Semantic Paradoxes and Abductive Methodology

Williamson, Timothy; Armour‐Garb, Bradley

doi:10.1093/oso/9780199896042.003.0013

Cited by 120 publications

(109 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…2 Since anti-exceptionalists reject apriorism, they need an alternative story about how logical theories are supported. This is precisely the challenge that Williamson (2015) attempts to answer.…”

Section: Priest and Williamson On Abductivism About Logicmentioning

confidence: 99%

“…Priest (2006a) is concerned with the normative project described above, but it is not clear that Williamson's aim is the same. Williamson (2015) develops a deflationary antiexceptionalist account of logical theories. 5 The theory has no overt normative component, nor does it purport to describe the psychology of deductive reasoning.…”

Section: A Deflationary Account Of Logical Theoriesmentioning

confidence: 99%

“…It cannot merely be a matter of avoiding contradictions, as some of the candidate theories embrace selective contradictions. Williamson's (2015) solution is to insist on a weaker conditionnon-triviality. Classically, non-triviality is equivalent to non-contradiction, but that is not the case in paraconsistent theories, where the law of explosion fails.…”

Section: A Non-deflationary Alternativementioning

confidence: 99%

See 2 more Smart Citations

Anti-exceptionalism about logic

Hjortland

2016

Philos Stud

100

View full text Add to dashboard Cite

Logic 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. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy (Proc Address Am Philos Williamson (Modal logic as metaphysics, Oxford University Press, Oxford, 2013b, The relevance of the liar, OUP, Oxford, 2015). Although these authors agree on many methodological issues about logic, they disagree about which logic anti-exceptionalism supports. Williamson uses an anti-exceptionalist argument to defend classical logic, while Priest claims that his anti-exceptionalism supports nonclassical logic. This paper argues that the disagreement is due to a difference in how the parties understand logical theories. Once we reject Williamson's deflationary account of logical theories, the argument for classical logic is undercut. Instead an alternative account of logical theories is offered, on which logical pluralism is a plausible supplement to anti-exceptionalism.

show abstract

Section: Priest and Williamson On Abductivism About Logicmentioning

confidence: 99%

Section: A Deflationary Account Of Logical Theoriesmentioning

confidence: 99%

Section: A Non-deflationary Alternativementioning

confidence: 99%

See 1 more Smart Citation

Anti-exceptionalism about logic

Hjortland

2016

Philos Stud

100

View full text Add to dashboard Cite

show abstract

“…1 Si bien esta posición nunca fue defendida explícitamente, está implícitamente contenida en Williamson (2013). Aquí se sostiene que la lógica clásica, al ser sostenida por la mayor parte de la comunidad, puede ser utilizada como punto de referencia para entender las otras lógicas.…”

Section: Introductionunclassified

Desacuerdo lógico y agregación

Tajer

2017

THEORIA

View full text Add to dashboard Cite

RESUMEN: En este artículo, exploro la posibilidad de aplicar los métodos y resultados de la Agregación de Juicios al problema del desacuerdo lógico. Es decir, desarrollo y evalúo maneras en que individuos que desacuerdan lógica-mente pueden generar una lógica colectiva. Pruebo una versión de la paradoja discursiva, donde el voto por mayoría en un grupo de lógicos estructurales puede generar lógicas subestructurales, y luego elaboro un resultado de imposibilidad más general. Más adelante, analizo diferentes maneras de evitar la paradoja, en particular aquellas que apelan a restricciones de dominio. Finalmente, analizo la aplicación de estos resultados al debate sobre paradojas semánticas.Palabras clave: Desacuerdo lógico; Agregación de juicios; Lógicas no-clásicas; Paradojas semánticas.ABSTRACT: In this paper, I explore the possibility of applying the methods and results of Judgement Aggregation to the problem of logical disagreement. I develop and evaluate different ways in which individuals who logically disagree can generate a collective logic. I prove a version of the discursive paradox, where the majority voting of a group of structural logicians can give rise to a substructural logic; then I develop a more general impossibility result. After this, I analyze different ways to avoid the paradox, in particular some methods which appeal to domain restrictions. Finally, I consider the application of these results to the discussion on semantic paradoxes.

show abstract

“…The general methodology applied here has been defended by Timothy Williamson in other areas of philosophy: see Williamson (2013, pp. 423–29, forthcoming).…”

mentioning

confidence: 99%

Higher-Order Abstraction Principles

Mount

2015

Thought: A Journal of Philosophy

View full text Add to dashboard Cite

I extend theorems due to Roy Cook (2009) on third‐ and higher‐order versions of abstraction principles and discuss the philosophical importance of results of this type. Cook demonstrated that the satisfiability of certain higher‐order analogues of Hume's Principle is independent of ZFC. I show that similar analogues of Boolos's new v and Cook's own ordinal abstraction principle soap are not satisfiable at all. I argue, however, that these results do not tell significantly against the second‐order versions of these principles.

show abstract

Semantic Paradoxes and Abductive Methodology

Cited by 120 publications

References 0 publications

Anti-exceptionalism about logic

Anti-exceptionalism about logic

Desacuerdo lógico y agregación

Higher-Order Abstraction Principles

Contact Info

Product

Resources

About