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[A photo of Daimonji-Yama taken from the Philosopher's walk in Kyoto]
Aim
The aim of this workshop is to discuss and exchange new ideas and recent developments related to dialetheism and paraconsistent logics.
Date & Venue
- Date: October 9--10, 2016.
- Venue: Kyoto University, Yoshida Izumidono. [map]
Speakers
- Franz Berto (University of Amsterdam)
- Colin Caret (Yonsei University)
- Filippo Casati (Lehigh University)
- Yasuo Deguchi (Kyoto University)
- Naoya Fujikawa (Tokyo Metropolitan University)
- Ryosuke Igarashi (Kyoto University)
- Takuro Onishi (Kyoto University)
- Adam Přenosil (Charles University & Czech Academy of Sciences)
- Daniel Skurt (Ruhr-University Bochum)
- Zach Weber (University of Otago)
- Timo Weiss (University of Bonn)
- Maiko Yamamori (Kyoto University)
Program
Oct. 9
Session 1: True Dialetheists discuss Dialetheism
10:00--11:00: Zach Weber: On what is possible, what is not, and what is both
11:00--12:00: Yasuo Deguchi: Non-dialetheic Dialetheism
12:00--13:30: Lunch break
Session 2: Theories based on LP
13:30--14:30: Timo Weiss: Inconsistent Math Foundations -- Cantor and Beyond
14:30--15:30: Daniel Skurt: Some remarks on identity in 1st and 2nd order minimal LP
15:30-15:50: Coffee break
Session 3: Philosophical issues related to Paraconsistency
15:50--16:50: Ryosuke Igarashi: An anti-Realistic interpretation of catuskoti
16:50--17:50: Colin Caret: No Cause for Alarm
18:30- Dinner
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Oct. 10
Session 4: Ineffability and Being: topics in Dialetheism
10:00--11:00: Maiko Yamamori: Inclosure, Curry and Ineffability
11:00--12:00: Filippo Casati: Seyn, Grund and der Letzte Gott.
12:00-13:30: Lunch break
Session 5: Extensions and expansions of FDE
13:30--14:30: Adam Přenosil: Super-Belnap logics: charting the terra incognita
14:30--15:30: Takuro Onishi: A four-valued frame semantics for the relevant logic R.
15:30--15:50: Coffee break
Session 6: Meinongians discuss Paraconsistency (and not?!)
15:50--16:50: Naoya Fujikawa: Possible and Impossible Objects in Modal Meinongianism
16:50--17:50: Franz Berto: As Good As It Gets: Modal-Epistemic Logic for Inconsistent Agents, Without Paraconsistency, or Impossible Worlds
18:30-- Dinner
Abstracts
Zach Weber
Title: On what is possible, what is not, and what is both
Abstract: What is possibility, from a fully dialetheic perspective? A possible world is a way things could be, and an impossible world is a way things could not have been. But there is a `not' in that formulation. Suppose we take it to be dialetheic negation. According to dialetheism, there are true contradictions in the actual world, and there are not. Does this mean that the actual world is an impossible world? In anything absolutely impossible?
To answer this question, and ones like it, we develop the rudiments of a dialetheic modal logic---using only paraconsistent substructural logic and naive set theory in the background metatheory, to recover some familiar model theory (definability theorems, neighborhood semantics, etc.). Through this lens, a new picture of modal space emerges. Part §1 motivates this work; Part §2 provides a technical sketch; and Part §3 considers some applications, e.g. to the problem of `advanced modalizing'. Dialetheists not only have a workable modal theory available to them, but one that can do useful philosophical work beyond the ambit of the consistent.
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Yasuo Deguchi
Title: Non-dialetheic Dialetheism
Abstract: Dialetheism means two-truths-ism. As its name suggests, in taking some contradictions as true, it has given them a true value glut; i.e., true and false. This talk will explore another sort of dialetheism, which takes some contradictions trans-dichotomously true rather than the glut. Truth is trans-dichotomous when both a proposition and its negation are true. This non-dialetheic or trans-dichotomous dialetheism commits an ontological claim that the reality consists of two sorts of truth-maker; dichotomous and trans-dichotomous ones. The dichotomous truth-maker makes a proposition true while its negation false. In contrast, the trans-dichotomous one makes the both of them as true.
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Timo Weiss
Title: Inconsistent Math Foundations -- Cantor and Beyond
Abstract: Georg Cantor introduced actually infinite objects in the form of infinite sets to the realm of mathematics, but many people tried to prove that these objects are contradictory and thus lead to triviality in a logically classical framework. Cantor indeed mentioned inconsistent multitudes (Ger. "inkonsistente Vielheiten") like the universe or the class of all ordinals, but excluded them from mathematical research qua being absolutely infinite and hence being of non-increasable magnitude, but he did not exclude them from metaphysical research. I wish to briefly sketch my understanding of the Cantorian dialectic towards the Absolute and its importance for metaphysical (and mathematical) considerations and perhaps give some examples on how paraconsistent logics (and set theories) try to deal with the unrelenting inconsistency of absolute infinity.
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Daniel Skurt
Title: Some remarks on identity in 1st and 2nd order minimal LP
Abstract: In this talk, I would like to investigate the behavior of 1st and 2nd order minimal LP with languages that contain identity. First, I will define (according to Graham Priest) two different notions of identity in 1st and 2nd order LP that do not have the properties of transitivity and substitutivity. Second, I will investigate if it is possible to regain those properties in consistent contexts.
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Ryosuke Igarashi
Title: An anti-Realistic interpretation of catuskoti
Abstract: This paper will be centred primarily on limning a reading of the catuskoti as an illocutionary device, and thereby presenting Nagarjunian thought as an anti-realist enterprise. That is to say, that we will attempt to establish that the kotis themselves are concerned with speech-acts rather than truth-tracking propositions, and that the perlocutionary effect of uttering or engaging with the kotis is the soteriological function of metaphysical quietism.
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Colin Caret
Title: No Cause for Alarm
Abstract: Methodological worries abound in philosophy, especially when it comes to debates about basic cognitive faculties like perception and deduction. Because logic is so basic, some philosophers claim that we are incapable of making substantive headway in debates about paraconsistency. Such debates are doomed to stalemate. At best we can accept or reject explosion as a matter of faith. There are at least three issues in the literature that exemplify this broadly skeptical outlook: the semantic categorization problem, the common ground problem, and the rational exclusion problem. Extant proposals by Priest, Beall, Restall, and Berto address different aspects of these issues. This paper aims to clarify the nature and extent of difficulties regarding the possibility of substantive debate about paraconsistency. In particular, we consider a paraconsistent semantics for rational discourse in a natural language like English supplemented with explicit post-semantic norms. Then we reflect on how discourse about doxastic methods may proceed in such a setting. Our conclusions are generally optimistic. We argue that there is no barrier to substantive debate about paraconsistency, at least none that is unique to paraconsistency.
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Maiko Yamamori
Title: Inclosure, Curry and Ineffability
Abstract: Graham Priest (1995, 2002) devises the Inclosure Schema to try to capture the general structure of paradoxes of self-reference. Since Ramsey, many people have thought that paradoxes are distinguished into two categories, set-theoretic paradoxes and semantic paradoxes, and that there is no general structure. Running counter to this main stream, Priest thinks they have the same structure; the Inclosure Schema.
This schema seems to work excellently, however there are some critiques to it. One of them is about Curry's Paradox. As Priest himself wonders, some scholars have raised question whether the Inclosure Schema can capture Curry's Paradox. In my opinion, the Inclosure Schema should not express Curry's Paradox in terms of dialetheism.
Pleitz (2014) also thinks that the Inclosure Schema is not fine for Curry's Paradox, and he devises a schema which also capture Curry's Paradox. His schema, Curry's Schema, also can express the paradoxes which the Inclosure Schema covers; Curry's Schema is more general than the Inclosure Schema.
Then, can all paradox of self-reference be captured by Curry's Schema? The answer is no. There is a paradox of self-reference which cannot be covered by Curry's Schema (and by the Inclosure Schema, of course). The paradox is Ineffability Paradox. 'Ineffability' usually means the impossibility of describing or expressing something. Some philosopher and religious figures in east and west have mentioned ineffability, such as 'God is ineffable'. It is, however, well known that a paradox arises from saying 'x is ineffable' because it seems that 'x is ineffable' implies 'x is effable'; this is Ineffability Paradox.
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Filippo Casati
Title: Seyn, Grund and der Letzte Gott.
Abstract: In my talk, I present a novel interpretation of the so-called late Heidegger. In the first part, I will discuss the paradox of being, according to which talking and thinking about being leads to a contradiction. I will also show that, in contrast to the early Heidegger, the late Heidegger endorses dialetheism, accepting the contradiction of being as a true one. In the second part of my talk, in light of this interpretation of Heidegger, I will discuss Heidegger’s theory of grounding. I will show that the early Heidegger endorses a particularly strong form of foundationalism and that the second Heidegger should have endorsed two paraconsistent versions of foundationalism (call them para-foundationalism 1.0 and para-foundationalism 2.0). I will show that these inconsistent grounding theories can accommodate the inconsistent views endorsed by the second Heidegger about being.
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Adam Přenosil
Title: Super-Belnap logics: charting the terra incognita
Abstract: The four-valued Belnap–Dunn logic, also known to many paraconsistent logicians as FDE, has two well-known three-valued extensions: the Logic of Paradox and the strong Kleene logic. However, most logicians would probably be hard put to name any other non-classical logic which extends FDE. It may therefore be surprising to learn that there are in fact continuum many such logics, called super-Belnap logics by analogy with superintuitionistic logics. In this talk, we shall review some recent research into these systems and provide a basic map to the vast landscape of super-Belnap logics. We shall in particular focus on (i) the structure of the lattice of super-Belnap logics, (ii) the connections between these logics and graph theory, and (iii) Gentzen-style proof theory, building on Pynko's idea of using LP to prove the admissibility of Cut in classical logic.
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Takuro Onishi
Title: A four-valued frame semantics for the relevant logic R.
Abstract: Attempts have been made to connect or reconcile two traditions in the semantics of relevant logic: Belnap-Dunn style four-valued semantics (American plan) which gives “classical” semantics to negation, and Routley-Meyer style frame semantics (Australian plan) which elegantly explains the meaning of relevant implication (Routley 1984, Priest and Sylvan 1992, Restall 1995, Mares 2004). In this talk I present yet another four-valued frame semantics for the relevant logic R.
Two problems are discussed in the literature. First, what is the correct falsity condition for relevant implication? Second, implicational principles like contraposition and reductio require a certain “cross-over” between truth and falsity. Then what is a sensible notion of “cross-over” in the four-valued framework in which truth and falsity are defined independently?
Following Routley (1984), I define the falsity condition for implication in terms of a ternary relation distinct from the one for its truth condition. The twin ternary relations allow us to define two binary relations compatibility and exhaustiveness on the frame, in terms of which a reasonable “cross-over” can be formulated. I show that this works well for the well-known and strong relevant logic R by applying the idea of “(generalized) star postulate”, and discuss how to transfer it to weaker logics.
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Naoya Fujikawa
Title: Possible and Impossible Objects in Modal Meinongianism
Abstract: Meinongianism is the view that accepts reference to and quantification over nonexistent objects, and is well-known for making the distinction between possible and impossible objects. Modal Meinongianism, a new version of Meinongianism which has been recently developed within the framework of world semantics (Priest, 2005, Berto, 2013), is no exception. However, unfortunately, no strict definition of possible and impossible objects is yet given within the framework of modal Meinongianism. This paper explores several ways of defining possible and impossible objects in modal Meinongianism, focusing on the question whether the modal status of an object is representation-dependent or not---whether it is the case that possibility and impossibility of objects depend on how they are characterized or represented by subjects. For example, Conan Doyle characterized Sherlock Holmes as having the properties of being a detective, being clever and so on. Does Holmes' being a possible object depend on the fact that he was characterized so? Admitting that we have apparently conflicting intuitions about whether possibility and impossibility of objects are representation-dependent or not, in this paper I show that our ambivalent intuitions about it can be explained only in terms of the representation-independent notion of possibility and impossibility of objects, without appealing to the representation-dependent one. In particular, I claim that our intuition which appears to support the representation-dependency of possibility and impossibility of objects is explained at the level of (meta)semantics, not at the level of metaphysics of properties.
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Franz Berto
Title: As Good As It Gets: Modal-Epistemic Logic for Inconsistent Agents, Without Paraconsistency, or Impossible Worlds
Abstract: Paraconsistent logics with non-normal or impossible worlds semantics have been used to model finite, fallible and occasionally inconsistent cognitive agents: agents that have inconsistent beliefs but do not thereby believe everything, and also, who do not believe “irrelevant” B’s just because they believe some A, although B follows from A in classical logic. Approaches in this ballpark include Levesque [1984]’s logic of explicit and implicit belief, and Cresswell’s [1973] classic work. In this paper I propose a modal semantics that achieves similar effects, by combining a standard possible worlds set-up with a mereology of contents (what the relevant epistemic states are about).
Logical consequence is completely classical modal, not paraconsistent; the semantics uses no impossible or non-normal worlds. Still, it can achieve various effects obtainable in a paraconsistent-relevant epistemic logic. For instance, irrelevant logical validities are not trivially believed (one can believe that A, without believing B -> B, and without believing B v ~B, for B’s unrelated to A). Also, agents can explicitly believe that A & ~A without thereby believing arbitrary B’s.
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Related events
- A talk by Franz Berto, October 12, 16:30--18:00 at Kyoto University. [See here for the details.]
- Tokyo Workshop on Meinongianism: Nonexistence, Contradiction and Metaontology, October 15. [See here for the details.]
Acknowledgment
Kyoto Workshop on Dialetheism and Paraconsistency is supported by Japan Society for the Promotion of Science (JSPS) through grants 16H03344 and 16K16684.
Organizers
The workshop is organized by Yasuo Deguchi and Hitoshi Omori. If you wish to attend the workshop, please write to Hitoshi at: hitoshiomori [at] gmail [dot] com.
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