Foundations of Logical Consequence
Lead Research Organisation:
University of St Andrews
Department Name: Philos Anthrop and Film Studies
Abstract
A philosophical problem often arises in the form of a dilemma: is it possible to give a characterisation of some notion which both explains its full nature and shows how we can have knowledge of it? One such problem is raised by the notion of inference, or to use the technical term, logical consequence. There is a distinction between good inference and bad, between sound reasoning and unsound reasoning, which any adequate account of logical consequence must draw correctly and explain. Yet this is a distinction which most people have an intuitive grasp of. Even if ignorant of the theoretical underpinnings of the nature of inference, we all have some conception of the difference between good and bad argument, and reason for the most part correctly. What account should be given of what logical consequence consists in which at the same time can explain our intuitive inferential competence?
There are two principal approaches to this challenge: model-theoretic, and inferentialist. The former uses the mathematical notion of a model, that is, roughly, a certain kind of admissible interpretation of the premises and conclusion. It conceives of logical consequence as consisting in preservation of truth from premises to conclusion under any such interpretation. An argument is valid just when, provided the premises are true, so interpreted, the conclusion must be true too. The inferentialist, in contrast, claims that logical consequence is to be explained primarily in terms of rules of inference. For example, it is the rule for the use of 'and' that from a premise of the form 'A and B' one can validly infer either A or B as conclusion. According to the inferentialist, valid inference then consists simply in the (successive) application of a basic repertoire of such rules.
But both proposals seem open to objection. What do everyday reasoners know about mathematical models? And what qualifies a rule for inclusion in the basic repertoire? The model-theoretic approach seems to lose touch with our intuitive inferential competence, but without an account makes the basic rules acceptable, the inferentialist approach seems merely to have postponed the question of explaining what logical consequence consists in?
We impose a further constraint on a satisfactory account of logical consequence: to shed light on the status of certain prominent philosophical debates that bear on it. Most particularly, we shall concentrate on the debates concerning the revision of logic. Traditionally, logic was conceived as unrevisable and certain. But views which challenge this have been vigorously defended for more than a century on a variety of counts and continue to be so. Can either of the approaches, model-theoretic or inferentialist, shed light on these debates (either by lending support to revisionists or conservatives, or by revealing the controversy to be misconceived)?
The project will work toward best versions of the two approaches, and explore the ability of the resulting accounts to address these difficulties; review the revisionary debates in the light of our findings; then finally return to the challenges posed by intuitive inferential competence.
There are two principal approaches to this challenge: model-theoretic, and inferentialist. The former uses the mathematical notion of a model, that is, roughly, a certain kind of admissible interpretation of the premises and conclusion. It conceives of logical consequence as consisting in preservation of truth from premises to conclusion under any such interpretation. An argument is valid just when, provided the premises are true, so interpreted, the conclusion must be true too. The inferentialist, in contrast, claims that logical consequence is to be explained primarily in terms of rules of inference. For example, it is the rule for the use of 'and' that from a premise of the form 'A and B' one can validly infer either A or B as conclusion. According to the inferentialist, valid inference then consists simply in the (successive) application of a basic repertoire of such rules.
But both proposals seem open to objection. What do everyday reasoners know about mathematical models? And what qualifies a rule for inclusion in the basic repertoire? The model-theoretic approach seems to lose touch with our intuitive inferential competence, but without an account makes the basic rules acceptable, the inferentialist approach seems merely to have postponed the question of explaining what logical consequence consists in?
We impose a further constraint on a satisfactory account of logical consequence: to shed light on the status of certain prominent philosophical debates that bear on it. Most particularly, we shall concentrate on the debates concerning the revision of logic. Traditionally, logic was conceived as unrevisable and certain. But views which challenge this have been vigorously defended for more than a century on a variety of counts and continue to be so. Can either of the approaches, model-theoretic or inferentialist, shed light on these debates (either by lending support to revisionists or conservatives, or by revealing the controversy to be misconceived)?
The project will work toward best versions of the two approaches, and explore the ability of the resulting accounts to address these difficulties; review the revisionary debates in the light of our findings; then finally return to the challenges posed by intuitive inferential competence.
Organisations
Publications
Aberdein A
(2009)
The Development of Modern Logic
Beall J
(2011)
Can u do that?
in Analysis
Beziau, Jean-Yves (University Of Neuchatel); Jacquette, Dale
(2012)
Around and Beyond the Square of Opposition
Buridan J
(2014)
Treatise on Consequences
De M
(2012)
Empirical Negation
in Acta Analytica
DeVidi, David; Hallett, Michael; Clark, Peter
(2011)
Logic, Mathematics, Philosophy, Vintage Enthusiasms
Dietz, Richard; Moruzzi, Sebastiano
(2010)
Cuts and Clouds: Vaguenesss, Its Nature and Its Logic
Dietz, Richard; Moruzzi, Sebastiano
(2010)
Cuts and Clouds: Vaguenesss, Its Nature and Its Logic
Haaparanta, Leila
(2009)
The Development of Modern Logic
Hales, Steven D.
(2011)
A Companion to Relativism
Le Poidevin, Robin; Simons, Peter; McGonigal, Andrew; Cameron, Ross P.
(2009)
The Routledge Companion to Metaphysics
Lear, Jonathan; Oliver, Alex
(2010)
The Force of Argument
Lindstrom, Sten; Palmgren, Erik; Segerberg, Krister; Stoltenberg-Hansen, Viggo
(2008)
Logicism, Intuitionism, and Formalism
Meadows T
(2012)
Revising Carnap's Semantic Conception of Modality
in Studia Logica
Meadows T
(2012)
Truth, Dependence and Supervaluation: Living with the Ghost
in Journal of Philosophical Logic
MEADOWS T
(2013)
WHAT CAN A CATEGORICITY THEOREM TELL US?
in The Review of Symbolic Logic
Murzi J
(2009)
Inferentialism and the categoricity problem: reply to Raatikainen
in Analysis
Pelis, Michal
(2010)
The Logica Yearbook 2009
Polkinghorne, John
(2011)
Meaning in Mathematics
Polkinghorne, John
(2011)
Meaning in Mathematics
Priest
(2010)
Logic
Priest G
(2010)
Inclosures, Vagueness, and Self-Reference
in Notre Dame Journal of Formal Logic
Priest G
(2010)
Hopes Fade For Saving Truth
in Philosophy
Priest G
(2010)
Moonshadows
Priest G
(2012)
The Realism-Antirealism Debate in the Age of Alternative Logics
Priest G
(2010)
First-Order da Costa Logic
in Studia Logica
Priest G
(2010)
Moonshadows
Priest G
(2009)
Badici on Inclosures and the Liar Paradox
in Australasian Journal of Philosophy
PRIEST G
(2009)
NEIGHBORHOOD SEMANTICS FOR INTENTIONAL OPERATORS
in The Review of Symbolic Logic
Priest G
(2010)
Cuts and Clouds - Vagueness, its Nature, & its Logic
Rahman, Shahid; Primiero, Giuseppe; Marion, Mathieu
(2011)
The Realism-Antirealism Debate in the Age of Alternative Logics
Rahman, Shahid; Primiero, Giuseppe; Marion, Mathieu
(2011)
The Realism-Antirealism Debate in the Age of Alternative Logics
Ravenscroft, Ian
(2009)
Minds, Ethics, and Conditionals: Themes from the Philosophy of Frank Jackson
Read S
(2010)
Field's Paradox and Its Medieval Solution
in History and Philosophy of Logic
READ S
(2015)
Aristotle and Lukasiewicz on Existential Import
in Journal of the American Philosophical Association
Read S
(2015)
Dag Prawitz on Proofs and Meaning
Read S
(2011)
The Cambridge History of Medieval Philosophy
Read S
(2010)
General-Elimination Harmony and the Meaning of the Logical Constants
in Journal of Philosophical Logic
Read S
(2010)
Saving Truth from Paradox, by Hartry Field.
in Mind
Read S
(2011)
The medieval theory of consequence
in Synthese
Read S
(2015)
Unifying the Philosophy of Truth
Salerno, Joe
(2009)
New Essays on the Knowability Paradox
Shapiro S
(2012)
Higher-Order Logic or Set Theory: A False Dilemma
in Philosophia Mathematica
Shapiro S
(2011)
EPISTEMOLOGY OF MATHEMATICS: WHAT ARE THE QUESTIONS? WHAT COUNT AS ANSWERS? Epistemology of Mathematics
in The Philosophical Quarterly
Shapiro S
(2011)
The Company Kept by Cut Abstraction (and its Relatives)
in Philosophia Mathematica
SHAPIRO S
(2009)
WE HOLD THESE TRUTHS TO BE SELF-EVIDENT: BUT WHAT DO WE MEAN BY THAT?
in The Review of Symbolic Logic
Shapiro S
(2011)
Theology and the Actual Infinite: Burley and Cantor
in Theology and Science
SHAPIRO S
(2012)
AN " i " FOR AN i : SINGULAR TERMS, UNIQUENESS, AND REFERENCE
in The Review of Symbolic Logic
Shapiro S
(2009)
Logicism, Intuitionism, and Formalism - What has Become of Them?