Abstracts

Sara Ayhan @Connexive Logic

Contradictions without negation and a proof-theoretic, bilateralist account of connexive logics

In this talk I will investigate a negation-free fragment of a connexive logic from the perspective of bilateralist proof-theoretic semantics and will argue that eliminating primitive negation has two important conceptual consequences. First, it requires a reconceptualization of contradictory logics: in a bilateralist framework, contradiction need not be understood in terms of negation inconsistency, but rather as the coexistence of proofs and refutations for certain formulas within a non-trivial system. Second, it challenges the standard definition of connexive logics, which typically rely on negation-based schemata. Finally, I will also address the issue of proof/refutation duality in the absence of negation, which can be formalized and recovered at a meta-level by extending the system with a two-sorted typed lambda-calculus.

Colin Caret @BLOT

The Dao of Dialetheism

In "Beyond the Limits of Thought", Graham Priest argues that a variety of Western philosophers are committed to the ineffability of certain states of affairs. He advocates for a dialetheic reading of these texts. In later work, he extends this reading to non-Western philosophical traditions, most notably Madhyamaka Buddhism and classical Daoism. My talk will hone in on the dialetheic reading of Daoism. The driving question is: What is it to 'embrace' a contradiction about the ineffable and how might it contribute to Daoist aims? Along the way we will try to unpack what inspires Daoist allusions to the ineffable. I argue that it is implausible that contradictions about the ineffable are the end point of the Daoist project, but that they are important stepping stones.

Michael De @Relevance Logic

Relevance, irrelevance, and the Lewis proof

I want to look at every possible way of blocking the Lewis proof of EFQ using a simple style of semantics for relevance logic.

Elena Ficara @BLOT

Hegel’s Infinities

In my paper I reconstruct Hegel’s conception of the infinite(s) (with special reference to the remark on "the mathematical infinite" in the Science of Logic's first part). The question of Hegel’s approach to the infinite is an interesting one, not only for exegetical reasons. Ultimately, Hegel’s idea of a good infinity, to be distinguished from a bad one, concerns a method “that is both venerable and powerful [and] characterizes philosophy itself” (Priest 2002, 4).

Naoya Fujikawa @BLOT

Two Nothings

There are at least two conceptions of nothingness: the fusion of no things and the complement of the totality (that is, the complement of the fusion of everything). Priest (forthcoming) characterizes nothingness as the fusion of no things and shows that it is also the complement of the totality in a mereological system. Casati and Fujikawa (2019) characterize nothingness as the complement of the totality and show that it needs not be the fusion of no things in a different mereological system. In this talk, I compare these two views and explore whether there are any theoretical advantages to distinguishing between the two kinds of nothingness. 

Nils Kürbis @Connexive Logic

Conditional Assertion, Norms of Assertion and Connexive Theses

Quine attributes to Rhinelander the thought that speakers use 'if' for a speech act of conditional assertion. An assertion of B conditionally on A amounts to an assertion of B if A is true, and if A is false, no assertion has been made. I shall argue that this simple idea naturally gives rise to principles in the vicinity of connexivity, i.e. Aristotle's and Boethius Theses. To spell this out I shall look at a number pf accounts concerning the norms and conventions governing the speech act of assertion. On all of them, the conditional assertion of A on not-A, of not-A on A and of B as well as of not-B on A flout conventions or norms of assertion. Belnap once proposed a semantics for conditional assertion which was axiomatised by Dunn, Cohen and van Fraassen: they all validate theses in the vicinity of connexivity. The problem with these approaches, however, is that they try to formalise the semantic content, the thought or the proposition, expressed by conditional assertions. It is not clear whether this makes sense. Instead, as a first step I propose a simple logic for the speech act conditional assertion, which is innocuous, but unexciting. On that basis I'll consider how it might be possible to 'internalise' the speech act into a conditional. 

Fei Liang @BLOT

Nothing as the Gluon of Everything

Abstract

Anna Malavisi @BLOT

Beyond the Limits of Western Thought

As we honor the 30th anniversary of the publication of Graham Priest’s book Beyond the Limits of Thought, one cannot deny the significant contribution the book has made to logic but also to philosophy in general. In the second edition of this book Priest goes beyond western philosophy to include a chapter co-authored with Jay Garfield on Nagarjuna. In this paper, I will discuss how this marked the beginning of a journey which took Priest well beyond thought limited to the western tradition, and how this has not only enriched the discipline of logic but also philosophy.

Florian Marion @Connexive Logic

On Wyman’s Theory of the Meaninglessness of Contradictions: Cancellation View of Negation and Reductio ad Absurdum

I will discuss a rarely commented passage from Quine's "On What There Is". In this very famous paper, Quine credits the strawman Wyman with the idea that contradictions are meaningless, then he makes two objections to this thesis (the meaninglessness of contradictions implies, first, that proofs by reductio ad absurdum are invalid, and, second, that that there is not a procedure that is an effective test of meaningfulness). I will analyze Wyman's position and Quine's objections in turn, before concluding that these objections have no reason to bother Wyman. The key-idea to my interpretation is that Wyman not only supports a kind of (pseudo-)Meinongian ontology (everything that is belongs either to the realm of actualia that exist, or to the 'ghostly' realm of mere possibilia which do not exist but subsist), but also defends non-classical views in logic (notably concerning the semantics of negation: I will suggest that Wyman's meaninglessness of contradictions is grounded on a cancellation model of negation which poses a threat to the validity of proofs by reductio). In doing so, I hope to provide a better understanding of perhaps the most important paper in metaontology.

Satoru Niki @Connexive Logic

Another variant of constructive connexivity (joint work with Norihiro Kamide)

H. Wansing's logic C is one of the most popular connexive logics on the market. This system is known for its characteristic treatment of negated implication, about which, at the same time, alternatives have been suggested by different authors as well.  In this talk, I will suggest yet another variant, inspired by some insights from H. Omori, M. Vidal and others.

Hitoshi Omori @Relevance Logic

tba

Takuro Onishi @Relevance Logic

Star-free semantics for weak relevant logics

In earlier work, I introduced a star-free semantics in which negation is defined in terms of implication and a falsum constant, for the relevant logic R (Onishi 2016). I later transferred this semantics to the framework of Restall and Standefer's collection frames (Onishi 2024). In this talk, I extend the same approach to weaker relevant logics, focusing in particular on a variant of the basic relevant logic B.

Graham Priest @BLOT

The Paradox at the Limit of Everything 

Beyond everything is nothing(ness). But nothing appears to be a paradoxical object, both something and nothing. In this talk I will look at the paradox of nothing more closely, defining nothing in mereological terms, and proving that it is a dialetheic object. The Inclosure Scheme is a scheme into which all the standard paradoxes of self-reference fit. The paradox of nothing is not a paradox of self-reference, but I will show that it fits the Inclosure Schema, and so has the same structure. As we will see, the paradox of nothing is a paradox at the limit of everything.

Graham Priest @Connexive Logic

Cooper's Logic of Ordinary Discourse

In 1968 William Cooper published a paper, 'The Propositional Logic of Ordinary Discourse'. The paper received virtually no uptake at the time—unjustly so, since it contains a number of significant ideas. It is now starting to receive some of the recognition it deserves. This talk reviews the paper and its ideas. It has three parts. In the first, I will describe the central contents of Cooper’s paper. In the second I will comment on the significant ideas it contains. In the third, I will discuss some shortcomings of the ideas (or at least, the way that they are executed).

Shuhei Shimamura @Connexive Logic

Coherence and Connexivity

Graham Priest has shown, based on model-theoretic considerations, that by requiring that the premise set is consistent (i.e., by requiring, model-theoretically, that there is a possible world in which all the members of the premise set is true), we can introduce a conditional that satisfies several connexive principles. Inspired by Priest’s considerations, in this talk, I pursue a similar idea for defining a connexive conditional in a proof-theoretic setting. First, I submit a hybrid sequent calculus equipped with a new logical operator—the tilde operator (~)—that expresses, in Robert Brandom’s sense, a proof-theoretic notion of coherence. This operator, in combination with others such as conjunction and material conditional, opens up possibilities of defining several new conditionals. I show not only that one of them satisfies the same set of connexive principles as Priest’s but also that another of them satisfies stronger “embedded” connexive principles as well.

Daniel Skurt @Connexive Logic

Solving a New Paradox of Deontic Logic (and a dozen other paradoxes) with RNmatrices for MC-based Modal Logics (joint work with Heinrich Wansing)

In this talk, we will present RNmatrices (restricted non-deterministic matrices) for normal and non-normal modal expansions of the material connexive logic MC. 

In particular we aim at the following, first, we will introduce a paradox of deontic logic that to the best of our knowledge has not yet been been discussed in the literature and that justifies the use of a connexive, and actually hyperconnexive, non-modal base logic. We shall call this new paradox the Paradox of Obligatory Negated Conditionals. Then we will show how to solve the paradox by introducing and applying mMC (minimal deontic material connexive logic) and RNmatrices for extensions of mMC. Additionally, the flexibility of restricted non-deterministic matrices will be further illustrated by modelling a certain understanding of conditional obligation that allows "factual detachment". 

Shawn Standefer @Relevance Logic

Avoiding collapse in epistemic doxastic logic

It is known that in the setting of classical logic, having a strong logic for knowledge, a strong logic for belief, and some plausible bridge principles together lead to the disastrous result that belief implies knowledge. We will show how a simple non-classical epistemic logic can be used to avoid this result.

Peter Verdée @BLOT

A plea for Default-Exclusion Dialetheism

In this talk I will introduce a specific kind of dialetheism called default-exclusion dialetheism and present some arguments in favour of this philosophical position. A default-exclusion dialetheist holds that there are indeed sentences that are true together with their negation, but that, nevertheless, it lies in the essence of negation that, by default, a sentence's truth excludes its negation's truth. Concretely this means that, without further information, one is justified in disbelieving the truth of not-A if A is believed, even if there are some cases where there are good reasons for both believing B and not-B (the dialetheias). This view requires the semantics of negation to be highly non-standard: it cannot be captured in absolute terms but requires reference to defeasible inference rules and defeasible model-theoretic clauses. I will discuss three advantages of such a view: (1) it accounts for classical recapture in non-paradoxical contexts, (2) it explains why a contradiction is still paradoxical even if it is a justified belief, (3) it allows for a deep understanding of important negative notions used by the dialetheist  like, "untrue",  "true only", "false only", "non-validity", etc. and how they still stand in tension with their positive counterparts, despite the radical dialetheist's incapacity to ultimately separate them from each other. Finally, I will also distinguish the view from superficially similar positions on the matter, such as, on the one hand, the mere heuristic use of default rules for dealing with contradictions and paradoxes in order to safe classical logic, or, on the other hand, merely epistemic or pragmatic methods proposed by dialetheists to deal with classical recapture, that do not affect the semantics of negation. 

Wen-fang Wang @BLOT (cancelled)

Reflections on Priest's Dialetheist Solution to the Sorites Paradox

According to Priest (2009, 2010), both the sorites paradox and the liar's paradox belong to the same schema, i.e., inclosure schema, and therefore should have the same solution according to the principle "the same kind of paradoxes should have the same solution", and the best solution to paradoxes belonging to inclosure schema is the dialetheist solution. I will argue in this talk: first, Priest's "proof" that "both the sorites paradox and the liar's paradox belong to the same schema" is defective; second, even if his proof were sound, it would not be necessary that the same kind of paradoxes should always have the same solution; and finally, even if the same kind of paradoxes should always have the same solution, the dialetheist solution is not the best solution to inclosure paradoxes.

Heinrich Wansing @BLOT

Remarks on strong dimathematism

In a sort of hostile review of Graham Priest's monograph Beyond the Limits of Thought, Cambridge University Press, 1995, that appeared in Review of Modern Logic, 1996, 437-439, Maria Frapolli comments on Priest's dialetheism, the view that there exist true contradictions, as follows:

"Contradictions are marks of error, not announcements of a deeper truth. Priest defends his position as if it were the battle of tolerance versus scholastic dogmatism. But, as I see it, we do not stand here in front of a dispute between antiquated orthodoxy and liberalizing heterodoxy, but between philosophy and charlatanism."

Thirty years after the publication of Beyond the Limits of Thought, dialetheism is widely regarded as a coherent and completely respectable view. Nevertheless, even if contradictions are not necessarily seen as marks of error, it may be irritating to consider it as theoretically rational to deal with non-trivial logics that are not only contradiction-tolerant in the sense of being paraconsistent but contain provable contradictions. In my talk, I will elaborate on a view that I have called "strong dimathematism" and that is meant as a contribution to making sense of provable contradictions in non-trivial negation inconsistent logics.

Heinrich Wansing @Connexive Logic

Constructiveness and connexivity

According to some authors, intuitionistic logic is the correct constructive logic. Sara Negri and Jan von Plato (Structural Proof Theory, Cambridge University Press, 2001, p. 25), for example, write that "[i]ntuitionistic reasoning and constructive reasoning ... are the same thing." In this talk, I will discuss the constructiveness of the non-trivial negation inconsistent hyperconnexive logic C, that is a conservative extension of positive intuitionistic logic. I will end with some comments on Leibniz-identity in second-order C. 

Zach Weber @BLOT

On the Outer Horizon

We can see that there are things we do not see, possibilities beyond us. This prompts the question: what is the outer horizon of all possibilities, the limit? A moderate answer to this immoderate question is: Nothing. Nothing is the absence of all things; Priest variously suggests Nothing is the fusion of the empty set, or the complement of Everything. But in a paraconsistent set theory, there are different empty sets, and different universal sets, depending on which property is used to form the set. Some empty sets are more empty, and some universal sets more universal, than others. This in turn leads to different 'nothings' and 'everythings' when taking complements and fusions. I will outline some formal details for making this precise, and consider some metaphysical conclusions one can draw. One technical note is that calculating powersets—all possible recombinations of a set—becomes very complicated, already at the level of the powerset of the empty set. One philosophical note is that, if Nothing is the outer horizon of Everything—all the possibilities that lie beyond any possibility, beyond the world-horizon—then there are more possibilities beyond heaven and earth than even dreamt of in Priest's philosophy.