In Pursuit of the Non-Trivial

Episteme ◽  
2019 ◽  
pp. 1-16
Author(s):  
Colin R. Caret
Keyword(s):  
Classical Logic ◽  
Fundamental Problem ◽  
Paraconsistent Logic ◽  
Paraconsistent Logics ◽  
Scientific Theories ◽  
Preferential Treatment ◽  
Logical Reconstruction ◽  
Inconsistent Theories

AbstractThis paper is about the underlying logical principles of scientific theories. In particular, it concerns ex contradictione quodlibet (ECQ) the principle that anything follows from a contradiction. ECQ is valid according to classical logic, but invalid according to paraconsistent logics. Some advocates of paraconsistency claim that there are ‘real’ inconsistent theories that do not erupt with completely indiscriminate, absurd commitments. They take this as evidence in favor of paraconsistency. Michael (2016) calls this the non-triviality strategy (NTS). He argues that this strategy fails in its purpose. I will show that Michael's criticism significantly over-reaches. The fundamental problem is that he places more of a burden on the advocate of paraconsistency than on the advocate of classical logic. The weaknesses in Michael's argument are symptomatic of this preferential treatment of one viewpoint in the debate over another. He does, however, make important observations that allow us to clarify some of the complexities involved in giving a logical reconstruction of a theory. I will argue that there are abductive arguments deserving of further consideration for the claim that paraconsistent logic offers the best explanation of the practice of inconsistent science. In this sense, the debate is still very much open.

FACING INCONSISTENCY: THEORIES AND OUR RELATIONS TO THEM

Episteme ◽  
2013 ◽  
Vol 10 (4) ◽  
pp. 351-367 ◽  
Author(s):  
Michaelis Michael
Keyword(s):  
Classical Logic ◽  
Paraconsistent Logic ◽  
Indispensability Argument ◽  
Mathematical Objects ◽  
The Face ◽  
Inconsistent Objects ◽  
Inconsistent Theories

AbstractClassical logic is explosive in the face of contradiction, yet we find ourselves using inconsistent theories. Mark Colyvan, one of the prominent advocates of the indispensability argument for realism about mathematical objects, suggests that such use can be garnered to develop an argument for commitment to inconsistent objects and, because of that, a paraconsistent underlying logic. I argue to the contrary that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity. Facing inconsistency does not force us to adopt an underlying paraconsistent logic. Moreover we will see that the argument to best explanation deployed by Colyvan in this context is unsuccessful. I suggest that Quinean approach which Colyvan champions will not lead to the revolutionary doctrines Colyvan endorses.

Paraconsistency, self-extensionality, modality

2018 ◽  
Vol 28 (5) ◽  
pp. 851-880
Author(s):  
Arnon Avron ◽  
Anna Zamansky
Keyword(s):  
Intuitionistic Logic ◽  
Modal Logics ◽  
The Other ◽  
Paraconsistent Logics ◽  
Classical Negation ◽  
Inconsistent Theories ◽  
Replacement Property ◽  
General Method

Abstract Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.

Logic and Philosophical Methodology

2016 ◽  
Author(s):  
John P. Burgess
Keyword(s):  
Set Theory ◽  
Model Theory ◽  
Classical Logic ◽  
Proof Theory ◽  
Recursion Theory ◽  
Theory Model ◽  
Philosophical Methodology ◽  
Paraconsistent Logics ◽  
Philosophical Logic

This article explores the role of logic in philosophical methodology, as well as its application in philosophy. The discussion gives a roughly equal coverage to the seven branches of logic: elementary logic, set theory, model theory, recursion theory, proof theory, extraclassical logics, and anticlassical logics. Mathematical logic comprises set theory, model theory, recursion theory, and proof theory. Philosophical logic in the relevant sense is divided into the study of extensions of classical logic, such as modal or temporal or deontic or conditional logics, and the study of alternatives to classical logic, such as intuitionistic or quantum or partial or paraconsistent logics. The nonclassical consists of the extraclassical and the anticlassical, although the distinction is not clearcut.

scholarly journals What Counts as Evidence for a Logical Theory?

2019 ◽  
Vol 16 (7) ◽  
pp. 250 ◽  
Author(s):  
Ole Thomassen Hjortland
Keyword(s):  
Classical Logic ◽  
A Priori ◽  
Scientific Theories ◽  
Alternative Account ◽  
Logical Theory ◽  
Crucial Question ◽  
Indispensability Arguments ◽  
Timothy Williamson ◽  
Graham Priest ◽  
Number Of Authors

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic.

scholarly journals Paraconsistent Annotated Logic Algorithms Applied in Management and Control of Communication Network Routes

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4219
Author(s):  
João Inácio Da Silva Filho ◽  
Jair Minoro Abe ◽  
Alessandro de Lima Marreiro ◽  
Angel Antonio Gonzalez Martinez ◽  
Cláudio Rodrigo Torres ◽  
...  
Keyword(s):  
Communication Network ◽  
Communication Networks ◽  
Classical Logic ◽  
Paraconsistent Logic ◽  
Logic Gates ◽  
Main Property ◽  
Computational Method ◽  
Stream Control ◽  
Routing Management ◽  
And Control

This paper presents a computational method based on non-classical logic dedicated to routing management and information stream control in communication networks. Paraconsistent logic (PL) was used to create an algorithmic structure whose main property is to accept contradiction. Moreover, a computational structure, the denominated paraconsistent data analyzer (PDAPAL2v), was constructed to perform routing management in communication networks. Direct comparisons of PDAPAL2v with a classical logic system that simulates routing conditions were made in the laboratory. In the conventional system, the paraconsistent algorithms were considered as binary logic gates, and in the tests, the same adjustment limits of PDAPAL2v were applied. Using a database with controlled insertion of noise, we obtained an efficacy of 97% in the detection of deteriorated packets with PDAPAL2v and 72% with the conventional simulation system. Functional tests were carried out, showing that PDAPAL2v is able to assess the conditions and degradation of links and perform the analysis and correlation of various inputs and variables, even if the signals have contradictory values. From practical tests in the laboratory, the proposed method represents a new way of managing and controlling communication network routes with good performance.

scholarly journals Rewriting the History of Connexive Logic

2022 ◽  
Author(s):  
Wolfgang Lenzen
Keyword(s):  
Twentieth Century ◽  
Classical Logic ◽  
Paraconsistent Logic ◽  
Historical Analysis ◽  
Relevance Logic ◽  
Overwhelming Majority ◽  
Lewis Carroll ◽  
Self Consistent ◽  
History Of ◽  
Connexive Logic

AbstractThe “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties (like the condition that no proposition implies its own negation) only apply to “normal” (e.g., self-consistent) antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning (“humbly”) connexive implication don’t give rise, however, to anything like a non-classical logic.

Paraconsistent logic

2018 ◽  
Author(s):  
Graham Priest
Keyword(s):  
Paraconsistent Logic ◽  
Paraconsistent Logics ◽  
Naturally Occurring

A logic is paraconsistent if it does not validate the principle that from a pair of contradictory sentences, A and ∼A, everything follows, as most orthodox logics do. If a theory has a paraconsistent underlying logic, it may be inconsistent without being trivial (that is, entailing everything). Sustained work in formal paraconsistent logics started in the early 1960s. A major motivating thought was that there are important naturally occurring inconsistent but non-trivial theories. Some logicians have gone further and claimed that some of these theories may be true. By the mid-1970s, details of the semantics and proof-theories of many paraconsistent logics were well understood. More recent research has focused on the applications of these logics and on their philosophical underpinnings and implications.

Enthymematic classical recapture 1

2018 ◽  
Vol 28 (5) ◽  
pp. 817-831
Author(s):  
Henrique Antunes
Keyword(s):  
Classical Logic ◽  
Paraconsistent Logics ◽  
Logical Theory ◽  
Oxford University ◽  
The One ◽  
Oxford University Press

AbstractPriest (2006, Ch.8, 2nd edn. Oxford University Press), argues that classical reasoning can be made compatible with his preferred (paraconsistent) logical theory by proposing a methodological maxim authorizing the use of classical logic in consistent situations. Although Priest has abandoned this proposal in favour of the one in G. Priest (1991, Stud. Log., 50, 321–331), I shall argue that due to the fact that the derivability adjustment theorem holds for several logics of formal (in)consistency (cf. W. A. Carnielli and M. E. Coniglio, 2016, Springer), these paraconsistent logics are particularly well suited to accommodate classical reasoning by means of a version of that maxim, yielding thus an enthymematic account of classical recapture.

Sign in / Sign up

Export Citation Format

Share Document