Abstracts

There are a number of systems of paraconsistent logics in the literature since the seminal works by Stanislaw Jaskowski and Newton C. A. da Costa. The aim of this talk is to reflect on the following three well-known results:
(i) Modal logic S5 is paraconsistent;
(ii) Paraconsistent logic LP is not functionally complete;
(iii) Connexive logic C is negation-inconsistent (but non-trivial). These observations are, of course, correct, and technically not very complicated. However, there seem to be other ways to view the related systems, I will present what are the background assumptions that are hidden in establishing the above results

Otávio Bueno

Otávio Bueno
University of Miami, USA
otaviobueno@mac.com

Overinterpreting Paraconsistent Logics

ABSTRACT

Paraconsistent logics, which I take here to be, minimally, those that are not explosive (that is, those for which not everything follows from a contradiction of the form A and not-A), have often been interpreted, from a philosophical point of view, by dialetheists (Priest [2006]), as supporting the existence of true contradictions. In this paper, I provide basic criteria for the philosophical interpretation of a logic and consider the costs of violating such criteria (overinterpretation). I argue that the overinterpretation enhances a metaphysical reading of logic that is not called for and that can be resisted on philosophically independent grounds. A more neutral stance toward logic, and of paraconsistent logic in particular, is then advanced.

Eduardo Barrio

Eduardo Barrio
University of Buenos Aires, Argentina
eabarrio@gmail.com

Paraconsistency:
applied and interpreted

ABSTRACT

In a series of works, Carnielli and Rodrigues have supported the claim that some paraconsistent logics (BLE and LETj) require an interpretation in epistemic terms. And Da Ré and I have argued that no pure logic necessarily leads to a particular philosophical interpretation. There are usually multiple interpretations for each logical system. There is not a single privileged interpretation. In particular, paraconsistent logics do not determine any philosophical interpretation. Recently, Carnielli and Rodrigues have responded to our position by conceding some points and offering new elements to evaluate. And Becker Arenhart, agreeing in part with our approach, questions the role of the notion of philosophical interpretation. In this paper, I will try to defend the distinctive role of the concept of philosophical interpretation, and to show that it should not be eliminated or confused with the notion of applied logic.

Ítala D'Ottaviano

Ítala D'Ottaviano
State University of Campinas, Brazil
itala@unicamp.br

Baptizing Paraconsistent Logic

ABSTRACT

In this paper we analyse the principal historical events surrounding the creation of the word ‘paraconsistent’, as well as its introduction as the name for inconsistent but non-trivial formal systems. Initially, these systems were called the ‘theory of inconsistent formal systems’ by Newton da Costa when he introduced his C-systems in 1963. In the early 1970’s, however, da Costa asked Francisco Miró Quesada to look for suggestions for a meaningful name for this new family of formal systems. The goal was achieved in correspondence exchanged in 1975, when Miró Quesada suggested to Newton da Costa an all-embracing name which finally came to predominate. Quesada master’s touch into history of paraconsistent logic was presented to the international academic community in a conference delivered by him at the Third Latin American Symposium on Mathematical Logic (III SLALM), held in 1976 at the University of Campinas.

Walter Carnielli

Walter Carnielli
State University of Campinas, Brazil
walterac@unicamp.br

Evidence and probability in the paraconsistent and paracomplete Logics
of Evidence and Truth:
their meaning and usefulness

ABSTRACT

This talk discusses some of the main ideas behind the notions of probability and evidence in non-standard logics. Evidence can be either contradictory or incomplete, or both, thus requiring paracomplete and paraconsistent logics. A logic with such characteristics, LET_F , extending Belnap-Dunn’s logic of first-degree entailment FDE with a classicality operator OA that recovers classical character for formulas in its scope was first proposed in [1]. together with a probabilistic semantics able to quantify the amount of evidence available for a judgement A. The main intuition is that information can be positive (A is true), negative (A is false), missing (no evidence for A) or conflicting (contradictory), while a formula OA means that the information about A, either positive or negative, is reliable. This proposal extends the interpretation of FDE as information-based logics. I argue that this framework can fruitfully expand Bayesian epistemology and the dynamics of belief change, as a result of updating procedures based on new evidence. As a non-deductive process, Bayesian reasoning cannot be itself submitted to strict logic, but it can take advantage of an enabling environment. The present paper proposes that paraconsistent and paracomplete logics can be helpful to some questions of Bayesian epistemology, to the point of starting a legitimate paraconsistent Bayesian epistemology. This talk is based on material from the book “Contradictions, Evidence and Truth: An epistemic Account of Paraconsistency” (W. A. Carnielli, M. E. Coniglio, A. Rodrigues, Synthese Library), to appear.

Reference:

[1]- Rodrigues,A; Bueno-Soler, J. and Carnielli, W. A. Measuring evidence: a probabilistic approach to an extension of. Belnap–Dunn logic. Synthese 198(22):5451–5480, 2021.

Abílio Rodrigues

Abílio Rodrigues
Federal University of Minas Gerais, Brazil abilio.rodrigues@gmail.com

What do 'evidence' and 'truth' mean in the logics of evidence and truth

ABSTRACT

The aim of this paper is twofold. First, we present and discuss some recent developments in the logics of evidence and truth (LETs), namely, finitely-valued propositional versions and first-order versions with Kripke-style semantics. Second, in order to answer some criticisms raised against LETs, we explain the notions of evidence and information underlying the intuitive interpretation of LETs, and also clarify in which sense the deductive behavior of conclusive evidence is expressed in terms of preservation of truth.

Guilherme Araújo Cardoso

Guilherme Cardoso
Federal University of
Ouro Preto, Brazil.
guilherme.cardoso@ufop.edu.br

The Logic of Impossible Truths and nonactual contradictions

ABSTRACT

There seem to be good reasons for paraconsistency when dealing with ordinary language, concepts, and reasoning. Consider for example inconsistent (impossible) situations (like the ones of fiction), counterpossibles (counterfactuals with impossible antecedents), inconsistent theories, and semantical paradoxes. As I intend to argue, if we want to provide nontrivial accounts for such cases, we would better base them on some sort of paraconsistent framework (roughly speaking). Dialetheism goes beyond and sustains the incredulous thesis according to which the aforementioned cases do not only claim for paraconsistency but for the existence of (actual) true contradictions. I've been working on a paraconsistent (and also paracomplete) framework (LIT - the Logic of Impossible Truths) for such cases. I shall argue that LIT resists Dialetheism, mostly separating inconsistent (impossible) situations from the actual ones. In this talk, my only aim is to present LIT as a framework for dealing with nonactual contradictions in a nontrivial (nonvacuous) way. I shall discuss mainly semantical paradoxes and counterpossibles.

Henrique Antunes

Henrique Antunes Federal University of
Bahia, Brazil.
henrique.antunes@ufba.br

Classicality and Ontological Independence:
An Ontology-Based Approach to Paraconsistency

ABSTRACT

In this talk I will outline an approach to paraconsistency according to which

the main difference between classical and some paraconsistent logics is based on the distinction drawn by Jody Azzouni [5] between ontologically dependent and independent objects. More specifically, I will discuss the view that while objects that do not depend on our linguistic practices and psychological practices “behave classically”, objects that do depend on those practices and processes (such as fictional characters and dream figures) are subject to a paraconsistent and paracomplete logic. In order to give a concrete example of the approach to paraconsistency being advanced, I will describe how (the first-order extension of) the paraconsistent and paracomplete system BS4 [8, 9] may be supplemented with formal principles that relate its classicality operator ◦ with a special predicate I standing for is ontologically independent. I will then show how those principles allow one to fully recover classical logic within BS4 whenever ontologically independent objects are concerned. While describing the aforementioned strategy, I will also discuss in passing whether one should adopt a free version of BS4 or opt for a non-free version thereof in which, contra Quine, the quantifiers ∀ and ∃ receive an ontologically neutral reading. I will pinpoint the advantages and disadvantages of either option.

References

[1] Antunes, H. On Existence, Inconsistency, and Indispensability. Principia:

An International Journal of Epistemology 22 (2018), 7–34.

[2] Antunes, H. Contradictions for free: Towards a nominalistic interpretation

of contradictory theories, 2019. url: http://repositorio.unicamp.br/jspui/bit

stream/REPOSIP/334810/1/Almeida_HenriqueAntunes_D.pdf.

[3] Antunes, H. Enthymematic Classical Recapture. The Logic Journal of

IGPL (2019). doi: https://doi.org/10.1093/jigpal/jzy061.

[4] Azzouni, J. Stipulation, Logic, and Ontological Independence. Philosophia

Mathematica 8 (2000), 225–243.

[5] Azzouni, J. Deflating Existential Consequence: A Case for Nominalism.

Oxford University Press, 2004.

[6] Balaguer, M. A Platonist Epistemology. Synthese 103 (1995), 303–325.

[7] Carnielli, W., and Antunes, H. An objectual semantics for first-order

LFI1 with an application to free logics. In A Question is More Illuminating

than an Answer – A Festschrift for Paulo A. S. Veloso, E. H. Haeusler, L. C.

Pereira, and J. P. Viana, Eds. College Publications, London, 2021, pp. 58–91.

[8] Omori, H., and Sano, K. da costa meets benalp and nelson. In Recent

Trends in Philosophical Logic, R. Ciuni, H. Wansing, and C. Willkommen,

Eds., vol. 41 of Trends in Logic. Springer, 2014, pp. 145–166.

[9] Omori, H., and Waragai, T. Some Observations on the Systems LFI1

and LFI1*. In Proceedings of DEXA2011 (2011), F. Morvan, A. M. Tjoa,

and R. Wagner, Eds., IEEE computer society, pp. 320–324.

Raoni Arroyo

Raoni Arroyo
State University of Campinas, Brazil
raoniarroyo@gmail.com
itala@unicamp.b

Accepting inconsistent quantum ontologies:
the quasi-way

ABSTRACT

Ontological underdetermination is an issue at the heart of the current state of the art in the foundations of quantum mechanics. Different solutions to foundational problems lead to ontological commitments to either particles or waves, quantum potentials, or multiverses---depending on the solution of the measurement problem one adopts. One traditional way to deal with this is by adopting a structural realist view, according to which we must believe in the existence of structures that represent empirical phenomena. A significant version of structural realism calls for adopting partial structures to resolve such ontological underdetermination. We use a current examination of non-relativistic quantum mechanics to illustrate the relevant issues and argue that the concept of quasi-truth involves an epistemological conception embedded in the formulation of partial structures. At issue here are inseparable theses that are not often acknowledged. Formulated in terms of quasi-truth, the structural realist approach to underdetermination states that we can accept (but not believe) each of the quantum theories insofar as they are all quasi-true, i.e., empirically adequate. As one cannot decide between rival quantum ontologies by empirical matters, one must accept them all as quasi-true, hence adopting paraconsistency in the background. A significant shift away from belief and truth has been implemented. But the distinctions between belief and acceptance as well as between representation and empirical adequacy are characteristic of empiricism, not realism. In the end, structural realism cannot use partial structures if it wants to remain a realist stance.

Jonas R. Becker Arenhart

Jonas Becker Arenhart
Federal University of
Santa Catarina jonas.becker2@gmail.com

Newton da Costa on the
‘paraconsistent programme’

ABSTRACT

One of the current major disputes concerning the philosophy of logic is related to logical theory choice: given the plurality of systems of logic, one is left wondering which system to choose. Typically, the answer is related to the idea that the system to be chosen is the correct one, the one that suits the actual data. Contradictions are typically considered to be among such data, but the nature of such contradictions are not quite clear. In a rather brief set of remarks (in “On paraconsistent set theory”, Logique et analyse 29(115), pp.361-371, 1986), Newton da Costa offered considerations that suggest in which direction he believes one may be led to adopt paraconsistent logics, or, more broadly, the whole ‘paraconsistent programme’ (as he calls it). In a nutshell, he suggests that paraconsistent logics can be seriously considered as the appropriate choice if they offer solutions to problems of concrete (i.e. empirical) science involving insurmountable contradictions. The remarks, however, are rather brief, and the nature of the problems to be solved by paraconsistent logic is not so clear. We propose to make such issues clear, by connecting the discussion with other works by da Costa published in the same period. We suggest that da Costa has a quite substantial view of contradictions that need to be tamed.

Ederson Safra Melo

Ederson Safra Melo
Federal University of
Maranhão
saframelo@gmail.com

Two lessons from contradictions

ABSTRACT

Paradoxes are derivations leading from the plausible to the implausible; when the conclusion is a contradiction, the implausible is the contradiction. With the rise of paraconsistent logics, contradictions need no longer be seen as implausible. Dialetheists, like Graham Priest, argue that paradoxes teach us that there are true contradiction and that we have to learn to accept contradictions as fact of our lives. As a result, contradictions that we can draw out from paradoxes, can be accommodated in our overall system. This approach, however, conflicts with more traditional approache, requiring that contradictions be eliminated by revision of the derivation. Lets us call the first approach an accommodation-strategy and the second a revision-strategy. We shall argue that some of the tenets of the accommodation-strategy face difficulties when a form of methodological naturalism is embraced. The accommodation-strategy violates what one could take as a good methodological practice of science of avoiding contradictions by theoretical revision, independently of how many platitudes may need to be sacrificed. We find that the revision-strategy is superior, and it seems is better to learn, from the steps of successful science, that the presence of a contradiction is a signal that something is wrong.