Writing

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 = {Ellie Ripley},
   title = {One step is enough},
   journal = {Journal of Philosophical Logic},
   writingUrl = {./papers/osie.pdf},
   abstract = {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.},
   year = {2021},
   volume = {51},
   number = {6},
   pages = {1233--1259},
   doi = {10.1007/s10992-021-09615-7},
}

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 = {Ellie Ripley},
   title = {Denial},
   booktitle = {The Oxford Handbook of Negation},
   editor = {Viviane D{\'{e}}prez and M. Teresa Espinal},
   publisher = {Oxford University Press},
   abstract = {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.},
   writingUrl = {./papers/denial.pdf},
   year = {2020},
   pages = {47--57}
}

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 = {Ellie Ripley},
   title = {Strong normalization in core type theory},
   booktitle = {The Logica Yearbook 2019},
   editor = {Igor Sedl{\'{a}}r and Martin Blicha},
   publisher = {College Publications},
   abstract = {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'.},
   writingUrl = {./papers/snctt.pdf},
   year = {2020},
   pages = {111--130}
}

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 = {Ellie Ripley},
   title = {Blurring: an approach to conflation},
   journal = {Notre Dame Journal of Formal Logic},
   writingUrl = {./papers/blurring.pdf},
   abstract = {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.},
   year = {2018},
   volume = {59},
   number = {2},
   pages = {171--188},
   }

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 = {Ellie Ripley},
   title = {On the 'transitivity' of consequence relations},
   journal = {Journal of Logic and Computation},
   writingUrl = {./papers/otocr.pdf},
   abstract = {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.},
   year = {2018},
   volume = {28},
   number = {2},
   pages = {433--450},
   }

@incollection{ripley:bcw,
   author = {Ellie Ripley},
   title = {Bilateralism, coherence, warrant},
   booktitle = {Act-Based Conceptions of Propositional Content},
   editor = {Friederike Moltmann and Mark Textor},
   publisher = {Oxford University Press},
   abstract = {},
   writingUrl = {./papers/bcw.pdf},
   year = {2017},
   pages = {307--324}
}

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 = {Ellie Ripley},
   title = {Vagueness is a kind of conflation},
   journal = {Logic and Logical Philosophy},
   writingUrl = {http://apcz.pl/czasopisma/index.php/LLP/article/view/LLP.2016.020},
   abstract = {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.},
   year = {2017},
   volume = {26},
   number = {1},
   pages = {115--135},
   }

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 = {Ellie Ripley},
   title = {Experimental philosophical logic},
   booktitle = {A Companion to Experimental Philosophy},
   editor = {Justin Sytsma and Wesley Buckwalter},
   publisher = {Wiley},
   abstract = {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.},
   writingUrl = {./papers/xpl.pdf},
   year = {2016},
   pages = {523--534}
}

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 = {Ellie 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},
   abstract = {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.},
   writingUrl = {./papers/tocr.pdf},
   year = {2015},
   pages = {328--340}
}

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 = {Ellie Ripley},
   title = {Anything goes},
   journal = {Topoi},
   writingUrl = {./papers/ag.pdf},
   abstract = {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.},
   year = {2015},
   volume = {34},
   number = {1},
   pages = {25--36},
   }

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 = {Ellie Ripley},
   title = {Comparing substructural theories of truth},
   journal = {Ergo},
   writingUrl = {http://dx.doi.org/10.3998/ergo.12405314.0002.013},
   abstract = {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.},
   year = {2015},
   volume = {2},
   number = {13},
   pages = {299--328},
   }

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 = {Ellie Ripley},
   title = {Contraction and closure},
   journal = {Thought},
   writingUrl = {./papers/cc.pdf},
   abstract = {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.},
   year = {2015},
   volume = {4},
   number = {2},
   pages = {131--138},
   }

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

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 = {Ellie Ripley},
   title = {Naive set theory and nontransitive logic},
   journal = {Review of Symbolic Logic},
   writingUrl = {./papers/nstntl.pdf},
   abstract = {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.},
   year = {2015},
   volume = {8},
   number = {3},
   pages = {553--571},
   }

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 = {Ellie Ripley},
   title = {Paraconsistent logic},
   journal = {Journal of Philosophical Logic},
   writingUrl = {./papers/pl.pdf},
   abstract = {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.},
   year = {2015},
   volume = {44},
   number = {6},
   pages = {771--780},
   }

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 = {Ellie Ripley},
   title = {Paradoxes and failures of cut},
   journal = {Australasian Journal of Philosophy},
   writingUrl = {./papers/pafc.pdf},
   abstract = {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.},
   year = {2013},
   volume = {91},
   number = {1},
   pages = {139--164},
   }

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 = {Ellie Ripley},
   title = {Revising up},
   journal = {Philosophers' Imprint},
   writingUrl = {http://quod.lib.umich.edu/cgi/p/pod/dod-idx/revising-up-strengthening-classical-logic-in-the-face.pdf?c=phimp;idno=3521354.0013.005},
   abstract = {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.},
   year = {2013},
   volume = {13},
   number = {5},
   pages = {1--13},
   }

@incollection{ripley:ss,
   author = {Ellie Ripley},
   title = {Sorting out the sorites},
   booktitle = {Paraconsistency: Logic and Applications},
   editor = {Francesco Berto and Edwin Mares and Koji Tanaka},
   publisher = {Springer},
   abstract = {},
   writingUrl = {./papers/sos.pdf},
   year = {2013},
   pages = {329--348}
}

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 = {Ellie Ripley},
   title = {Conservatively extending classical logic with transparent truth},
   journal = {Review of Symbolic Logic},
   writingUrl = {./papers/cecltt.pdf},
   abstract = {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.)},
   year = {2012},
   volume = {5},
   number = {2},
   pages = {354--378},
   }

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 = {Ellie Ripley},
   title = {Structures and circumstances},
   journal = {Synthese},
   writingUrl = {./papers/sc.pdf},
   abstract = {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.},
   year = {2012},
   volume = {189},
   number = {1},
   pages = {97--118},
   }

@incollection{ripley:catb,
   author = {Ellie 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},
   abstract = {},
   writingUrl = {./papers/catb.pdf},
   year = {2011},
   pages = {169--188}
}

@incollection{ripley:ii,
   author = {Ellie 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},
   abstract = {},
   writingUrl = {./papers/ii.pdf},
   year = {2011},
   pages = {41--58}
}

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 = {Ellie Ripley},
   title = {Negation, denial, and rejection},
   journal = {Philosophy Compass},
   writingUrl = {./papers/ndr.pdf},
   abstract = {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.},
   year = {2011},
   volume = {6},
   number = {9},
   pages = {622--629},
   }