*Bulletin of Symbolic Logic*, 52(2):145-186, 2023.@article{vdrg:ctt, author = {Emma van Dijk and David Ripley and Julian Gutierrez}, title = {Core type theory}, journal = {Bulletin of Symbolic Logic}, year = {2023}, volume = {52}, number = {2}, pages = {145--186} }

*Review of Symbolic Logic*, 15(1):259-275, 2022.We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.

@article{fgr:clco, author = {Rohan French and Patrick Girard and David Ripley}, title = {Classical counterpossibles}, journal = {Review of Symbolic Logic}, year = {2022}, volume = {15}, number = {1}, pages = {259--275} }

*Journal of Philosophical Logic*, 51(6):1233-1259, 2021.The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more and more classical at each level. I think this seeming is misleading: for certain purposes, anyhow, metainferential hierarchies give us no reason to move on from ST. ST is indeed only the first step on a grand metainferential adventure; but one step is enough. This paper aims to explain and defend that claim. Along the way, I take the opportunity also to develop some formal tools and results for thinking about metainferential logics more generally.

@article{ripley:osie, author = {David Ripley}, title = {One step is enough}, journal = {Journal of Philosophical Logic}, year = {2021}, volume = {51}, number = {6}, pages = {1233--1259} }

Tolerant reasoning: nontransitive or nonmonotonic?

*Synthese*, 199:681-705, 2021.The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.

@article{cervr:trnn, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Tolerant reasoning: nontransitive or nonmonotonic?}, journal = {Synthese}, year = {2021}, volume = {199}, number = {}, pages = {681--705} }

Two traditions in abstract valuational model theory

*Synthese*, 198(22):5291-5313, 2021.We investigate two different broad traditions in abstract valuational model theory for nontransitive and nonreflexive logics. The first of these traditions makes heavy use of the natural Galois connection between sets of (many-valued) valuations and sets of arguments. The other, originating with work by Grzegorz Malinowski on nonreflexive logics, and best systematized in (Blasio et al 2017), lets sets of arguments determine a more restricted set of valuations. After giving a systematic discussion of these two different traditions, we turn to looking at the ways in which we might try to compare two sets of valuations determining the same set of arguments.

@article{fr:ttavmt, author = {Rohan French and David Ripley}, title = {Two traditions in abstract valuational model theory}, journal = {Synthese}, year = {2021}, volume = {198}, number = {22}, pages = {5291--5313} }

A counterfactual approach to explanation in mathematics

*Philosophia Mathematica*, 28(1):1-34, 2020.Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

@article{bcr:caem, author = {Sam Baron and Mark Colyvan and David Ripley}, title = {A counterfactual approach to explanation in mathematics}, journal = {Philosophia Mathematica}, year = {2020}, volume = {28}, number = {1}, pages = {1--34} }

In

*The Oxford Handbook of Negation*, ed Viviane Déprez, M. Teresa Espinal. Pages 47-57, Oxford University Press 2020.Denial is something we do; it is a speech act. Negation, on the other hand, is a particular lexical item. Despite being very different kinds of things, denial and negation certainly seem to have something to do with each other. There's something negative about them both. This negative aspect, whatever it is, unifies denial and negation across these categories. There are a range of theories about the relationships between negation and denial. This chapter aims to give a brief overview of these theories, and to indicate some of the reasons for and against each.

@incollection{ripley:denial, author = {David Ripley}, title = {Denial}, booktitle = {The Oxford Handbook of Negation}, editor = {Viviane D{\'{e}}prez and M. Teresa Espinal}, publisher = {Oxford University Press}, year = {2020}, pages = {47--57} }

Inferences and metainferences in ST

*Journal of Philosophical Logic*, 49(6):1057-1077, 2020.In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K3+. We clarify the distinction between internal and external logic and argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K3+.

@article{cervr:imst, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Inferences and metainferences in ST}, journal = {Journal of Philosophical Logic}, year = {2020}, volume = {49}, number = {6}, pages = {1057--1077} }

Qua solution, 0-Qua has problems: a response to Beall and Henderson

*Journal of Analytic Theology*, 8:405-411, 2020.We present an objection to Beall and Henderson's recent paper defending a solution to the fundamental problem of conciliar Christology using qua or secundum clauses. We argue that certain claims the acceptance/rejection of which distinguish the Conciliar Christian from others fail to so distinguish on Beall and Henderson's 0-Qua view. This is because on their 0-Qua account, these claims are either acceptable both to Conciliar Christians as well as those who are not Conciliar Christians or because they are acceptable to neither.

@article{prt:qua-0-qua, author = {Andrew Tedder and Grace Paterson and David Ripley}, title = {Qua solution, 0-Qua has problems: a response to Beall and Henderson}, journal = {Journal of Analytic Theology}, year = {2020}, volume = {8}, number = {}, pages = {405--411} }

Strong normalization in core type theory

In

*The Logica Yearbook 2019*, ed Igor Sedlár, Martin Blicha. Pages 111-130, College Publications 2020.This paper presents a novel typed term calculus and reduction relation for it, and proves that the reduction relation is strongly normalizing---that there are no infinite reduction sequences. The calculus bears a close relation to the implication-negation fragment of core logic, and so is called 'core type theory'.

@incollection{ripley:snctt, author = {David Ripley}, title = {Strong normalization in core type theory}, booktitle = {The Logica Yearbook 2019}, editor = {Igor Sedl{\'{a}}r and Martin Blicha}, publisher = {College Publications}, year = {2020}, pages = {111--130} }

The sorites paradox in psychology

In

*The Sorites Paradox*, ed Sergi Oms, Elia Zardini. Pages 263-286, Cambridge University Press 2019.This chapter examines some aspects of the influence of the sorites paradox in psychology. Section 1 starts out with a brief discussion of the analysis of slippery slope arguments in the psychology of reasoning, to introduce the relevance of probabilistic considerations in that domain. We then devote most of this chapter to the analysis in psychophysics and in the psychology of concepts of the complex relationship between discrimination and categorization for items that differ very little. Section 2 emphasizes the centrality of probabilistic modeling to represent the way in which small differences between stimuli affect decisions of membership under a common catopen egory. Section 3 focuses on experimental data concerning unordered transitions between prototypes, then section 4 looks at data concerning ordered transitions between prototypes (dynamic sorites).

@incollection{erv:spp, author = {Paul Egr{\'{e}} and David Ripley and Steven Verheyen}, title = {The sorites paradox in psychology}, booktitle = {The Sorites Paradox}, editor = {Sergi Oms and Elia Zardini}, publisher = {Cambridge University Press}, year = {2019}, pages = {263--286} }

Valuations: bi, tri, and tetra

*Studia Logica*, 107(6):1313-1346, 2019.This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

@article{fr:vals, author = {Rohan French and David Ripley}, title = {Valuations: bi, tri, and tetra}, journal = {Studia Logica}, year = {2019}, volume = {107}, number = {6}, pages = {1313--1346} }

Blurring: an approach to conflation

*Notre Dame Journal of Formal Logic*, 59(2):171-188, 2018.I consider the phenomenon of conflation---treating distinct things as one---and develop logical tools for modeling it. These tools involve a purely consequence-theoretic treatment, independent of any proof or model theory, as well as a four-valued valuational treatment.

@article{ripley:blurring, author = {David Ripley}, title = {Blurring: an approach to conflation}, journal = {Notre Dame Journal of Formal Logic}, year = {2018}, volume = {59}, number = {2}, pages = {171--188} }

Oxford University Press 2018.

This book is our attempt at a brief sketch of the landscape in formal theories of truth.

@book{bgr:ftot, author = {Jc Beall and Michael Glanzberg and David Ripley}, title = {Formal Theories of Truth}, publisher = {Oxford University Press}, year = {2018} }

Nonclassical theories of truth

In

*the Oxford Handbook of Truth*, ed Michael Glanzberg. Pages 739-754, Oxford University Press 2018.This chapter attempts to give a brief overview of non-classical(-logic) theories of truth.

@incollection{br:nctt, author = {Jc Beall and David Ripley}, title = {Nonclassical theories of truth}, booktitle = {the Oxford Handbook of Truth}, editor = {Michael Glanzberg}, publisher = {Oxford University Press}, year = {2018}, pages = {739--754} }

On the 'transitivity' of consequence relations

*Journal of Logic and Computation*, 28(2):433-450, 2018.The relations logicians tend to think of as consequence relations are almost never transitive, at least not in the usual relation-theoretic sense of 'transitive'. Yet it is common to hear them described as 'transitive', and to see rules imposed to ensure 'transitivity' of these relations. This paper attempts to clarify the situation.

@article{ripley:otocr, author = {David Ripley}, title = {On the 'transitivity' of consequence relations}, journal = {Journal of Logic and Computation}, year = {2018}, volume = {28}, number = {2}, pages = {433--450} }

Williamson on counterpossibles

*Journal of Philosophical Logic*, 47(4):693-713, 2018.A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.

@article{bfpr:woc, author = {Francesco Berto and Rohan French and Graham Priest and David Ripley}, title = {Williamson on counterpossibles}, journal = {Journal of Philosophical Logic}, year = {2018}, volume = {47}, number = {4}, pages = {693--713} }

Bilateralism, coherence, warrant

In

*Act-Based Conceptions of Propositional Content*, ed Friederike Moltmann, Mark Textor. Pages 307-324, Oxford University Press 2017.@incollection{ripley:bcw, author = {David Ripley}, title = {Bilateralism, coherence, warrant}, booktitle = {Act-Based Conceptions of Propositional Content}, editor = {Friederike Moltmann and Mark Textor}, publisher = {Oxford University Press}, year = {2017}, pages = {307--324} }

How mathematics can make a difference

*Philosophers' Imprint*, 17(3):1-19, 2017.Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts (in part) by mathematical facts. Using a structural-equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We then address some objections to our approach.

@article{bcr:hmmd, author = {Sam Baron and Mark Colyvan and David Ripley}, title = {How mathematics can make a difference}, journal = {Philosophers' Imprint}, year = {2017}, volume = {17}, number = {3}, pages = {1--19} }

Vagueness is a kind of conflation

*Logic and Logical Philosophy*, 26(1):115-135, 2017.This paper sketches an understanding of conflation and vagueness according to which the latter is a special kind of the former. First, I sketch a particular understanding of conflation. Then, I go on to argue that vague concepts fit directly into this understanding. This picture of vagueness is related, but not identical, to a number of existing accounts.

@article{ripley:vkc, author = {David Ripley}, title = {Vagueness is a kind of conflation}, journal = {Logic and Logical Philosophy}, year = {2017}, volume = {26}, number = {1}, pages = {115--135} }

Comparing some substructural strategies dealing with vagueness

In

*Information Processing and Management of Uncertainty in Knowledge-Based Systems, Part II: Proceedings of IPMU 2016*, ed Joao Paolo Carvalho, Marie-Jeanne Lesot, Uzay Kaymak, Susana Vieira, Bernadette Bouchon-Meunier, Ronald R. Yager. Pages 161-172, Springer 2016.We compare some nonmonotonic and nontransitive logical approaches to vague predicates, exploring ways to build nonmonotonic logics sensitive to at least some pragmatic constraints on top of our earlier work on nontransitive logics.

@incollection{cervr:cssv, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Comparing some substructural strategies dealing with vagueness}, booktitle = {Information Processing and Management of Uncertainty in Knowledge-Based Systems, Part II: Proceedings of IPMU 2016}, editor = {Joao Paolo Carvalho and Marie-Jeanne Lesot and Uzay Kaymak and Susana Vieira and Bernadette Bouchon-Meunier and Ronald R. Yager}, publisher = {Springer}, year = {2016}, pages = {161--172} }

Experimental philosophical logic

In

*A Companion to Experimental Philosophy*, ed Justin Sytsma, Wesley Buckwalter. Pages 523-534, Wiley 2016.This paper explores the intersection of experimental philosophy and philosophical logic. I sketch some ways in which experimental results, and empirical results more broadly, can inform and have informed debates within philosophical logic.

@incollection{ripley:xpl, author = {David Ripley}, title = {Experimental philosophical logic}, booktitle = {A Companion to Experimental Philosophy}, editor = {Justin Sytsma and Wesley Buckwalter}, publisher = {Wiley}, year = {2016}, pages = {523--534} }

'Transitivity' of consequence relations

In

*Logic, Rationality, and Interaction: Proceedings of LORI V*, ed Wiebe van der Hoek, Wesley Holliday, Wen-Fang Wang. Pages 328-340, Springer 2015.The relations logicians tend to think of as consequence relations are almost never transitive, at least not in the usual relation-theoretic sense of 'transitive'. Yet it is common to hear them described as 'transitive', and to see rules impose to ensure 'transitivity' of these relations. This paper attempts to clarify the situation.

@incollection{ripley:tocr, author = {David Ripley}, title = {'Transitivity' of consequence relations}, booktitle = {Logic, Rationality, and Interaction: Proceedings of LORI V}, editor = {Wiebe van der Hoek and Wesley Holliday and Wen-Fang Wang}, publisher = {Springer}, year = {2015}, pages = {328--340} }

*Topoi*, 34(1):25-36, 2015.What sorts of sequent-calculus rules succeed in specifying a legitimate piece of vocabulary? Following on Arthur Prior’s discussion of the connective tonk, there have been a flurry of criteria offered. Here, I step back a bit, examining the role of structural rules in an inferentialist theory of meaning, and sketch a theory on which any way at all of giving left and right sequent rules for a piece of vocabulary is ok. Tonk, among other things, is a full citizen of coherent-idea-land.

@article{ripley:ag, author = {David Ripley}, title = {Anything goes}, journal = {Topoi}, year = {2015}, volume = {34}, number = {1}, pages = {25--36} }

Comparing substructural theories of truth

*Ergo*, 2(13):299-328, 2015.Substructural theories of truth are theories based on logics that do not include the full complement of usual structural rules. Existing substructural approaches fall into two main families: noncontractive approaches and nontransitive approaches. This paper provides a sketch of these families, and argues for two claims: first, that substructural theories are better-positioned than other theories to grapple with the truth-theoretic paradoxes, and second---more tentatively---that nontransitive approaches are in turn better-positioned than noncontractive approaches.

@article{ripley:cstt, author = {David Ripley}, title = {Comparing substructural theories of truth}, journal = {Ergo}, year = {2015}, volume = {2}, number = {13}, pages = {299--328} }

*Thought*, 4(2):131-138, 2015.In this paper, I consider the connection between consequence relations and closure operations. I argue that one familiar connection makes good sense of some usual applications of consequence relations, and that a largeish family of familiar noncontractive consequence relations cannot respect this familiar connection.

@article{ripley:cc, author = {David Ripley}, title = {Contraction and closure}, journal = {Thought}, year = {2015}, volume = {4}, number = {2}, pages = {131--138} }

Contractions of noncontractive consequence relations

*Review of Symbolic Logic*, 8(3):506-528, 2015.Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relative of multiplicative-additive affine logic with transparent truth, or MAALT.

@article{fr:cncr, author = {Rohan French and David Ripley}, title = {Contractions of noncontractive consequence relations}, journal = {Review of Symbolic Logic}, year = {2015}, volume = {8}, number = {3}, pages = {506--528} }

In

*Foundations of Logical Consequence*, ed Colin Caret, Ole Hjortland. Pages 289-309, Oxford University Press 2015.@incollection{ripley:ed, author = {David Ripley}, title = {Embedding denial}, booktitle = {Foundations of Logical Consequence}, editor = {Colin Caret and Ole Hjortland}, publisher = {Oxford University Press}, year = {2015}, pages = {289--309} }

Naive set theory and nontransitive logic

*Review of Symbolic Logic*, 8(3):553-571, 2015.In a recent series of papers, I and others have advanced new logical approaches to familiar paradoxes. The key to these approaches is to accept full classical logic, and to accept the principles that cause paradox, while preventing trouble by allowing a certain sort of nontransitivity. Earlier papers have treated paradoxes of truth and vagueness. The present paper begins to extend the approach to deal with the familiar paradoxes arising in naive set theory, pointing out some of the promises and pitfalls of such an approach.

@article{ripley:nstntl, author = {David Ripley}, title = {Naive set theory and nontransitive logic}, journal = {Review of Symbolic Logic}, year = {2015}, volume = {8}, number = {3}, pages = {553--571} }

*Journal of Philosophical Logic*, 44(6):771-780, 2015.In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I give some examples of techniques for developing paraconsistent logics. In Section 3, I discuss what seem to me to be some promising applications of certain paraconsistent logics. In fact, however, I don’t think there’s all that much to the concept ‘paraconsistent’ itself; the collection of paraconsistent logics is far too heterogenous to be very productively dealt with under a single label. Perhaps that will emerge as we go.

@article{ripley:pl, author = {David Ripley}, title = {Paraconsistent logic}, journal = {Journal of Philosophical Logic}, year = {2015}, volume = {44}, number = {6}, pages = {771--780} }

Pragmatic interpretations of vague expressions

*Journal of Philosophical Logic*, 44(4):375-393, 2015.Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In "Tolerant, classical, strict", we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new (nonmonotonic) consequence relation and discuss some of its properties.

@article{cervr:pive, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Pragmatic interpretations of vague expressions}, journal = {Journal of Philosophical Logic}, year = {2015}, volume = {44}, number = {4}, pages = {375--393} }

Vagueness, truth, and permissive consequence

In

*Unifying the Philosophy of Truth*, ed Theodora Achourioti, Henri Galinon, José Martínez Fernández, Kentaro Fujimoto. Pages 409-430, Springer 2015.We say that a sentence A is a permissive consequence of a set X of premises whenever, if all the premises in X hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisite of transparency. Permissive consequence is non-transitive, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

@incollection{cervr:vtpc, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Vagueness, truth, and permissive consequence}, booktitle = {Unifying the Philosophy of Truth}, editor = {Theodora Achourioti and Henri Galinon and Jos{\'{e}} Mart{\'{i}}nez Fern{\'{a}}ndez and Kentaro Fujimoto}, publisher = {Springer}, year = {2015}, pages = {409--430} }

Priest's motorbike and tolerant identity

In

*Recent Trends in Philosophical Logic*, ed Roberto Ciuni, Heinrich Wansing, Caroline Wilkommen. Pages 75-85, Springer 2014.@incollection{cervr:pmti, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Priest's motorbike and tolerant identity}, booktitle = {Recent Trends in Philosophical Logic}, editor = {Roberto Ciuni and Heinrich Wansing and Caroline Wilkommen}, publisher = {Springer}, year = {2014}, pages = {75--85} }

*Mind*, 123(491):813-828, 2014.In an approach to vagueness using the paraconsistent logic LP, borderline cases of vague predicates are contradictory---logical gluts. In ‘Finding Tolerance without Gluts’, Jc Beall argues against such an account of vagueness. He constructs an alternative theory, and argues that ‘[t]he result enjoys all the virtues of the LP solution but without the gluts’. He concludes that his alternative is therefore preferable to the LP solution. In what follows, we will demonstrate that this is not the case: Beall’s account does not do all the things that a paraconsistent solution can do. In fact, it is the other way around: the paraconsistent account can do everything that Beall’s theory can do, and more. And some of the ‘more’ is very important. We will demonstrate this by discussing each of the three objections to his own project which Beall raises and rejects, arguing that his replies fail in each case. This note is not solely a reply to Beall. Several quite new points emerge in the discussion, clarifying the paraconsistent account.

@article{wrphc:tg, author = {Zach Weber and David Ripley and Graham Priest and Dominic Hyde and Mark Colyvan}, title = {Tolerating gluts}, journal = {Mind}, year = {2014}, volume = {123}, number = {491}, pages = {813--828} }

Identity, Leibniz's law, and nontransitive reasoning

*Metaphysica*, 14(2):253-264, 2013.Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

@article{cervr:illntr, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Identity, Leibniz's law, and nontransitive reasoning}, journal = {Metaphysica}, year = {2013}, volume = {14}, number = {2}, pages = {253--264} }

*Australasian Journal of Philosophy*, 91(1):139-164, 2013.This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning—one which takes meaning to be constituted by assertibility and deniability conditions—and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system--—ST--—that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered and responded to.

@article{ripley:pafc, author = {David Ripley}, title = {Paradoxes and failures of cut}, journal = {Australasian Journal of Philosophy}, year = {2013}, volume = {91}, number = {1}, pages = {139--164} }

*Mind*, 122(488):841-866, 2013.This paper presents and defends a way to add a transparent truth predicate to classical logic, such that T(A) and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.

@article{cervr:rtt, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Reaching transparent truth}, journal = {Mind}, year = {2013}, volume = {122}, number = {488}, pages = {841--866} }

*Philosophers' Imprint*, 13(5):1-13, 2013.This paper provides a defense of the full strength of classical logic, in a certain form, against those who would appeal to semantic paradox or vagueness in an argument for a weaker logic. I will not argue that these paradoxes are based on mistaken principles; the approach I recommend will extend a familiar formulation of classical logic by including a fully transparent truth predicate and fully tolerant vague predicates. It has been claimed that these principles are not compatible with classical logic; I will argue, by both drawing on previous work and presenting new work in the same vein, that this is not so. We can combine classical logic with these intuitive principles, so long as we allow the result to be nontransitive. In the end, I hope the paper will help us to handle familiar paradoxes within classical logic; along the way, I hope to shed some light on what classical logic might be for.

@article{ripley:ru, author = {David Ripley}, title = {Revising up}, journal = {Philosophers' Imprint}, year = {2013}, volume = {13}, number = {5}, pages = {1--13} }

In

*Paraconsistency: Logic and Applications*, ed Francesco Berto, Edwin Mares, Koji Tanaka. Pages 329-348, Springer 2013.@incollection{ripley:ss, author = {David Ripley}, title = {Sorting out the sorites}, booktitle = {Paraconsistency: Logic and Applications}, editor = {Francesco Berto and Edwin Mares and Koji Tanaka}, publisher = {Springer}, year = {2013}, pages = {329--348} }

Vagueness and order effects in color categorization

*Journal of Logic, Language, and Information*, 22(4):391-420, 2013.This paper proposes an experimental investigation of the use of vague predicates in dynamic sorites. We present the results of two studies in which subjects had to categorize colored squares at the borderline between two color categories. Our main aim was to probe for hysteresis in the ordered transitions between the respective colors, namely for the longer persistence of the initial category. Our main finding is a reverse phenomenon of enhanced contrast (i.e. negative hysteresis), present in two different tasks, a comparative task involving two color names, and a yes/no task involving a single color name, but not found in a corresponding color matching task. We propose an optimality-theoretic explanation of this effect in terms of the strict-tolerant framework of Cobreros et al.'s "Tolerant, classical, strict", in which borderline cases are characterized in a dual manner in terms of overlap between tolerant extensions, and underlap between strict extensions.

@article{egr:voe, author = {Paul Egr{\'{e}} and Vincent de Gardelle and David Ripley}, title = {Vagueness and order effects in color categorization}, journal = {Journal of Logic, Language, and Information}, year = {2013}, volume = {22}, number = {4}, pages = {391--420} }

Conservatively extending classical logic with transparent truth

*Review of Symbolic Logic*, 5(2):354-378, 2012.This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth-involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system features admissible Cut, but the other does not.)

@article{ripley:cecltt, author = {David Ripley}, title = {Conservatively extending classical logic with transparent truth}, journal = {Review of Symbolic Logic}, year = {2012}, volume = {5}, number = {2}, pages = {354--378} }

Explaining the abstract/concrete paradoxes in moral psychology

*Review of Philosophy and Psychology*, 3(3):351-368, 2012.For some reason, participants hold agents more responsible for their actions when a situation is described concretely than when the situation is described abstractly. We present examples of this phenomenon, and survey some attempts to explain it. We divide these attempts into two classes: affective theories and cognitive theories. After criticizing both types of theories we advance our novel hypothesis: that people believe that whenever a norm is violated, someone is responsible for it. This belief, along with the familiar workings of cognitive dissonance theory, is enough to not only explain all of the abstract/concrete paradoxes, but also explains seemingly unrelated effects, like the anthropomorphization of malfunctioning inanimate objects.

@article{mr:nbar, author = {Eric Mandelbaum and David Ripley}, title = {Explaining the abstract/concrete paradoxes in moral psychology}, journal = {Review of Philosophy and Psychology}, year = {2012}, volume = {3}, number = {3}, pages = {351--368} }

On the ternary relation and conditionality

*Journal of Philosophical Logic*, 41(3):595-612, 2012.One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley–Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

@article{ternary, author = {Jc Beall and Ross Brady and J. Michael Dunn and Allen P. Hazen and Edwin Mares and Robert K. Meyer and Graham Priest and Greg Restall and David Ripley and John Slaney and Richard Sylvan}, title = {On the ternary relation and conditionality}, journal = {Journal of Philosophical Logic}, year = {2012}, volume = {41}, number = {3}, pages = {595--612} }

*Synthese*, 189(1):97-118, 2012.This paper discusses two distinct strategies that have been adopted to provide fine-grained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on fineness-of-grain issues: just how finely should propositions be individuated? Here, I compare the two strategies with an eye to the fineness-of-grain question, arguing that when a wide enough range of data is considered, we can see that a circumstance-based approach, properly spelled out, outperforms a structure-based approach in answering the question. (Part of this argument involves spelling out what I take to be a reasonable circumstance-based approach.) An argument to the contrary, due to Soames, is also considered.

@article{ripley:sc, author = {David Ripley}, title = {Structures and circumstances}, journal = {Synthese}, year = {2012}, volume = {189}, number = {1}, pages = {97--118} }

Tolerance and mixed consequence in the s'valuationist setting

*Studia Logica*, 100(4):855-877, 2012.In a previous paper (‘Tolerant, Classical, Strict’), we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that classical tautologies or contradictions are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning.

@article{cervr:tmcss, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Tolerance and mixed consequence in the s'valuationist setting}, journal = {Studia Logica}, year = {2012}, volume = {100}, number = {4}, pages = {855--877} }

*Journal of Philosophical Logic*, 41(2):347-385, 2012.In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.

@article{cervr:tcs, author = {Pablo Cobreros and Paul Egr{\'{e}} and David Ripley and Robert van Rooij}, title = {Tolerant, classical, strict}, journal = {Journal of Philosophical Logic}, year = {2012}, volume = {41}, number = {2}, pages = {347--385} }

In

*Vagueness in Communication*, ed Rick Nouwen, Robert van Rooij, Uli Sauerland, Hans-Christian Schmitz. Pages 169-188, Springer 2011.@incollection{ripley:catb, author = {David Ripley}, title = {Contradictions at the borders}, booktitle = {Vagueness in Communication}, editor = {Rick Nouwen and Robert van Rooij and Uli Sauerland and Hans-Christian Schmitz}, publisher = {Springer}, year = {2011}, pages = {169--188} }

In

*Understanding Vagueness*, ed Petr Cintula, Christian G. Fermüller, Lluís Godo, Petr Hájek. Pages 41-58, College Publications 2011.@incollection{ripley:ii, author = {David Ripley}, title = {Inconstancy and inconsistency}, booktitle = {Understanding Vagueness}, editor = {Petr Cintula and Christian G. Ferm{\"{u}}ller and Llu{\'{i}}s Godo and Petr H{\'{a}}jek}, publisher = {College Publications}, year = {2011}, pages = {41--58} }

Negation, denial, and rejection

*Philosophy Compass*, 6(9):622-629, 2011.At least since Frege and Geach, there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection.

@article{ripley:ndr, author = {David Ripley}, title = {Negation, denial, and rejection}, journal = {Philosophy Compass}, year = {2011}, volume = {6}, number = {9}, pages = {622--629} }

Responsibility and the brain sciences

*Ethical Theory and Moral Practice*, 12(5):511-524, 2009.Some theorists think that the more we get to know about the neural underpinnings of our behaviors, the less likely we will be to hold people responsible for their actions. This intuition has driven some to suspect that as neuroscience gains insight into the neurological causes of our actions, people will cease to view others as morally responsible for their actions, thus creating a troubling quandary for our legal system. This paper provides empirical evidence against such intuitions. Particularly, our studies of folk intuitions suggest that (1) when the causes of an action are described in neurological terms, they are not found to be any more exculpatory than when described in psychological terms, and (2) agents are not held fully responsible even for actions that are fully neurologically caused.

@article{dbmr:rbs, author = {Felipe De Brigard and Eric Mandelbaum and David Ripley}, title = {Responsibility and the brain sciences}, journal = {Ethical Theory and Moral Practice}, year = {2009}, volume = {12}, number = {5}, pages = {511--524} }

*Analysis*, 64(1):30-35, 2004.Graham Priest argues that dialethism alone avoids familiar revenge problems, and in this respect enjoys expressive virtues that rival theories lack. In this paper we present a rival theory---analetheism---that seems to enjoy precisely the expressive virtues that dialetheism enjoys. Analetheism, for us, is the thesis that some sentences lack truth value, coupled with the willingness to assert such sentences.

@article{br:ad, author = {Jc Beall and David Ripley}, title = {Analetheism and dialetheism}, journal = {Analysis}, year = {2004}, volume = {64}, number = {1}, pages = {30--35} }