Graham Priest – Überconsistent Logics and Dialetheism: Some Initial Thoughts

The following excerpt is extracted from Graham’s website with minor edits:
Graham Priest grew up as a working class kid in South London. He read mathematics and (and a little bit of of logic) at St. John’s College, Cambridge. He obtained his doctorate in mathematics at the London School of Economics. By that time, he had come to the conclusion that philosophy was more fun than mathematics. So, luckily, he got his first job (in 1974) in a philosophy department, as a temporary lecturer in the Department of Logic and Metaphysics  at the University of St Andrews.
The first permanent job he was offered was at the University of Western Australia. He moved to Australia when he took up the position, and has spent most of his working life there. After 12 years at the University of Western Australia, he moved to take up the chair of philosophy at the University of Queensland, and after 12 years there, he moved again to take up the Boyce Gibson Chair of Philosophy at Melbourne University, where he is now emeritus. While he was there, he was a Fellow of Ormond College. During the Melbourne years, he was also an Arché Professorial Fellow at the University of St Andrews. He is a past president of the Australasian Association for Logic , and the Australasian Association of Philosophy , of which he was Chair of Council  for 13 years. He was elected a Fellow of the Australian Academy of Humanities  in 1995, and awarded a Doctor of Letters by the University of Melbourne in 2002. In 2009 he took up the position of Distinguished Professor at the Graduate Center , City University of New York, where he now lives and works.
Graham has published in nearly every leading logic and philosophy journal. At the last count, he had published close to [400] papers . He has also published [15] monographs  (mostly with Oxford University Press), as well as a number of edited collections . Much of his work has been in logic, especially non-classical logic, and related areas. He is perhaps best know for his work on dialetheism , the view that some contradictions are true. However, he has also published widely in many other areas, such as metaphysics, Buddhist philosophy, and the history of philosophy, both East and West.
Graham has travelled widely , lecturing and addressing conferences in every continent except Antarctica. For many years, he practiced karatedo. He is a third dan in Shobukai , and a fourth dan in Shitoryu (awarded by the head of style, Sensei Mabuni Kenei  in Osaka, when he was training there). Before he left Australia he was an Australian National kumite referee  and kata judge . Nowadays, he swims and practices taichi. He loves (good ) opera, jazz , and 60s rock … and East Asian art.
For many decades now, logics which permit inconsistent but non-trivial theories have been investigated and discussed. However, in recent years, we have seen the recognition that there are logics which not only permit contradictions, but which deliver contradictions: the logical truths are themselves inconsistent. As yet, they have no standard name as far as I know. Let us call them überconsistent logics.
Dialetheism is the view that some contradictions are true. It might well be thought that these logics which deliver contradictory logical truths provide an open-and-shut case for dialetheism. After all, as Quine puts it, ‘if sheer logic is not conclusive, what is?’ Matters are not that straightforward, however.
This talk is an investigation of the relationship between überconsistent logics and dialetheism. The investigation is a provisional and preliminary one. Since überconsistent logics are themselves a relatively novel phenomenon, so is the issue at hand.

Gillian Russell – Logic for Virtual Worlds

The following excerpt is extracted from Gillian’s website:
Gillian is a professor in the school of philosophy/RSSS at the Australian National University. Gillia is also a visiting Professorial Fellow (1/5th time) in the Arché Research Center at the University of St Andrews, in Scotland. She visits St Andrews for six weeks each year. In 2025, she will be serving as Honours Convenor for philosophy at the ANU. Until July 2020, she was Alumni Distinguished Professor in Philosophy at the University of North Carolina at Chapel Hill. And then from 2020–2024, she was a research-only professor at the Dianoia Research Institute in Analytic Philosophy at ACU in Melbourne. Her first job out of grad school was at Washington University in St Louis (2004–2014), and she was also a Kil lam Postdoc at the Univer sity of Alberta in Edmonton in 2005. Her Ph.D. is from Princeton (2004) and before that she was an undergraduate in Scotland at the University of St Andrews. Along the way, she has been a visitor at UC Berkeley, Melbourne University, the University of Queensland, and the RSSS at the Australia National University, as well as a visiting fellow at Tilburg Center for Logic and the Philosophy of Science in the Netherlands.
Gillian’s most recent book is Barriers to Entailment. It’s about a family of theses that say that you can’t get certain sorts of conclusion from certain sorts of premises, like: you can’t get an ought from an is (Hume’s Law), or you can’t get conclusions about the future from premises about the past, or universal claims from particular ones. Those who are interested can read the beginning via Preview on Google books. Other topics that she has worked on include the analytic/synthetic distinction and issues in the philosophy of logic, like logic’s epistemology, the normativity of logic, logic and indexicals, logical pluralism, logical nihilism, whether there could be feminist logic etc.
In the second half of ``Two Dogmas", Quine argued that there could be empirical grounds to revise logic–at least in principle. Since then, the most (though still not very) popular proposal for what those empirical grounds look like has involved quantum mechanics. Still, most logicians seem to think that this does not give us good enough reason to revise. This paper considers and evaluates an alternative proposal for empirical grounds for revision of logic: perhaps the experiences acquired in virtual reality give us reason to adopt an assessment-sensitive logic.

Eduardo Barrio – Inconsistent Validity

The following excerpt is extracted from IIF-SADAF-CONICET’s website:
Eduardo is Vice-director of IIF-SADAF-CONICET and Director of BA-Logic . He is a full professor at the Department of Philosophy at the University of Buenos Aires and CONICET Superior Researcher. He has been a Visiting Professor at MIT, CUNY, Oxford University, and MCMP-Munich. He is a specialist in non-classical logics, in particular in multivalued, metainferential, and substructural logics. His works on non-classical logics have been published in high impact international journals (Scopus Q1), such as Journal of Philosophical Logic, Analysis, Synthese, Review of Symbolic logic, Journal of Applied Non-Classical Logics, Logical Journal of the IGPL and Studia Logica, among others. He has co-edited three special issues: one in the Journal of Philosophical Logic and two in the Logical Journal of the IGPL. He is the director of the EUDEBA Logical Encyclopedia collection. He has published three books: two in EUDEBA and one in Collage Pu. He is also the director of international cooperation projects at the British Academy, DAAD, DFG, NEH.
Validity is usually taken to be a consistent property: every inference is either valid or invalid, and never both. In this talk, I argue for the controversial thesis that, if someone endorses a many-valued semantics for the object language formulas, then they should also endorse a many-valued notion of validity.
I'll present logical systems based on Belnap’s algebra 4 whose notion of validity is non-bivalent. Then I claim that such systems should be paraconsistent and/or paracomplete also at the level of metainferences (viz. inferences whose premises and conclusions are themselves inferences ), and show how this paraconsistency and/or paracompleteness can be achieved. Indeed, I prove that there is a sense in which the metalogic of each of our systems coincides with some well-know paraconsistent and/or paracomplete logic. Finally, I am also going to give some philosophical motivation to adopt an inconsistent logic.
(This presentation is based on Barrio, Fiore & Pailos "Non-Bivalent Validity")

Suki Finn – Nothing

Dr Suki Finn is a Lecturer in Philosophy and Gender Studies at Royal Holloway University of London. Previously, she was a Postdoctoral Researcher at the University of Southampton on the ERC-funded ‘Better Understanding the Metaphysics of Pregnancy’ project, and has held visiting fellowships at the University of Oslo (2023), University of Vienna (2023), Australian National University (2019), New York University (2018), and City University of New York Graduate Center (2014). Dr Finn is currently leading a project on gender diversity in reproduction, specifically trans pregnancy. Her areas of research are wide-ranging, spanning feminist and queer theory, the philosophy of logic, metaphysics, philosophy of science, and epistemology. She has published articles on these topics in Bioethics, Synthese, Alternatives, European Journal of the Philosophy of Science,Australasian Journal of Logic, and more. She is the author of What’s in a Doughnut Hole? And other philosophical food for thought (Icon, forthcoming) and editor of Women of Ideas: Interviews from Philosophy Bites (Oxford University Press, 2021). Dr Finn is co-Director of the Society for Women in Philosophy UK, a University and College Union representative, and is on the Council for the Royal Institute of Philosophy. For more information, see: www.sukifinn.com
This talk will be about Nothing. It is not the case that there will be no-thing that I will be talking about, nevertheless I will indeed talk about absence of referents as well as reference to absence. Nothing is said to have many extraordinary properties, but in predicating anything of Nothing we contradict its nothingness. In trying to avoid such misleading descriptions, Nothing could be theorised as ineffable, apart from perhaps being expressed as a dialetheia. Since Nothing could quickly explode into infinity, and having only restricted finite time, this talk covers some introductory thoughts on conceptualising (or modelling) Nothing as the empty set, which contains no-thing.

Abbas Ahsan – Metaphysical Anti-Exceptionalism and the Law of Non-contradiction

Abbas Ahsan received his Ph.D. in Philosophy at the University of Birmingham in 2021. His doctoral research focused on the application of dialetheism, paraconsistent logics, and formal theories of truth to Islamic theological paradoxes. His research interests are in the following areas: Philosophy of Logic, Metaphysics, Analytic Theology, and Islamic Philosophy. He has published several articles, which can be found here: https://orcid.org/0000-0002-0277-8882
I advocate for Metaphysical Anti-Exceptionalism about Logic (MAEL) by critically examining the foundational status of the law of non-contradiction (LNC). Traditionally regarded as a universal, necessary, and self-evident law of rationality, LNC asserts that contradictory statements cannot simultaneously be true. I challenge this view, arguing that LNC lacks the metaphysical and epistemological properties traditionally ascribed to logical laws, instead being contingent, context-dependent, and empirically conditioned.
The critique deconstructs five key metaphysical properties attributed to LNC—generality, formality, normativity, necessity, and analyticity. LNC’s supposed universality falters in domains like quantum mechanics, where contradictions may hold under paraconsistent logics. Its formality is undermined by contextual dependencies on propositional content. Normatively, LNC is shown not to be universally binding, as rationality can tolerate contradictions in certain frameworks, such as inconsistent mathematics. Additionally, LNC's necessity across possible worlds is disputed by paraconsistent logicians. Finally, its reliance on empirical contexts challenges its analyticity.
Epistemologically, LNC’s contingent application questions its status as a priori, foundational, or analytic. This analysis aligns with MAEL’s thesis that logical laws are revisable, descriptive, and contextually grounded, contrasting with their traditional portrayal as inviolable truths. Thus, LNC emerges not as a logical fact but as a theoretically revisable principle.

Anthony Stoner – Access Anti-exceptionalism

Anthony Stoner is a 5th-year PhD student at the University of California, Riverside. His dissertation will concern the historical production of formal thought, and the problem of distinguishing formal thought from historicizing, “dialectical” thought. His goal is to provide a basis for a limited pluralism about “ways of thinking” in order to give a different basis for Marxist philosophy of science than orthodox “dialectical materialism.” He is currently also working on a project on Hermann Cohen’s 1883 The Principle of the Infinitesimal Method and its History; and one on I.E. Orlov’s 1928 paper “The Calculus of the Compatibility of Sentences” and the connection between his invention of relevance logic with his Marxist philosophical work in Soviet journal Under the Banner of Marxism.
I intend to argue that logic is not epistemically exceptional with respect to our access to the content of logic; nevertheless, logic is importantly exceptional with respect to the explanatory structuring role it takes in our scientific endeavors. Our epistemic access to logic (and thereby what we take as logical content) is always mediated through historical and cultural forms—e.g., conventions of representing inferences, especially those dealing with formal and mathematical notations in a given culture, and the dialogical context in which notions of logic are formulated—and is thereby continuous with the sciences. Nothing about my argument hinges on a position on logical monism or pluralism, although I believe the argument is strengthened significantly by the wholesale adoption of logical pluralism.[1]
Catarina Dutilh Novaes’ 2022 The Dialogical Roots of Deduction has helped raise to prominence a metaphysically deflationary and more historically grounded conception of the etiology of logic as a discipline. On Novaes’ quasi-Lakatosian genealogy, deduction in Greek contexts—rather than being analyzed as an ahistorical feature of thought as such—is best treated as an internalization of specific dialogical norms in Greek public philosophy, an abstraction which, once made, can be further developed, reflected upon, and made more precise by later philosophers, mathematicians, and logicians—especially once the crucial cognitive task has been performed of providing a formal notation to do the “grunt work” of checking for validity. A comparative approach to the history of logic can further Novaes’ dialogical hypothesis: Logic in classical Indian philosophy arose in the context of philosophical and religious debates between Nyya and Buddhist philosophers, whose rival conceptions of syllogistic logic served as ammunition for each side. In classical India, not only was epistemic access to logic culturally and historically mediated, but logic as a discipline explicitly served as a meta-analysis of structuring norms of debate.
Given the long and varied history of logic as an intellectual endeavor, I propose that to determine our epistemic access to logic, we must follow Novaes and do history of logic. We must trace the concrete role logic has played in different societies and thereby the access to earlier forms of logic that earlier logicians had. Rather than speculate on the possibility of our access to atemporal forms of all inferences, we must assume at the outset that certain concrete conditions must be in place for either the discovery/invention of some form of logic, or its pedagogical/philosophical practice. The burden, in other words, must be on the access exceptionalist to prove that our epistemic access to logic occurs in a different way than that of every other science—careful study on the individual level, and the accumulated knowledge acquired through theoretical misfires on the disciplinary level.
An advocate of access exceptionalism could respond to the historical argument by insisting on the strict separation of the context of discovery and that of justification of logics. One might say that, even granting Novaes’ dialogical hypothesis, there might still be some atemporally true set of deductive norms, regardless of the empirical origin of the concept of deduction. The epistemic access the original inventors/discoverers of deductive syllogistic logic had was the same (or epistemically exceptional in the same way) as that of current logicians. First, while I grant that this remains a possibility in some sense, it becomes more futile as a philosophical explanation the more thoroughly we know the empirical origins of specific forms of logic: Similarly, while metaphysical realism may always be in some sense true and the right ontology has just not yet been found, metaphysical realism becomes a less plausible form of explanation the more thoroughly we have a history of attempts at metaphysics. Second, regardless of whether logic is “true,” or is true atemporally, the notion of “epistemic access” loses much of its ambiguity once we distinguish (1) the phenomenology of doing logic, and (2) the conditions of logic being done. On (1), many self-report a felt necessity in drawing inferences, a clarity in the relation of different sentential units once a system is understood. If there is any hope for the access exceptionalist, it is by appeal to the phenomenology of logic. Concerning (2), these conditions must always include personal and historical conditions: I can learn S4 because I have been educated in a certain way, because I have studied other logics, because I have certain capacities, because logic is an organized academic discipline, and one in which we now take it to be the case that we can treat modality formally, etc. The ultimate difference between my view and the access exceptionalist is that, on my view, the very phenomenology of doing logic is always itself conditioned by the situatedness of the logician, and so appeal to the phenomenology of doing logic to establish access exceptionalism will universalize a quite particular experience of contemporary academic logicians and thereby fail.
That said, we can preliminarily grant a certain sense in which exceptionalism holds true: Logic explanatorily structures thought in a way or to a degree that other sciences don’t. How to cash this out is where different philosophies of logic will differ. On my view, logic is a meta-theoretical enterprise in which we self-consciously reflect on our theoretical activity and thereby structure it.

[1] The distinction I draw between “access” and “explanatory” exceptionalism is not equivalent to the distinction made by Martin and Hjortland (2019) between “epistemological” and “metaphysical” exceptionalism.

Bas Kortenbach – The (In)Coherency of Mixed Metainferential Logics

Bas Kortenbach is a PhD student in Philosophy at the Scuola Normale Superiore in Pisa, Italy, under the supervision of Prof. Mario Piazza. His project concerns metainferential logic, focusing especially on core foundational—as opposed to more application-oriented— issues in and about the field. These include the appropriate validity criteria, the structure and size of the inferential hierarchy, what counts as a legitimate metainferential logic, and how the framework must be adapted to accommodate logics whose language goes beyond
1the propositional syntax. His general research interests lie broadly with formal logic and analytic philosophy, and in particular with the application of one of these disciplines to the other, as in philosophical logic or the philosophy of logic and mathematics. Previously he completed the MSc. in Logic at the ILLC, University of Amsterdam, graduating with a thesis on Epistemic Multilateral Logic under the supervision of Profs. Luca Incurvati and Julian Schloeder.
Mixed metainferential logics are logics which are metainferential, in the sense that they are characterized by their standards at higher inferential levels, and mixed, in the sense that the standards for premises and conclusions at a given level need not be identical either to each other or to the standard for the previous level (Pailos, 2019; Barrio et al., 2020). Such logics, in particular those in the so-called ST-hierarchy, have recently seen extensive application, for instance to semantic paradoxes related to truth (Barrio et al., 2021; Pailos, 2020) or validity (Barrio & Bezerra, 2024). However, a family of worries has emerged about some of the more peculiar behaviors of these logics. In particular, the logics appear, in various senses, not to be ‘self-obeying’ or ‘closed under their own rules’ (Golan, 2023; Porter, 2022; Scambler, 2020). It is easy to see that these phenomena are tightly connected to the fact that the logics are mixed, in the sense defined above. Thus a general doubt emerges about whether it is coherent, even in principle, to mix one’s metainferential standards. If so, to what extent does this depend on the sequence of standards, or the full consequence relation, displaying (despite its mixed nature) certain structural ‘coherence’ (Pasqualini, 2024; Ripley, 2022) or ‘uniformity’ (Barrio et al., 2024) properties?
The purpose of this talk is to clarify and review the debate surrounding these questions. First of all, we will untangle the variety of senses in which mixed logics can be (and have been) said not to be self-obeying or closed under their own laws. Secondly, we explore the relations to such structural features as uniformity (under translation) and up- and downwards coherence, as well as to the divide between local and global validity. Finally, we will evaluate the main response which proponents of mixed logics have offered to this type of objection. Namely: advocates of the ST-hierarchy based approach to paradox have claimed that in mixed contexts, the demand for a naive form of self-obedience is misplaced, and that instead only a tailor-made notion of ‘mixed obedience’ may be required (Barrio & Bezerra, 2024; Barrio et al., 2021; Roff ́e & Pailos, 2021). However, we argue that this kind of response misunderstands the motivation underlying the demand for self-obedience, and that the objectionist can reject the move to mixed obedience, insisting on their initial demand. We thus conclude that, pending a more assuaging reply on behalf of the mixed logician, the plausibility of mixed metainferential logics remains questionable.
References
Barrio, E., & Bezerra, E. (2024). The logics of a universal language. Asian Journal of Philosophy, 3(1), 12.
Barrio, E., Fiore, C., & Pailos, F. (2024). Meta-classical Non-classical logics. The Review of Symbolic Logic.
Barrio, E., Pailos, F., & Szmuc, D. (2020). A hierarchy of classical and paraconsistent logics. Journal of Philosophical Logic, 49(1), 93–120.
Barrio, E., Pailos, F., & Toranzo Calder ́on, J. (2021). Anti-exceptionalism, truth and the BA-plan. Synthese, 199(5), 12561–12586.
Golan, R. (2023). On the metainferential solution to the semantic paradoxes. Journal of Philosophical Logic, 52(3), 797–820.
Pailos, F. (2019). A family of metainferential logics. Journal of Applied Non-Classical Logics, 29(1), 97–120.
Pailos, F. (2020). A fully classical truth theory characterized by substructural means. The Review of Symbolic Logic, 13(2), 249–268.
Pasqualini, M. D. (2024). A review of the notion of coherence from the perspective of logic defined as a sequence of notions of consequence. Ana ́lisis Filos ́ofico, 44(1), 105–116.
Porter, B. (2022). Supervaluations and the strict-tolerant hierarchy. Journal of Philosophical Logic, 51(6), 1367–1386.
Ripley, D. (2022). One step is enough. Journal of Philosophical Logic, 51, 1233–1259. Roff ́e, A. J., & Pailos, F. (2021). Translating metainferences into formulae: satisfaction
operators and sequent calculi. The Australasian Journal of Logic, 18(7), 724–743.
Scambler, C. (2020). Classical logic and the strict tolerant hierarchy. Journal of Philosophical Logic, 49(2), 351–370.

Bogdan Dicher – Conditionals and Tolerance

Bogdan obtained his doctorate from the University of Melbourne (Australia) in 2015 and went on to hold postdoctoral appointments at the University of Cagliari (Sardegna, Italy) and at the University of Lisbon (Portugal). Since January 2024 he is a lecturer in the Philosophy Department at the University of the Witwatersrand. His areas of specialism are logic and the philosophy of logic, with a particular focus on substructural logics and the philosophy of logical consequence, mainly in the proof-theoretic semantics tradition.
The abstract can be found here.

Camilla Gallovich – Ungroundedness in Yablo’s Theory of Truth

Camila Gallovich is a Graduate Fellow at the Institute for Research in Philosophy of the National Scientific and Technical Research Council of Argentina (CONICET). She is also affiliated with the Philosophy Department of the University of Buenos Aires (UBA), where she holds a teaching position in Logic. Her areas of specialization are philosophical logic, the philosophy of mathematics, and formal metaphysics, with a particular interest in formal theories of truth and semantic and logical paradoxes. Her work has been published in journals such as Synthese and Análisis Filosófico and included in volumes edited by Synthese Library and Cambridge University Press. Her current research explores the relationship between the fixed-point and the graph-theoretic conceptions of paradoxicality, as well as the role the notion of groundedness plays in classical and non-classical formal theories of truth. She is a member of the Buenos Aires Logic Group and of the Argentinian Society for Analytic Philosophy (SADAF).
The thought that our attributions of truth and falsity must be grounded in non-semantic states of affairs constitutes an important semantic intuition. According to Stephen Yablo in Grounding, Dependence, and Paradox [4], this intuition is two-sided. Its first aspect—inheritance—draws on the way in which a complex statement inherits its meaning from certain simpler statements. Its second aspect—dependence—shows the way in which the meaning of a complex statement depends on simpler statements. Paradigmatically, the fixed-point con- struction given by Saul Kripke in his Outline of a Theory of Truth [1] provides an inheritance-style characterization of grounding, whereas the dependence-based construction introduced by Yablo [4] provides a dependence-style characteriza- tion. Yablo’s article states a further result: “any collection with an inheritance- style characterization admits a canonically related dependence-style characteri- zation” ([4], p.119). That means the statements that are sanctioned as grounded by these approaches are the same. Yablo also shows that the result extends to a fragment of the set of ungrounded statements; namely, to the set of statements that according to these theories are paradoxical.
The guiding question of the talk is how far Yablo’s result can be pushed. To settle the question, it will be useful to consider fragments of the ungrounded statements precluded in Yablo’s analysis and also to consider languages enriched by means of additional semantic predicates other than Tr(x). The talk will run as follows. First, I will show how to extend Yablo’s dependence-based char- acterization of grounding to a language containing a paradoxicality predicate. Then, I will provide a fine-grained treatment of ungroundedness by distinguish- ing between paradoxes, hypodoxes, and safely ungrounded statements. The resulting dependence-style characterization of truth and paradoxicality resem- bles an inheritance-style characterization recently provided by Lucas Rosenblatt and myself in the context of the fixed-point conception (cf. [2] and [3]).
References
[1] S. Kripke. Outline of a theory of truth. Journal of Philosophy, 72(19):690– 716, 1975.[2] L. Rosenblatt. Paradoxicality without Paradox. Erkenntnis, 88:13471366, 2023.
[3] L. Rosenblatt and C. Gallovich. Paradoxicality in Kripke’s Theory of Truth. Synthese, 200(71), 2022.
[4] S. Yablo. Grounding, dependence, and paradox. Journal of Philosophical Logic, 11(1):117–37, 1982.

Camillo Fiore – LP+, K3+, FDE+ and Their Generalised Classical Collapse

Camillo completed his Licentiate degree in Philosophy at the University of Buenos Aires (UBA), where he has served as a teaching assistant in Logic since 2020. In March of 2022 he started his five-year PhD studies in Philosophy also at UBA, with the funding of CONICET and under the supervision of Lucas Rosenblatt and Bruno Da R ́e. He is interested in a number of problems within the philosophy of logic, with particular emphasis on substructural logics, semantic paradoxes and the meaning of logical expressions. His Phd project, called “Mixed Logics, Metainferences and Truth” aims to study the non-transitive logic ST, the non-reflexive logic TS, and the metainferential hierarchies based upon them; in particular, it tackles the application of these systems to formal theories of truth. His articles have been published in journals such as Review of Symbolic Logic, Analysis and Mind, among others; they can be found at https://philpeople.org/profiles/camillo-fiore. Camillo works at Sociedad Argentina de An ́alisis Filos ́ofico (SADAF) and is part of the Buenos Aires Logic Group (https://ba-logic.com/).
(joint work w/ Lucas Rosenblatt)
Suppose you support a sub-classical logic L. Very roughly, a classical recapture result for L tells you that, if certain ‘safety conditions’ hold for a given domain of discourse, then the logical principles that are valid in classical logic but not in L are nonetheless sound for that domain. Having a result of this nature is of great importance for you as a supporter of L. Among other things, it allows you to answer what arguably is the most echoed ob- jection against sub-classical logics, namely, that they are deductively too weak: given an arbitrary collection of theoretical assumptions, its classical consequences strictly include its L-consequences. The answer consists in arguing that many key domains of discourse (such as, for instance, arithmetic) satisfy the safety conditions specified by the recapture result, and thus the objection does not apply to those domains.1
In his work entitled “LP+, K3+, FDE+ and their classical collapse”, Jc Beall [2] provides classical recapture results for the multiple-conclusion presentations of the paraconsistent logic LP [9], the paracomplete logic K3 [6] and the paraconsistent and paracomplete logic FDE [3]. Informally, each result says that, if a given inference holds in multiple-conclusion classical logic, CL+, then there is certain other inference (with some additional premises and/or conclusions) that holds in the target non-classical system. However, the philosophical significance of Beall’s results has been put into question. One of the main criticisms is that they presuppose that a non-logical theory is just a set of statements closed under logical consequence, but many theories based on paracomplete logics (such as K3+ or FDE+) cannot be plausibly formulated in this guise; rather, they need to be understood as sets of inferences.2 Thus, for instance, a naive paracomplete theory of truth over logic K3+ cannot have, on pain of triviality, all the statements of the form “A if and only if ‘A’ is true” as theorems; instead, it has to express the naivety of truth by validating all the inferences going from A to “‘A’ is true” and viceversa. Alas, when theories are understood in this more refined way, Beall’s results do not apply any more: we have no guidance for recapture.
In this work, we provide a series of generalizations of Beall’s results that help to overcome this criticism. The new results can be described as extending Beall’s recapture procedure to the so-called meta-inferential levels. Intuitively, a metainference of level 1 is just an inference with a unique conclusion whose premises and conclusion are themselves inferences; in turn, a metainference of level n > 1 is an inference with a unique conclusion whose premises and conclusion are metainferences of level n − 1. Thus, our our first generalization says that, if a given meta-inference of level 1 is valid in CL+, then for each of our target logics there is another metainference of level 1 (with some additional premises) that is valid in that logic. In turn, our last and most encompassing generalization applies to metainferences of arbitrary finite levels: it says that if a given meta-inference of level n > 1 is valid in CL+, then for each of our logics there is another meta-inference of the same level (with some additional premises) that is valid in that logic. We argue that our generalized recapture results put to rest the line of criticism we are considering, because they are compatible with understanding non-logical theories as sets of inferences and/or meta-inferences of any arbitrary level.
1 See [5, 7] and [1, 10] for arguments against and in favor of this kind of response, respectively.
2 The objection can be found in Nicolai [8] and Fiore & Rosenblatt [4]
References
1. [1] E. Barrio, C. Fiore, and F. Pailos. Meta-classical non-classical logics. The Review of Symbolic Logic, page 1–26, 2024.
2. [2] J. Beall. LP+, K3+, FDE+, and their Classical Collapse’. The Review of Symbolic Logic, 6(4):742–754, 2013.
3. [3] N. D. Belnap Jr. A useful four-valued logic. In Modern uses of multiple-valued logic, pages 5–37. Springer, 1977.
4. [4] C. Fiore and L. Rosenblatt. Recapture results and classical logic. Mind, 132(527):762– 788, 2023.
5. [5] V. Halbach and C. Nicolai. On the Costs of Nonclassical Logic. Journal of Philosophical Logic, 47:227–257, 2018.
6. [6] S. C. Kleene. Introduction to Metamathematics. North-Holland, Amsterdam, 1952.
7. [7] J. Murzi and L. Rossi. Generalized Revenge. Australasian Journal of Philosophy,
  98(1):153–177, 2020.
8. [8] C. Nicolai. The dream of recapture. Analysis, 82(3):445–450, 2022.
9. [9] G. Priest. The logic of paradox. Journal of Philosophical logic, 8(1):219–241, 1979.
10. [10] L. Rosenblatt. Should the Non-Classical Logician be Embarrassed? Philosophy and Phenomenological Research, 104(2):388–407, 2022.

Daniel Molto – A New Way to Make Sense of Copredication

Dr Daniel Molto is an Assistant Professor in the philosophy department at the University of Sussex. He has previously worked at Leeds Trinity University and the University of York, where he did his PhD (2015). He specializes in Philosophy of Language, Philosophical Logic and Philosophy of Religion, as well as the intersection of these areas. Some of his current research topics include glutty theology, that is inconsistent theories of the divine, and the semantics of copredicative sentences. With respect to the latter, he defends a view according to which, in the context of some sentence tokens, singular terms can refer to multiple entities at the same time, while the truth conditions for such sentence tokens remain determinate and consistent. This account involves distinguishing between the referent of a singular term (which can turn out to be more than one thing) and the interpretation of a singular term (which is always just one thing).
Copredication has been the source of a great deal of focus over the past fifteen years or so. The reason for this is that it provides a set of examples of the most intractable sort of polysemy. A sentence like ‘lunch was delicious, but went on forever’ seems to involve a singular noun (‘lunch’) which is picking out two things at once (a tasty meal and a long event). And yet the sentence seems otherwise unexceptional and sometimes true. But how can it be true when ‘lunch’ is singular and the sorts of lunches that have tastes are different things from the sorts of lunches that have durations (the physical food has a taste, and the event a duration)?
In part 1 of this paper, we introduce copredication, and we distinguish between different categories of response to copredication. These include proposals that involve rejecting or heavily modifying truth-conditional semantics, proposals which posit complex mereologically-structured referents of polysemous nouns, and a proposal the so-called “Activation Package Theory”. As the goal of the paper is to demonstrate the compatibility of truth-conditional semantics with polysemy, we will largely set aside the first category and instead focus on arguing that there are serious problems with the second and third category. Part 2, we make our own attempt.
On our account, a semantics is an ordered quadruple <D, C, S, I>, where D is a domain, C is a set of contexts which index terms of L0 according to the following rule
For any term t of L0, whenever t is indexed by context cn, every sentence of which t is a component is indexed by cn, and whenever a sentence is indexed by a context cn, every term of that sentence is indexed by cn.
S is a set of functions from C onto partitions of D.
Finally, I is a mapping of terms of L0 such that:
For any singular term tc0 of L0 and for some Sn ϵ S, I(tc0) ϵ Sn(c0).
For any 1-place predicate F1c0 of L0 and for some Sn ϵ S, I(Fc0) ⊆ Sn(c0)
For any 2-place predicate F2c0 of L0 and for some Sn ϵ S, I(F2cn) ⊆ Sn(c0) x Sn(c0).
Part 3 involves some further explanation of our account and attempts to correct some possible confusions. Finally, in Part 4, we show how our account can satisfy intuitions about some more complicated instances of copredication.

Ebubekir Deniz – Towards a Protologic: A Transcendental Analysis of Formal Systems

Ebubekir M. Deniz is a faculty member in the Philosophy Department at Istanbul Medeniyet University. His research focuses on the foundational aspects of logic and its philosophical implications. He completed his PhD in 2024 with a dissertation examining the fundamental concepts, principles, and connectives of protologic. During his master’s studies, he explored dialetheic logic and its relationship to the metaphysics of time, further enriching his expertise in the philosophy of logic.
From 2021 to 2022, he was a visiting researcher at the CUNY Graduate Center, conducting research under the supervision of Graham Priest. His current work addresses the intersections of logic, metaphysics, and the philosophy of formal systems, with a particular interest in debates surrounding logical pluralism and anti-exceptionalism.
This paper explores the possibility of a protologic–a foundational logic that underlies the structure of any formal system. Although philosophers like Robert Hanna and Penelope Maddy have proposed foundational logics as necessary for human cognition, they leave the principles and conditions of such logics largely undeveloped. I argue that these foundational logics, rather than serving only cog- nitive functions, are essential conditions for the structure and coherence of formal systems themselves, enabling symbols to function as meaningful and coherent units within any logical framework.
Using a transcendental method, this paper examines the core requirements that make formal systems possible, focusing on the necessity of unitization, or the recognition of symbols as discrete and identifiable entities within a system. I term this process symbolic unification, which hinges on three fundamental relational concepts: sameness, otherness, and togetherness. Including a symbol in a system demands an awareness of its distinctness from other symbols; without this awareness, the system risks collapsing into a homogeneous, indistinct entity. Thus, the construction of multiplicity within a formal system fundamentally relies on differentiating units. Recognizing a symbols distinctness requires seeing it as the same with itself and different from others, such that sameness and otherness are in necessary unity. This unity, in turn, presupposes togetherness as a distinct concept, providing the cohesive relational framework within which sameness and otherness can operate.
Rather than aiming to fully develop a comprehensive protologic, this paper introduces these protological concepts and argues that they form the basis for any formal languages coherence and differentiation. By positing sameness, otherness, and togetherness as the fundamental conditions for symbolic operation within formal systems, I suggest that a deeper understanding of these concepts will enable further exploration into the universal principles required for any logical structure. This approach positions protologic as an indispensable foundation for formal logic, providing an essential framework that grounds diverse logical systems in a common set of transcendental conditions.

Elia Zardini – Unstable Knowledge

Elia Zardini completed his undergraduate studies in philosophy, mathematics and history at the Ca' Foscari University of Venice and the Technical University of Berlin. He obtained his PhD in philosophy from the University of St Andrews in 2008. Since then he has held positions at the University of St Andrews, the University of Aberdeen, the National Autonomous University of Mexico, the University of Barcelona and the University of Lisbon. He is currently a Ramón y Cajal Researcher at the Complutense University of Madrid, Chief Research Fellow at the Higher School of Economics and Chief Editor of Disputatio. At present he works mainly on the application to questions of metaphysics of the conceptual tools and techniques he initially developed in his solutions to the paradoxes of vagueness and self-reference. In addition to this approach, he also pursues other lines of research in epistemology (immediate justification, transparency of knowledge and other states, the logic of knowability, know-how), philosophy of logic (nature and properties of logical consequence) and philosophy of language (reference, context, conditionals).
The Knower paradox appeals to a sentence meaning that k is not known (by anyone at any time). The paradox argues that we can prove by reductio that is not known (for, if it were known, by the principle of factivity of knowledge, it would be not known), i.e. we can prove , which, by the principle that proof yields knowledge, entails that is known, thereby landing us in a contradiction.
I shall start by arguing that the Knower paradox offers underappreciated resistance to standard nonclassical approaches to the paradoxes of selfreference, because of the divergence they require between rejecting a sentence and accepting its negation. To wit, on the one hand, antialethic approaches (e.g. Field [2008]) deny the law of excluded middle, and so reject a paradoxical sentence without accepting its negation. However, presumably, if one rejects one should accept that one does not know , so that rejection of implies that one should accept that is not known, i.e. implies that one should accept , and so the antialetheist would after all be committed to accepting ! On the other hand, dialethic approaches (e.g. Priest [2006]) deny the law of contradiction, and so accept a paradoxical sentence without rejecting its negation. However, presumably, if one accepts one rejects that one does not know , so that acceptance of implies that one should reject that is not known, i.e. implies that one should reject , and so the dialetheist would after all be committed to rejecting !
I shall move on to address a problem which the Knower paradox raises for my own favoured non-contractive, instability-based (“abebeotic”) approach, and which consists in the apparent lack of a suitable principle of “epistemic ascent”. To wit, the abebeotic approach solves the semantic paradoxes by denying the metaentailment of contraction (that is, roughly, if entails , then entails ) , and, in turn, explains failure of to contract in terms of the state-of-affairs (SA) expressed by being unstable (that is, roughly, its causing a SA that does not coobtain with it). In the case of , that would seem to require that the SA < is not known> cause < is known>, but it’s not in general the case that <P> causes <‘P’ is known>. I shall address this problem by noting that, assuming that is not known, (1) its negation must hold at some (epistemic) possibility, while the plausible principle that <It is not the case that P> causes <‘P’ is not known> entails that, (2) at all possibilities where the negation of (i.e. ‘It is not the case that is not known’) holds, the obtaining of <It is not the case that is not known> leads to the obtaining of <‘ is not known’ is not known> (i.e. leads to the obtaining of < is not known>); (1) and (2) can then plausibly be taken jointly to cause < is known>.
One of the distinguishing features of a noncontractive approach is that paradoxical sentences are neither inconsistent (as they are on an antialetheic approach) nor valid (as they are on a dialetheic approach). Shifting from logic and metaphysics to pragmatics, I shall consequently defend the coherence of accepting sentences that express (ungrounded) unstable SAs. The key principle here is that, if expresses an unstable SA, one can coherently accept , but only “once”, in the sense that the acceptance in question can only be used to occupy one, and only one, position among all those licensed by its conceptual role. This key principle has several consequences: firstly, if one infers from , one must abandon one’s acceptance of ; secondly, for every “coherence condition” on accepting (‘ is true’, ‘ is known’, ‘ can be accepted’ etc.), one shouldn’t accept and accept that such condition holds; thirdly, one shouldn’t accept the selfconjunction . I shall show how several arguments purporting to show the incoherence of accepting a paradoxical sentence actually violate one or the other of these consequences of the key principle.
On this basis, I shall further argue that, not only can we coherently accept a paradoxical sentence, we also have (epistemic) justification for doing so. Focussing without loss of generality on the case of truth, in its essence the argument observes that instability of the SAs expressed by the paradoxical sentences ‘P’ and ‘~P’ requires e.g. that <~P> does not coobtain with <‘~P’ is true>, which entails, by naive truth and the relevant DeMorgan principle, ‘Either P or P’ (with ‘either… or…’ being a multiplicative disjunction). While, in a noncontractive logic, such a disjunction does not entail ‘P’, it still offers an excellent (nondeductive) reason for accepting ‘P’. Since the same argument applies for ‘~P’, we have justification for accepting ‘P’ and justification for accepting ‘~P’ (but, by the law of noncontradiction, of course no justification for accepting both). Therefore, we have a theoretical choice between accepting ‘P’ and accepting ‘~P’—for example, it’s up to us whether the Liar sentence is true or false. I shall conclude by proposing that this situation is adequately described by employing an operation of free-choice disjunction that is very naturally identified in a noncontractive logic with the operation of additive conjunction, so that, to continue with the example of the Liar sentence, that sentence’s status is adequately described by saying that either it is true or it is false (with ‘either… or…’ now being a free-choice disjunction, as e.g. in ‘Either you have fish or you have meat’).
References
Hartry Field. Saving Truth from Paradox. Oxford University Press, Oxford, 2008.
Graham Priest. In Contradiction. Oxford University Press, Oxford, 2nd edition, 2006.

Federico Pailos – Metainferentially Substructural Validity Theories

Federico pailos is a Postdoctoral Researcher at the University of Tübingen (Germany). He has been an Independent Researcher at IIF-SADAF, an academic center of the National Scientific and Technical Research Council of Argentina (CONICET), and an Assistant Professor at the Department of Philosophy at the University of Buenos Aires.
His research is mainly in Philosophical Logic. Nowadays he is working on Metainferential Logics, Many-valued Logics, Substructural Logics and Contra-Classical Logics. His work revolves around the notions of truth, validity, and logicality specially in semantic paradoxes and the expressive limits of formal languages, and also in the meaning of logical constants and the relation between proof systems and semantics. He has also work on metaphilosophy and philosophy of language, specially on the semantics of knowledge attributions.
He has received a Humboldt Fellowship for Experienced Researchers to work at the Wilhelm-Schickard-Institut für Informatik form the Eberhard-Karls-Universität Tübingen during 2020-2021. He is a member of the Buenos Aires Logic Group and the Argentinian Society of Philosophical Analysis (SADAF). More about this work here.
Brian Porter ([3]) has presented higher-level metainferential versions of the validity Curry argument introduced by Beall and Murzi ([2]). What is peculiar of these paradoxes is that no operational rule nor any structural rule play any role in the derivation of the unpleasant result. Thus, to block them and have a uniform solution to, at least, every validity Curry paradox, something else needs to be done. We introduce, as an answer to Porter’s challenge, validity theories that are substructural at every metainferential level. In this sense, they are free from Porter’s criticism. These theories count as both theories of naïve validity (because they do not give up VP or VD, nor any higher-level version of them) and as offering a uniform solution to validity curries, in the more traditional and intuitive sense: either they give up every higher-level version of Cut—as well as every higher-level version of it—or they give up Contraction—as well as every higher-level version of it. We provide philosophical justifications for each of these options. Finally, we will assess another way to reply to Porter’s challenge to substructural positions. On [1], Ahmad claims to have proven that it is possible to reduce higher-level metainferential versions of the validity Curry paradox to the original validity Curry paradox by Beall and Murzi. If he is right, then our work, and Porter’s challenge as well, is pointless, as substructuralists need not to engage in higher-level versions of this paradox. We will explain why Ahmad does not succeed in his attempt. As a consequence, the substructuralist still needs to answer Porter’s challenge, either by finding an appropriate way of reducing higher- level paradoxes to a traditional inferential paradox, like Beall-Murzi’s, or she should reject, at every metainferential level, the same kind of metainferential schema—i.e., the corresponding metainferential version of Cut or Contraction—, thus providing a uniform solution to each of these paradoxes (in the traditional sense, not in Porter’s way to understand uniformity).
References
[1] R. Ahmad. Higher-Level Paradoxes and Substructural Solutions. Studia Logica, June 2024.
[2] J. Beall and J. Murzi. Two Flavors of Curry’s Paradox. Journal of Philosophy, 110(3):143–165, 2013.
[3] B. C. Porter. Three Essays on Substructural Approaches to Semantic Paradoxes. PhD thesis, City University of New York (CUNY), 2023.

Fernando Cano-Jorge – Inconsistent Sets and How to Compute Them

Fernando Cano-Jorge is a postdoctoral fellow at the University of Otago and the University of Canterbury working in a joint project with Zach Weber and Jack Copeland on paraconsistent computability theory. He is also a researcher at Universidad Panamericana in Mexico City, where he has also been a lecturer in the past. He is interested in non-classical logics, especially in paraconsistent, relevant and connexive logics, and in inconsistent mathematics. He is part of the LógicaMexa research group at UNAM, as well as a member of the Australasian Association for Logic, and the Logicians’ Liberation League.
The abstract can be found here.

Jason Carter – Diodorean Modal Logic and The Reaper

Jason Carter is a lecturer in philosophy at the University of St Andrews. He has previously held positions at Exeter College, University of Oxford, the University of Edinburgh, LMU Munich, and the University of Glasgow. His research centres on ancient Greek psychology, metaphysics, logic, and ethics. He also has research and teaching interests in philosophy of religion and Islamic philosophy. He is the author of ‘Aristotle of Earlier Greek Psychology: The Science of Soul’, published by Cambridge University Press, as well as a number of articles on psychology and ethics in ancient philosophy. His most recent work revolves around understanding the modal logic of ancient theories of future contingents, and the logic of negation in Neoplatonism.
The Reaper Argument is a Hellenistic philosophical argument, originating in the so-called Dialectical School, against future contingent truths. It may be reconstructed as follows: (1) Necessarily, either you will reap or you will not reap. (2) If you will reap, then it is certain that you will reap. (3) If you will not reap, then it is certain you will not reap. (4) Therefore, it is not the case that perhaps you will reap and perhaps you will not reap. (5) Therefore it is not contingent that you will reap or not reap. Evaluating the argument is difficult for several reasons, amongst which are that we do not know what modal theory its author relied upon. However, scholars have argued that the Reaper Argument is likely related to the temporalized modal theory of the third century Greek philosopher, Diodorus Cronus. Diodorus affirmed the following temporalized modal axioms: (I) a proposition p is possible if and only if p is true now, or p will be true at some later time [◇p ↔ (p ∨ Fp)]; (II) a proposition p is impossible if and only if p is false now and it will not be the case that p is true at some later time [¬◇p ↔ (¬p ∧ ¬Fp)]; (III) a proposition p is necessary if and only if p is true now and it is not the case that at some later time it will be true that not-p [□p ↔ (p ∧ ¬F¬p)]; and (IV) a proposition p is non-necessary if and only if p is false now, or p will be false at some later time [¬□p ↔ (¬p ∨ F¬p)]. While some scholars, such as Gerhard Seel, have argued that the Reaper argument is compatible with Diodorus’ modal axioms, other scholars, such as Suzanne Bobzien, have argued that he could not be its author, because its premises commit the author to unrealised possibilities, and thus a notion of contingency, that is non-Diodorean. In this paper, I argue that the Reaper Argument is valid within Diodorus’ modal logic, if one extends his modal logic to include dated future contingents. To show this, I offer a formal reconstruction and proof of the Reaper argument, based on A.N. Prior’s work on Diodorean modality.

Jeremiah Joven Joaquin – The Simplest Solution to all Deontic Paradoxes?

Jeremiah Joven Joaquin is the Dominga Cecilia Cabangon Chair in Comparative Philosophy and a Founding Research Fellow of the Southeast Asia Research Center and Hub (SEARCH) at De La Salle University (DLSU), Manila, Philippines. He was the former President of the Philosophical Association of the Philippines (PAP; 2017-2023) and was the Founding Secretary General of the Union of Societies and Associations of Philosophy in the Philippines (USAPP; 2018-2019). He specializes in philosophical logic, metaphysics, moral philosophy, and the philosophy of religion.
In his 1981 paper, “The paradoxes of deontic logic: the simplest solution to all of them in one fell swoop,” Hector-Neri Castañeda develops a deontic logic, which, as his title suggests, presents the simplest solution to all deontic paradoxes, like Ross’s paradox of obligation, Prior’s good Samaritan paradox, Chisholm’s contrary-to-duty puzzle, and Forrester’s gentle murder paradox (aka the deepest paradox in deontic logic). In this paper, I discuss what this deontic logic amounts to and examine whether it truly is the simplest solution to all deontic paradoxes.

Jonathan Erenfryd – Capturing Validity, and Beyond

Jonathan Erenfryd is a PhD student in Philosophy at the University of Buenos Aires, specializing in logic and currently holding a doctoral scholarship from CONICET. He is a member of the Buenos Aires Logic Group and serves as an assistant professor at the University of Buenos Aires. His research cur- rently focuses on the concept of validity in substructural logics, with particular attention to how these logics can accommodate a validity predicate that avoids paradoxes while capturing both valid inferences and meta-inferences. Addition- ally, he is interested in exploring alternative logical statuses beyond validity, such as invalidity, antivalidity, and contravalidity, as well as in formal theories of truth. Erenfryd participates in various projects addressing these and other topics. He has presented some of his research at regional and international conferences.
The abstract can be found here.

Katarina Maksimović, Miloš Adžić , and Jovana Kostić – Reflexive Paradoxes

Milos Adžić serves as an Associate Professor in the Department of Philosophy at the Faculty of Philosophy, University of Belgrade. His research focuses on logic, the philosophy of mathematics, and related fields.
Jovana Kostić is an Assistant Professor in the Department of Philosophy at the Faculty of Philosophy, University of Belgrade. Her primary interests lie in logic, the philosophy of mathematics, and the philosophy of language.

Katarina Maksimović is a Research Associate affiliated with the Institute for Philosophy, University of Belgrade. She specializes in logic, the philosophy of mathematics, and the philosophy of computation.
This paper examines reflexive paradoxes, focusing on their nature, significance, and implications for philosophical and mathematical reasoning. Reflexive paradoxes, exemplified by the Liar paradox, are often categorized as “paradoxes of self-reference”, a term that is descriptively accurate for some cases but not all. We suggest “reflexive paradoxes” as a broader and less misleading label, following Russell’s terminology in Principia Mathematica. Reflexive paradoxes arise when a statement refers to or depends on itself, generating contradictions or indeterminacy. The mathematical interest in these paradoxes is largely due to their potential for generating contradictions, while philosophers are drawn to their puzzling nature and their implications for language, logic, and self-reference.
Philosophically, reflexive paradoxes intersect with broader concerns about the consistency of ordinary language and the foundations of in- tellectual activity, including mathematics. Defenders of ordinary language argue against claims that it is inherently inconsistent, a position that is vital for philosophy, which relies on language to operate. Reflexivity is central to philosophical inquiry, as it features in self-refutation arguments, self-conscious reasoning, and even in philosophy’s attempts to justify itself. The denial of reflexive modes of expression could paradoxically undermine philosophy itself, as such denial would often require reflexive reasoning to be coherent.
We discuss Mackie’s treatment of reflexive paradoxes in Truth, Probability and Paradox. Mackie distinguishes between reflexive statements that are self-dependent and those that are not, suggesting that the former generate paradoxical indeterminacy. While he rejects blanket bans on self-reference, Mackie argues that indeterminacy emerges from the meaning of reflexive statements rather than from their exclusion. Mackie’s nuanced position attempts to balance the meaningfulness of reflexive statements with their indeterminate truth value, asserting that indeterminacy does not necessitate their rejection. However, his framework raises questions about the distinction between indeterminacy and meaninglessness. For Mackie, understanding the meaning of a paradoxical statement leads to an awareness of its paradoxical nature, but this claim invites further exploration.
Finally, we offer a critique of Mackie’s framework, questioning whether his approach avoids self-refutation. If reflexive statements are inherently indeterminate, then Mackie’s own claims about the nature of reflexivity risk falling into reflexive-paradoxical territory. His dismissal of hierarchical solutions, while persuasive, complicates the task of resolving reflexive paradoxes without introducing inconsistencies. Moreover, the relationship between meaning and paradoxicality remains contentious. The tension between reflexivity and coherence underscores the broader philosophical challenge of reconciling reflexive reasoning with the need for determinate meaning in philosophical and logical systems.

Kevin Purkhauser – From Paradoxes to Perspectives: A Metainferential Approach to Semantic and Vagueness Paradoxes

Purkhauser trained in physics, philosophy, as well as in the cognitive and neurosciences. Interested in combining all these areas of expertise, his research is concerned with a broader and deeper understanding of emergent phenomena in the context of adaptive biological systems. In particular, he is focusing on the application of synthetic approaches to the dynamics of living processes, and their limitations. This includes exploring how emergent phenomena arise from complexity, where individual interactions give rise to completely different system properties. His work also investigates modes of formalization, examining not only their boundaries but also their potential for uncovering new perspectives on the behavior and organization of complex systems.
This paper explores the application of metainferential and hierarchical logics to address semantic paradoxes (e.g., the Liar Paradox, Curry’s Paradox) and vagueness paradoxes (e.g., the Sorites Paradox). While classical frameworks struggle to resolve these issues without sacrificing foundational coherence, metainferential logics offer a structured approach that aligns inference rules with hierarchical perspectives of truth and meaning.
Building on perspectival realism and emergence theory, I propose that paradoxes arise from the failure to account for the multi-level dynamics of inference and meaning. By conceptualizing logical systems as emergent processes—where the relationship between rules and metarules mirrors biological and computational organization—we gain new insights into how to resolve these paradoxes without collapsing into triviality.
This framework also engages with logical pluralism, arguing that different paradoxes reveal the need for context-sensitive inferential hierarchies. I will illustrate the approach using examples from proof-theoretic semantics and inferentialism, showing how metainferential strategies clarify the epistemic status of paradoxes while preserving consistency and explanatory power.

Kurt Tubera and Mark Dacela – On Ineffability and Hypodox

Kurt Christian B. Tubera is an instructor from the Department of Philosophy, University of the Philippines, Diliman. He earned his BA in Philosophy at De La Salle University. He aims to specialize in the field of Epistemology. He also dabbles in the fields of Metaphysics, Philosophy of Mind, Logic, and Moral Philosophy. Contact: kbtubera@up.edu.ph.
Mark Anthony L. Dacela earned his PhD from De La Salle University Manila where he is also an Associate Professor and serves as the current Chair of the Department of Philosophy. He has published works in epistemology, ethics, and education in Intersections, Educational Philosophy and Theory, Diametros, Kritike, Asia-Pacific Social Science Review, and Philosophia: International Journal of Philosophy. He is one of the editors of the book Stephen Hetherington on Epistemology: Knowing, More or Less, recently published by Bloomsbury. Contact: mark.anthony.dacela@dlsu.edu.ph.
The ineffability paradox arises from a proposition stating that φ is ineffable, where φ typically represents religious concepts such as God, Dao, and similar entities. This leads to a contradiction: φ is both ineffable and not ineffable at the same time, same respect given that there is at least one thing we can say about φ that is, it is ineffable. This study explores this paradox in relation to Russells paradox, as both share structural similarities as self-referential paradoxes. Building on Eldridge-Smiths method of resolving paradoxes by transforming them into hypodoxes which defuse the explosive contradiction resulting from the overdetermination of propositional values, this paper intends to do two things. First, to extend the hypodox method to resolve the contradiction inherent in the proposition φ is ineffable. Second, to critically examine existing counterarguments to the hypodox method as it applies to the ineffability paradox. Through this analysis, the paper illustrates the limitations of the hypodox method as a universal solution to paradoxes, while suggesting that the paradox of ineffability remains contradictory even if we treat it as a hypodox.

Masanobu Toyooka – Humberstone’s Ω in Curry’s Logic D

Masanobu Toyooka is a postdoctoral researcher working on philosophical logic. He received his Ph.D. from Hokkaido University in June 2024 under the supervision of Katsuhiko Sano. The dissertation ``An Investigation Into Addition of Classical Negation to First-Order and Generalized Intuitionistic Logic'' investigates proof-theoretically and semantically various ways of adding classical negation on top of first-order intuitionistic logics and subintuitionistic logics. The main interests are proof theory, intuitionistic logic, negation, and inferentialist approaches to a logical connective. He is also interested in intermediate logics, relevant and paraconsistent logics, modal logics, non-monotonic reasoning, various proof theories, and philosophy of language and logic. He is currently engaging in the project ``Proof-Theoretic Research of Coexistence of Different Logics Focusing on the Concepts of Negations'', which started in April 2022 and will end in March 2025. This project has been financially supported by JSPS and the contribution in this conference is also part of it.
The abstract can be found here.

Meha Mishra – From Mythology to Machine: Integrating Paraconsistent Logic into AI Ethics

I hold undergraduate and postgraduate degrees in Mathematics and Philosophy, and I earned PhD in Logic from IIT Kanpur, India. My PhD research revolves around the logical representation of moral conflicts. A lack of appropriate representation of conflicting obligations in the existing logics compelled me to identify the tools for an inconsistency tolerant logical system which provides a treatment to deontic explosion. I studied the missing link between inconsistency tolerance with respect to accepting two morally possible and conflicting duties and use paraconsistent deontic logics to deal with contradictory obligations. I proposed to extend the standard system of deontic logic to paraconsistent deontic logic, by dropping some of the strong and impractical axioms. In 2024, I was an academic visitor at the Institute for Ethics in AI, University of Oxford. My current research focuses on integrating Indian philosophical traditions into AI ethics.
Philosophical and ethical debates on moral conflicts have persisted for centuries. The Indian mythological text Bhagavad Gita provides an interesting example of a moral conflict in the character of Arjuna. Arjuna’s moral dilemma is a conflict between his obligation to uphold his duty as a warrior and his obligation to his family and loved ones. This highlights the intricate nature of moral conflicts and the importance of considering all relevant factors when making ethical decisions. Standard deontic logic provides a framework for analyzing moral conflicts, but it has limitations. An alternative approach is to use paraconsistent logic, which acknowledges that contradictions can exist without leading to absurd conclusions. Adopting paraconsistent deontic logic can significantly enhance AI decision-making by providing a more robust framework for handling ethical dilemmas. Traditional logic systems, which operate on the principle that a single contradiction invalidates the entire system, often fail when faced with morally conflicting obligations. In contrast, paraconsistent logic allows for contradictions to coexist without leading to logical collapse, enabling AI to process and navigate complex moral scenarios more effectively. For instance, an AI designed for autonomous vehicles might face a scenario where it must choose between causing harm to different parties. Traditional logic would struggle with such conflicting directives, potentially leading to inaction or inappropriate decisions. A paraconsistent approach, however, would allow the AI to weigh the conflicting obligations and make a decision that best aligns with human ethical considerations, even if some obligations are compromised. Moreover, this approach ensures that AI systems remain functional and coherent even when encountering contradictory information or moral imperatives. By reflecting the complexity of human moral values, paraconsistent deontic logic helps AI systems make decisions that are more acceptable and understandable to humans. This alignment fosters greater trust and collaboration between humans and AI, as the decisions made by AI are more likely to resonate with human ethical standards.

Michalis Christou – Contradiction and Inconsistency: Different… But the Same. (+ Some Thoughts on 3-valued Logics)

Michalis Christou is a PhD researcher in the Institute of Philosophy and Scientific Method at the Johannes Kepler University (JKU) in Linz, Austria. His research interests lie in the role that Logic plays in the Philosophy of Science. More specifically, he is studying the way inconsistencies and contradictions are (and were) treated in science and the effects they (may) have on scientific reasoning and on scientific theories in general. In relation to that, he is furthermore interested about the nature of inconsistencies between theory and observation in science and, at the same time, at the very notion of observation as it is currently being used in differing ways within the Philosophy of Science literature which poses a problem in analyses of the phenomenon of inconsistencies in (empirical) science. He finished his Bachelors (with Honours) in Philosophy at the University of Stirling in Scotland, and his Masters (in Philosophy) at the University of Bristol, England.
In various philosophical fields people usually distinguish between a contradiction (having a pair of statements which one is the negation of the other) and an inconsistency (having a pair of statements which cannot both be true, but both can be false): Strawson (1952) differentiates between them on logical grounds. About beliefs, Foley (1979) regards inconsistent beliefs as posing a serious problem, but not as serious as contradictory beliefs. Concerning quantum mechanics, Arenhart and Krause (2016) argue that quantum superpositions (the multiple states a quantum system is in before measurement) is an example of an inconsistent situation, not of a contradictory one. Concerning the history of science, Vickers (2013) holds that it can be the case that inconsistencies in scientific theories (e.g. in Bohr’s theory of the atom and in Newtonian cosmology) may not eventually reach a contradiction.
What these cases have in common is that they see an inconsistency as being less serious than a contradiction. The main sentiment seems to be that ‘it is just a mere inconsistency. It is serious and we need to deal with it, but at least it is not a contradiction'. And since these two are taken to lie on different problematic levels, different ways of solving them are needed. In science, for example, if an inconsistency is detected in our theories, then we can tolerate it for a bit until a solution is found. Whereas if a contradiction arises, then we need to immediately stop everything else and try to solve it. The reason is simple: classical logic, which is usually taken to be the underlying logic of (reasoning in) science, can work with inconsistencies but it cannot tolerate contradictions. A contradiction would lead to logical explosion and render the theory as useless. I concede that prima facie there is a difference between them.
In this paper, however, I want to argue that an inconsistency always involves a contradiction: it is just ‘hidden’, but it is still there and poses the same problems as a plain and explicit contradiction. To show how and why this is the case, I will use an example from the history of science where there was an inconsistency between theory and observation. Because an example from the history of science will be used, it is important to say that scientists (at least in some degree) have to follow the rules of logic in their reasoning and workings in order to avoiding unwarranted conclusions. The reason can be derived from Dewey (even though the context here differs from what he had in mind when writing this): “To engage in an inquiry is like entering into a contract. It commits the inquirer to observance of certain conditions. A stipulation is a statement of conditions that are agreed to in the conduct of some affair [and it is] first implicit in the undertaking of inquiry” (Dewey 1938: 16).
This paper will take on an example raised in Priest (2002). Namely, with the precession of the perihelion of Mercury’s orbit between prediction (5776 seconds of arcs per century) and actual observation (5600 seconds). On the face of it, one will notice that this does not show a clear contradiction. 5600 is not the negation of 5557. Furthermore, both (propositions) can be false if the actual precession of Mercury’s orbit is 4000 seconds. Let p be ‘5600 seconds’ and let q be ‘5557 seconds’. q implies the following set of propositions: ‘not 5000 seconds’; ‘not 5100 seconds’; ‘not 5600 seconds’; and so on for all rational positive real numbers. That is, we have a situation in which q essentially implies (¬r & ¬s & … & ¬p). From this, I argue that we can derive p ꓥ ¬p, which is a contradiction. The main point here is that the mere appearance of a conjunction (the addition of further elements in one of the two propositions) does not change the fact that a contradiction is still in place. I will be following Strawson in that by applying “apredicate to something, we implicitly exclude from application to that thing the predicates which lie outside the boundaries of the predicate we apply” (Strawson 1952: 6).
It is important to attend this issue because the treatment or the explanation given for a contradiction in the sciences depends on whether we consider the said issue as a contradiction or not. In other words, we first need to correctly identify the problem in order to then try and find a fitting solution or explanation for it.
To conclude, some further thoughts will be given regarding (any) implications this analysis might have on multivalued logics and, more specifically, for 3-valued logics.
References
Arenhart, J. R. B., & Krause, D. (2016). CONTRADICTION, QUANTUM MECHANICS, AND THE SQUARE OF OPPOSITION. Logique et Analyse, 235, 301–315. https://www.jstor.org/stable/26767830
Dewey, J. (1938). Logic. The Theory of Inquiry, New York
Foley, R. (1979). Justified Inconsistent Beliefs. American Philosophical Quarterly, 16(4), 247–257. http://www.jstor.org/stable/20009767
Priest. G. (2002) Inconsistency and the Empirical Sciences. In: Meheus J. (eds) Inconsistency in Science. Origins (Studies in the sources of scientific creativity), vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0085-6_7
Strawson, P.F. (1952). Introduction to Logical Theory. London, England: Routledge.
Vickers, P. (2013) Understanding Inconsistent Science, Oxford University Press.

Morteza Moniri – Rule-following Paradox and Logic

Morteza Moniri is an Associate Professor of Mathematical Sciences at Beheshti University in Tehran, Iran. He earned his PhD from the Institute for Studies in Fundamental Sciences in Tehran. Dr. Moniri has authored several papers on mathematical logic, with a focus on intuitionistic bounded arithmetic and Kripke models. Recently, he has developed an interest in the applications of logic within the philosophy of science, mathematics, and logic. He is also the author of the book "Philosophy of Mathematics for Mathematicians," written in Farsi. His current areas of study include the rule-following paradox, revisability versus unrevisability of logic, pluralism versus monism in logic, and the adoption problem in logic raised by Saul Kripke. His goal is to integrate these issues into a cohesive research project.
This paper explores Wittgenstein's paradox of rule-following within the context of logic. We examine whether accepting the rule-following paradox can coexist with the irreversibility of logical rules. Our argument posits that if doubt is plausible concerning basic arithmetic operations like addition, then similar doubt applies to logic.
Wittgenstein's paradox, introduced in "Philosophical Investigations," has been pivotal in philosophical discourse. Kripke's extensive discussions on this paradox highlight its significance in Wittgenstein's work. Following Brown's interpretation of Kripke and Wittgenstein, we analyze the paradox's impact on mathematics.
Using natural numbers' summation as an illustration, Kripke questions the certainty of addition's intended meaning, suggesting no natural evidence guarantees consistent function beyond a large number N. Wittgenstein contends that doubts about sums beyond N lack evidential basis, framing the issue as a semantic paradox.
To address the paradox, Wittgenstein argues that universal doubt is unreasonable, as it implies an impossible external standpoint. He posits that doubt within a dream differs fundamentally in meaning. Despite Wittgenstein's potential rejection of skepticism in logic, the historically greater stability of arithmetic over logic suggests higher doubt susceptibility in logical rules. Non-classical logics predominantly stem from alternate interpretations of logical rules. Intuitionistic logic, for instance, restricts Reductio ad absurdum to negative formulas.
Kripke argued that doubt about basic logical rules is untenable, as these rules underpin meaningful doubt itself. This epistemic circularity in learning logical rules, akin to the rule-following paradox, emphasizes the a priori nature of logic for many philosophers and logicians. But according to the original paradox, this resolution is untenable. Wittgenstein's argument that universal doubt is unreasonable does not fully address the inherent issue presented by the rule-following paradox. The core of the paradox lies in the idea that for any given rule, our understanding and application of it are not rooted in any objective evidence but are instead subject to individual interpretation and internal consistency.
If, as Wittgenstein suggests, our grasp of arithmetic functions such as addition can be doubted beyond a certain point due to lack of evidence, the same doubt must extend to the logical rules we take for granted. This brings us back to the heart of the paradox: the difficulty in asserting that any rule, logical or otherwise, holds universally when our understanding is inherently finite and potentially flawed.
Kripke’s notion of the epistemic circularity in learning logical rules echoes this concern, emphasizing that without an initial certainty of these rules, we remain trapped in an infinite regress. Hence, even the most basic rules of logic, like modus ponens, cannot escape this skeptical scrutiny. The rule-following paradox thus remains a significant challenge to our understanding of both arithmetic and logic.

Nesim Aslantatar – Solving Turri’s Puzzle

I hold an MA and PhD in Philosophy of Religion from Ankara University, Turkey. My doctoral research focused on the epistemology of agnosticism, examining its foundations, implications, and conditions for rationality. After completing my PhD in 2022, I first joined Inonu University (Turkiye) and then to Usak University (Turkiye) as an assistant professor of philosophy of religion. My broader research interests include the intersections of religious epistemology, metaphysics, and the philosophy of religion, including non-Western traditions, with a particular focus on the logic of belief formation and the epistemic dynamics of suspending judgment. Since July 2024, I have been a research scholar in the Department of Philosophy at Indiana University Bloomington, where I continue my studies on the epistemology of suspensions of judgment and the problem of disagreement in epistemology; the problem of evil and theodicies in philosophy of religion.
In a case about withholding [1] belief presented by John Turri (2012), a group of prominent mathematicians engages in a lengthy discussion about whether a particular set of axioms entails a proposition (P). S, who has sufficient mathematical training but is not an expert, is tasked with recording their verdicts as the mathematicians leave the venue. Their advice divides into two distinct possibilities: (i) Each Mathematician states that withholding judgment is the appropriate course of action and (ii) Each Mathematician states that withholding judgment is not the appropriate course of action. In (i), it seems clear that S should withhold judgment regarding P. The evidence neither supports belief nor does disbelief; withholding judgment remains the only viable option. There is nothing puzzling about this conclusion. In (ii), however, it becomes unclear what S should do. S’s evidence still does not support belief or disbelief, so neither belief nor disbelief is justified. Withholding judgment appears to be the remaining option. Yet, the Mathematicians unanimously assert that withholding judgment is not the correct stance. If they had collectively stated that belief is not appropriate, it would follow that you should not believe; similarly, if they had said that disbelief is not appropriate, you should not disbelieve. By this reasoning, if they unanimously claim that withholding judgment is not the right course of action, it seems you should not withhold judgment either. This, according to Turri, is puzzling.
The puzzle stems from the presupposition that the justification conditions for belief, disbelief, and suspension are symmetrical. Suspending or withholding judgment is a doxastic attitude, so I agree that triad view is correct. However, while suspending judgment can be epistemically justified based on one’s evidence, this justification does not equate to inventing positive evidence in favor of suspension. Instead, it involves one’s cognitive engagement with the evidence. If Turri’s puzzle is accepted as valid, where S has no doxastic attitude --neither belief, disbelief nor withholding, then the following two will be possible:
(1) To suspend judgment on all propositions one holds.
(2) To suspend judgment exclusively on all of one’s beliefs without holding any.
I argue that this is cognitively impossible, so Turri’s puzzle must be wrong. Thus, I argue that even if there is no positive evidence for agnosticism, it is still grounded by a reference to the (Cog-A) an agnostic is aware of her attitude that she is agnostic:
Cognitive Awareness (Cog-A): Suspension of judgment can only be rational iff it excludes the possibility of S being agnostic about a given p when S has not developed cognitive awareness of p.
and, (BEL) an agnostic believes that ‘she is justified in being agnostic’:
Belief Condition (BEL): Suspension of judgment is rational iff it requires accepting that it is impossible for one to suspend all of their beliefs and necessitates a second-order (meta) belief about one’s own suspension.
This is interpreted as follows: the agnostic must, by cognitive necessitation, have at least one belief, which is the belief, or non-suspension of the judgment of on the belief that one’s attitude towards p is true and one is aware of this fact. This is a belief about one’s epistemic basing. One can come to this position by simply evaluating the evidence for belief for p and disbelief for p, and reaching the conclusion that evidence is ambiguous in showing that p or –p is justified, and this is a justification for suspending on p.[2] Referring back to (ii) of Turri’s argument, S, as an agnostic, can independently interpret the mathematicians’ stance as indicative of ambiguity.
This study argues that Turri’s puzzle relies on a highly specific interpretation of agnosticism, one that he does not fully elaborate on in his discussion. Agnosticism requires a certain level of cognitive sophistication, in which S is aware of her stance and considers various factors --primarily evidence, though not exclusively. The study further defends a philosophical agnostic position in which suspension is reductive (to belief), higher order (meta-cognitive) and a proposition-directed attitude. Drawing on this framework of philosophical agnosticism, I will demonstrate that Turri’s puzzle does not present a genuine philosophical problem.
[1] I use withholding judgment, suspension of judgment, and agnosticism interchangeably to mean the same thing.
[2] Such justification, often referred to as privative justification for agnosticism, is discussed in detail by Draper (2002, pp. 197–214), Oppy (2018, pp. 28–48), Poidevin (2010, pp. 56–76), Feldman and Conee (1985, p. 15), and Machuca (2015, p. 177).

Paola Fontana – Abductivism, Paradoxes and Paraconsistency

Paola Fontana is a Phd student in philosophy at the University of Genoa, as part of the Northwest Italy Philosophy Program (FINO). She has recently started working on a research project entitled “Logical Pluralism and Paraconsistency”, which aims at finding a new direction for the monism/pluralism debate, in light of recent developments in paraconsistent logics. Before that, she completed her bachelor’s studies in philosophy at the University of Catania (Italy) and later obtained a master’s degree in philosophy at the University of Italian Switzerland, in Lugano. Her master thesis, which she wrote under the supervision of Professor Timothy Williamson, was concerned with the motivations and methodological issues in paraconsistent approaches to Logic. Her main research interests focus onAbductivism, Logical Pluralism, Paradoxes and nonclassical Logics.
This presentation aims at providing a philosophical discussion of some methodological issues in logic in relation to paraconsistency. More precisely, the purpose is to assess whether an abductive argument for paraconsistent logics can be invoked, on the basis of logical paradoxes. In science, the abductive method allows one to choose the correct theory on the basis of criteria as adequacy to evidence, simplicity and strength. Assuming an abductivist stance, and supposing that logics can be regarded as theories of the relation of consequence, would an abductive evaluation select a paraconsistent logic? What role would paradoxes play in such an evaluation?
A further question, related to the previous ones, is what should count as evidence in logic. Priest (2016) argues that this role should be played by our intuitions about the validity of arguments. Moreover, he regards paradoxes of self-reference 1as showing that our natural reasoning is inconsistent (Priest 2006 a,b), which in turn motivates the adoption of a paraconsistent logic.
Similarly, Beall (2017, 2018) holds that paradoxes motivate the choice of a non-explosive logic, even though he adds that this logic should be weaker, as it is supposed to accommodate truth value gaps as well as gluts. It is interesting to note that Beall’s view about the role of logic, on which his argument for a paraconsistent logic relies, appears to be in tension with some assumptions of Abductivism. Beall takes logic to be a closure relation to be used in all our true theories - that is, it is employed to derive all the consequences of these theories’ claims (Beall 2017, p. 5). Beall regards logic as a tool to be used in other theories, rather than a theory itself, putting forward a view that Hlobil identifies with a version of what he calls the ancilla scientiae conception of logic (Hlobil 2020, pp. 11-12). Beall emphasises that logic in itself does not allow us to derive topic-specific claims: that is why, on top of the logical consequence relation, extra-logical closure operators are usually adopted in theories (Beall 2017, p. 6). On the other hand, the abductive method offers a procedure for theory choice. The view that the abductive method should be applied to logics seems to presuppose that each logic comes with certain theoretical commitments, which apparently clashes with Beall’s general conception of logic.
A crucial objection to arguments for paraconsistency hinging on paradoxes is put forward Williamsons (2017). He argues that an abductive assessment of logics arguably favours classical logic. According to him, paradoxes - specifically, semantic paradoxes - do not provide a sufficient reason to reject classical logic, and that its explanatory power, combined with is simplicity, is not dispensable. This is confirmed, Williamson argues, by extra-logical applications of classical logic in scientific theories.
I will discuss the strategies available to Priests and Bealls to reply to Williamsons argument, highlight some criticisms in them and propose a different and more effective approach.
The idea I explore here is that two possible approaches to the paradoxes should be distinguished. On the one hand, one might regard them as a single, uniform phenomenon concerning our natural reasoning or our intuitive notions. However, this does not look very promising from an abductive point of view, not only because the idea that our intuitions should count as evidence for a logic is controversial. Indeed, the classical logician could argue that the existence of just one kind of paradoxical phenomenon does not constitute enough evidence to justify the loss of simplicity that comes with choosing a paraconsistent logic.
On the other hand, one might look at each paradox separately, as concerning specific notions, for example truth or sets. Each paradox arises in the context of a particular theory and can be investigated independently from the others. Whether a paradox tells something meaningful about the relevant concepts depends on the theory at issue and the specific contents it deals with. This means that the focus should be on the material aspect of the paradoxes, rather than their formal structure. The thesis defended here is that, if there are different paradoxes independently motivated - in relation to the subject matter they are concerned with - then one can make a stronger case for non-explosive logics. This focus on a material characterisation of paradoxes is in line with Sher’s (2017, 2022) stance about the Liar paradox and its solution. Just as classical solutions, a paraconsistent treatment of paradoxes should aim at material adequacy and prioritise the latter over formal adequacy. If it can be showed that different theories make use of inconsistent concepts, therefore - provided that such theories can be independently supported - a paraconsistent logic should be chosen to account for this evidence.
1As a matter of fact, he includes the Sorites paradox in the same category - that of Inclosure paradoxes - even though it does not involve self-reference (Priest 2010).
References
Beall, J. (2017). There is no logical negation: True, false, both, and neither. Australasian Journal of Logic, 14(1), Article no. 1.
Beall, J. (2018). The simple argument for subclassical logic. Philosophical Issues, 28(1), 30–54.
Priest, G. (1994). The structure of the paradoxes of self- reference. Mind, 103(409), 25–34.
Priest, G. (2006a). Doubt truth to be a liar. New York: Oxford University Press.
Priest, G. (2006b). In contradiction: A study of the transconsistent. New York: Oxford University Press.
Priest, G. (2010). Inclosures, vagueness, and self-reference. Notre Dame Journal of Formal Logic, 51(1), 69–84.
Priest, G. (2016). Logical disputes and the a priori. Logique et Analyse, (236), 347–366.
Sher, G. (2017). Truth & transcendence: Turning the tables on the liar paradox. In B. P. Armour-Garb (Ed.), Reflections on the liar (pp. 281–306). Oxford University.
Sher, G. (2022). A new defense of tarski’s solution to the liar paradox. Philosophical Studies, 180(5-6), 1441–1466.
Williamson, T. (2017). Semantic paradoxes and abductive methodology. In B. P. Armour-Garb (Ed.), Reflections on the liar (pp. 325–346). Oxford University.

Paul Poledna – On the Foundations of Biological Logic: A Meta-theoretical Investigation

Poledna has a background in physics and philosophy. His current research combines his interests in both fields, focusing on far-from-equilibrium thermodynamics, complex dynamic systems, and semiotic processes. In particular, Paul investigates how insights from these areas combine to yield new insights into the emergence of self-organization and the distinctive self-manufacturing behavior of living systems. His work aims to develop formal frameworks for understanding the unique organizational logic of living systems, examining how biological processes achieve coherence through dynamic patterns of temporal coordination. This approach bridges thermodynamic constraints and emergent purposive behavior, contributing to our understanding of how physical processes give rise to the distinctive organizational patterns characteristic of life. By integrating perspectives from physics, logic and philosophy, his research explores how living systems maintain themselves through recursive enabling relationships that generate novel possibilities while preserving systemic integrity.
This paper examines the meta-theoretical foundations of logical systems through the lens of biological organization. While contemporary discussions in philosophical logic have primarily focused on truth-preservation and inferential validity within atemporal frameworks, we propose an alternative meta-logical perspective grounded in the study of biological systems. This approach suggests that the structural features of logical systems might be fundamentally related to the organizational principles that characterize living processes.
We investigate how the meta-logical properties of reasoning systems might be understood through an analysis of recursive constraint structures in biological organization. This investigation raises significant questions about the nature of logical necessity and the foundations of inferential validity. Of particular relevance is the contribution this perspective offers to the adoption problem in logic: rather than encountering the classic rule-circularity in justifying basic logical principles, we propose that the validity of inference rules may be grounded in their structural correspondence with fundamental biological constraints.
The meta-theoretical framework developed here suggests novel approaches to several contemporary debates in philosophical logic, including the tension between logical monism and pluralism, the nature of logical consequence, and the grounds of normative force in logical systems. While the complete formalization of this meta-logical framework remains under development, the theoretical implications suggest promising directions for investigating the relationship between biological organization and the foundations of logical reasoning.

Ryan Simonelli– Yes, No, Neither, and Both

Ryan Simonelli is an International Postdoctoral Research Fellow at Wuhan University in China. He received his Ph.D. at University of Chicago in 2022, was a visiting scholar at University of Pittsburgh in 2019, and received his undergraduate degree from New College of Florida. He works mainly at the intersection of philosophy of language, metaphysics, and philosophical logic. In general, his work is focused on formally developing an inferentialist theory of content and articulating its philosophical consequences. In logic in particular, he has worked to develop non-classical and substructural bilateral logics with an eye towards their implementation in an inferentialist account of content. His papers include “An Act-Based Approach to Assertibles and Instantiables” (Ergo, forthcoming), “A General Schema for Bilateral Proof Rules” (Journal of Philosophical Logic, 2024), “How to Be a Hyper-Inferentialist” (Synthese 2023), “Why Must Incompatibility Be Symmetric” (Philosophical Quarterly, 2023), and “Sellars’s Ontological Nominalism” (European Journal of Philosophy, 2021).
The abstract can be found here.

Samet Büyükada and Enver Şahin – Kātibī’s Approach to the Liar Paradox and His Proposed Solutions to Other Paradoxes

Dr. Samet Büyükada is a faculty member at Recep Tayyip Erdoğan University, Faculty of Theology, Department of Philosophy and Religious Sciences in the field of History of Philosophy. His academic studies focus on the history of logic, Islamic logic, contemporary essentialism, modal logic and modal epistemology.
Dr. Enver Şahin is a faculty member at Recep Tayyip Erdoğan University, Faculty of Theology, Department of Philosophy and Religious Sciences in the field of Logic. His academic studies focus on the history of logic, Islamic logic, modalities and paradoxes.
Within Islamic scholarship, various versions of the liar paradox have been noted in the context of theological and philosophical discussions. In brief, the liar paradox involves considerations over the truth value of the proposition “I am lying at this very moment.” In other words, is this proposition true or false? Can it be regarded as a proposition not subject to verification or falsification? Alternatively, can it be both true and false at the same time? Or should its verification and falsification be sought outside the scope of what the proposition itself conveys? If it can be both true and false simultaneously, would this not amount to violating one of the fundamental principles of reason—what may be summarized as the principle of non-contradiction, namely that “it is impossible for something to be both true and false at the same time”? If this proposition is true, how can telling a lie and telling the truth be reconciled in a statement that conveys information? If this proposition is false, how can truthful speech and lying be brought together? Searching for answers to all these questions is the endeavor of this paper. More generally, another primary aim of the paper is to ask whether, apart from the liar paradox—currently more prominently highlighted—there have been mentions of other paradoxes in the history of Islamic logic. If so, what were their logical formulations, and what solutions were proposed? In this paper, we plan to penetrate the sources of the paradoxes discussed in the history of Islamic logic and to examine the solutions that Najm al-Dīn al-Kātibī (d. 1277) offered for these paradoxes.
We investigate how the meta-logical properties of reasoning systems might be understood through an analysis of recursive constraint structures in biological organization. This investigation raises significant questions about the nature of logical necessity and the foundations of inferential validity. Of particular relevance is the contribution this perspective offers to the adoption problem in logic: rather than encountering the classic rule-circularity in justifying basic logical principles, we propose that the validity of inference rules may be grounded in their structural correspondence with fundamental biological constraints.
The meta-theoretical framework developed here suggests novel approaches to several contemporary debates in philosophical logic, including the tension between logical monism and pluralism, the nature of logical consequence, and the grounds of normative force in logical systems. While the complete formalization of this meta-logical framework remains under development, the theoretical implications suggest promising directions for investigating the relationship between biological organization and the foundations of logical reasoning.

Sherif Salem– Against the Logicians: Ibn Taymiyya’s Rejection of the Aristotelian Theory of Definition

Sherif Salem is a lecturer at University Canada West. He holds an MSc in Economics from Queen Mary University of London, as well as two MAs in Philosophy—one from the American University in Cairo and another from Simon Fraser University.
This paper aims to briefly explore Ibn Taymiyya’s (1263-1328) criticism of the Aristotelian logical tradition, especially his theory of definition. Ibn Taymiyya attempts to prove that Aristotle’s logic, based as it is upon unchanging metaphysical principles, cannot be a practical tool for dealing with scientific knowledge production as claimed. Some of his arguments are grounded in the principles of relativism and skepticism, while others are grounded in empirical evidence about the function of language. However, we will mainly focus on Ibn Taymiyya’s criticism of the Aristotelian theory of definition through the refutation of the following two distinctions: a) essential and accidental attributes, and b) the distinction between quiddity and its existence.

Wendi Zhou – Shifting the Phenomena: Against Predictivism in Logical Theory Choice

Wendi Zhou is studying for the BPhil in Philosophy at the University of Oxford. She works primarily in the philosophy of logic and epistemology and also has interests in social philosophy and feminist philosophy. She completed her bachelor's degree from the University of Washington, where she was awarded a Dean's Medal from the College of Arts & Sciences.
In rejecting the view that logical rules are unchanging and known a priori, W. V. O. Quine’s “Two Dogmas of Empiricism” inaugurated what Ole Hjortland calls anti-exceptionalism about logic (AEL): the broad view that
[l]ogic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. (Hjortland 2017: 632)
In contrast to exceptionalists such as Kant and Frege, more philosophers and logicians have recently turned toward AEL regardless of logical allegiance (Maddy 2002; Russell 2015; Priest 2016; Williamson 2017; forthcoming); in particular, some anti-exceptionalists have proposed a broadly abductive methodology for choosing logical theories: one that considers us justified in endorsing a logical theory insofar as it (1) better accommodates the data and (2) exemplifies other theoretical virtues to a greater degree than other logical theories (see, in particular, Priest 2016 and Williamson 2017).
My paper presents a critique of a recent rival approach to abductivism: what Ben Martin and Ole Hjortland (hereafter M&H) call logical predictivism (M&H 2021). To argue that predictivism does not pose a serious threat to abductivism, I target a key feature of predictivist theory choice that abductivism is not committed to: using judgments of argumentative acceptability as the main source of evidence for logical theories. My objection is that M&H commit the error of “shifting the phenomena” when they take acceptability judgments as data for the phenomenon of validity: such data can only serve as evidence for theories about what the given community finds acceptable instead of theories of validity itself. Drawing on Bogen and Woodward’s (1988) influential data-phenomena distinction, I show how predictivism fails to achieve its aims in both (1) showing how logical theories can explain the phenomenon of validity and in (2) delineating a way to choose between logical theories based on their predictive success. I consider and reject a potential conventionalist rebuttal from M&H, such that validity simply is what is acceptable according to a given community. The upshot of my argument is that the predictivist must find a suitable type of data to serve as evidence for validity itself, or risk endorsing the view that logic is exceptional after all.

Horia Lixandru – An Inferentialist Approach to the Adoption Problem

Horia Lixandru is a Master of Logic student at the Institute for Logic, Language and Computation at the University of Amsterdam. He holds a BSc in Computer Science from TU Delft, The Netherlands. His main interests include logic and philosophy of logic, philosophy of language, (formal) epistemology, and philosophy of mathematics. He is currently writing his Master's thesis on Kripke's Adoption Problem.
The abstract can be found here.