagle
[More on this:] Ant's site is really useful too, but I basically just grabbed the expand idea from him.

Erdos Number

My Erdös number is 3:

Logicians' Liberation

League

Logic Scene Links