About this topic
Summary The epistemology of logic focuses on issues concerning the normative status of our beliefs about logical truth and logical validity. It seems that we know that certain claims are logically true and that certain arguments are logically valid. What explains this knowledge? This question is an instance of a more general question about what explains our knowledge of (apparent) a priori truths. It is also closely connected to issues in the epistemology of modality, since logical truths are necessarily true. A long tradition in the epistemology of logic has it that logical truths are analytic -- that is, "true in virtue of meaning". In the middle of the twentieth century, Quine challenged this view. He argued that logical and mathematical claims are empirical claims that can in principle be revised on empirical grounds. In recent years, there have been a number of different proposals put forward about our knowledge of logic. Some philosophers follow Quine in viewing logic as empirical. Other philosophers have tried to rehabilitate the analytic theory of our knowledge of logic. Still other philosophers have appealed to intuitions or rational seemings to explain our knowledge of logic.
Key works For Quine's critique of the analytic theory of logical knowledge, see Quine 1936 and Quine 1960Putnam 1968 argues that logic is empirically reviseable.  Haack 1996 discusses Quine's views, in the context of a discussion of alternative logics. BonJour 1998 presents a theory of a priori knowledge based on rational insight. Boghossian 2000 and Boghossian 2001 are part of a sequence of papers trying to rehabilitate the analytic theory of logical knowledge. See Wright 2001 and Wright 2004 for a discussion of the role of intuitions in logical knowledge. Also see the key works for "Deductive Reasoning".
Introductions Boghossian 2000 provides an opinionated introduction to views in the epistemology of logic. BonJour 1998 provides an in depth discussion of theories of the apriori that is highly relevant to the case of logical knowledge. Field 2005 discusses some recent debates concerning the a priori in general and logical and mathematical knowledge in particular.
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  1. Wff'n Proof. [REVIEW]B. A. - 1963 - Review of Metaphysics 16 (3):578-578.
  2. Idealization in Applied First-Order Logic.Ernest W. Adams - 1998 - Synthese 117 (3):331-354.
    Applying first-order logic to derive the consequences of laws that are only approximately true of empirical phenomena involves idealization of a kind that is akin to applying arithmetic to calculate the area of a rectangular surface from approximate measures of the lengths of its sides. Errors in the data, in the exactness of the lengths in one case and in the exactness of the laws in the other, are in some measure transmitted to the consequences deduced from them, and the (...)
  3. A Definition of the Logical Concept of Proof.Kazimierz Ajdukiewicz - 1966 - Studia Logica 19 (1):46 -.
  4. The Logical Concept of Proof.Kazimierz Ajdukiewicz - 1966 - Studia Logica 19 (1):12-45.
  5. Classification of Reasonings.Kazimierz Ajdukiewicz - 1955 - Studia Logica 2 (1):300-300.
  6. Boghossian's Implicit Definition Template.Ben Baker - 2012 - In Piotr Stalmaszczyk (ed.), Philosophical and Formal Approaches to Linguistic Analysis. Ontos-Verlag. pp. 15.
    In Boghossian's 1997 paper, 'Analyticity' he presented an account of a prioriknowledge of basic logical principles as available by inference from knowledge of their role in determining the meaning of the logical constants by implicit definitiontogether with knowledge of the meanings so-determined that we possess through ourprivileged access to meaning. Some commentators (e.g. BonJour (1998), Glüer (2003),Jenkins (2008)) have objected that if the thesis of implicit definition on which he relieswere true, knowledge of the meaning of the constants would presuppose (...)
  7. Carnielli, Walter (ed.). Logic and Philosophy of the Formal Sciences: A Festscrift for Itala M. Loffredo D´ Ottaviano. São Paulo: Centro de Lógica, Epistemología e Historia da Ciência, UNICAMP (Número especial de Manuscrito, Revista Internacional de Filosofia, vol. 28, n. 2, jul-dez.) pp. 191-591.(2005). [REVIEW]Tomás Barrero - 2006 - Ideas Y Valores 55 (132):124-126.
  8. Logical Knowledge and Ordinary Reasoning.Corine Besson - 2012 - Philosophical Studies 158 (1):59-82.
    This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.
  9. Propositions, Dispositions and Logical Knowledge.Corine Besson - 2010 - In M. Bonelli & A. Longo (eds.), Quid Est Veritas? Essays in Honour of Jonathan Barnes. Bibliopolis.
    This paper considers the question of what knowing a logical rule consists in. I defend the view that knowing a logical rule is having propositional knowledge. Many philosophers reject this view and argue for the alternative view that knowing a logical rule is, at least at the fundamental level, having a disposition to infer according to it. To motivate this dispositionalist view, its defenders often appeal to Carroll’s regress argument in ‘What the Tortoise Said to Achilles’. I show that this (...)
  10. Understanding the Logical Constants and Dispositions.Corine Besson - 2009 - The Baltic International Yearbook of Cognition, Logic and Communication 5 (1):1-24.
    Many philosophers claim that understanding a logical constant (e.g. ‘if, then’) fundamentally consists in having dispositions to infer according to the logical rules (e.g. Modus Ponens) that fix its meaning. This paper argues that such dispositionalist accounts give us the wrong picture of what understanding a logical constant consists in. The objection here is that they give an account of understanding a logical constant which is inconsistent with what seem to be adequate manifestations of such understanding. I then outline an (...)
  11. Inferentialism and the Epistemology of Logic: Reflections on Casalegno and Williamson.Paul Boghossian - 2012 - Dialectica 66 (2):221-236.
    I defend an inferential account of the logical constants against objections made to it by Paolo Casalegno and Timothy Williamson.
  12. Blind Reasoning.Paul Boghossian - 2003 - Aristotelian Society Supplementary Volume 77 (1):225–248.
    The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ‘blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.
  13. Knowledge of Logic.Paul Boghossian - 2000 - In Paul Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori.
  14. Epistemic Rules.Paul A. Boghossian - 2008 - Journal of Philosophy 105 (9):472-500.
  15. Transcendental Logic Redefined.Manuel Bremer - 2008 - Review of Contemporary Philosophy 7.
    Traditionally transcendental logic has been set apart from formal logic. Transcendental logic had to deal with the conditions of possibility of judgements, which were presupposed by formal logic. Defined as a purely philosophical enterprise transcendental logic was considered as being a priori delivering either analytic or even synthetic a priori results. In this paper it is argued that this separation from the (empirical) cognitive sciences should be given up. Transcendental logic should be understood as focusing on specific questions. These do (...)
  16. A Carnapian Approach to Counterexamples to Modus Ponens.Constantin C. Brîncuș & Iulian D. Toader - 2013 - Romanian Journal of Analytic Philosophy 7:78-85.
    This paper defends a Carnapian approach to known counterexamples to Modus Ponens (MP). More specifically, it proposes that instead of rejecting MP as invalid in certain interpretations, one should regard the interpretations themselves as non-normal, in Carnap’s sense.
  17. The Impact of Computing on Epistemology: Knowing Gödel's Mind Through Computation.Selmer Bringsjord - unknown
    I know that those of you who know my mind know that I think I know that we can't know Gödel's mind through computation: ``The Impact : Failing to Know " If computationalism is false, observant philosophers willing to get their hands dirty should be able to find tell-tale signs today: automated theorem proving tomorrow (Eastern APA): robots as zombanimals But let's start with little 'ol me, and literary, not mathematical, creativity: Selmer (samples) vs. Brutus1 (samples again).
  18. Rival Logics, Disagreement and Reflective Equilibrium.Georg Brun - 2012 - In C. Jaeger W. Loeffler (ed.), Epistemology: Contexts, Values, Disagreements (Proceedings of the 34th International Ludwig Wittgenstein Symposium). pp. 355-368.
    Two challenges to the method of reflective equilibrium have been developed in a dispute between Michael D. Resnik and Stewart Shapiro: because the method itself involves logical notions, it can neither be specified in a logic-neutral way nor can it allow logical pluralism. To analyse and answer these claims, an explicit distinction is introduced between judgements held prior to the process of mutual adjustments and judgements in agreement with the systematic principles, which result from the process. It is then argued (...)
  19. Logic and Analyticity.Tyler Burge - 2003 - Grazer Philosophische Studien 66 (1):199-249.
    The view that logic is true independently of a subject matter is criticized—enlarging on Quine's criticisms and adding further ones. It is then argued apriori that full reflective understanding of logic and deductive reasoning requires substantial commitment to mathematical entities. It is emphasized that the objectively apriori connections between deductive reasoning and commitment to mathematics need not be accepted by or even comprehensible to a given deductive reasoner. The relevant connections emerged only slowly in the history of logic. But they (...)
  20. The Right Order of Concepts: Graßmann, Peano, Gödel and the Inheritance of Leibniz's Universal Characteristic.Paola Cantù - 2014 - Philosophia Scientiæ 18 (1):157-182.
    This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive investigations, but (...)
  21. Logic and the Structure of the Web of Belief.Matthew Carlson - 2015 - Journal for the History of Analytical Philosophy 3 (5).
    In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This raises two (...)
  22. On the Philosophical Motivations for the Logics of Formal Consistency and Inconsistency.Walter Carnielli & Rodrigues Abilio - manuscript
    We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.
  23. The Universal Generalization Problem.Carlo Cellucci - 2009 - Logique Et Analyse 52.
    The universal generalization problem is the question: What entitles one to conclude that a property established for an individual object holds for any individual object in the domain? This amounts to the question: Why is the rule of universal generalization justified? In the modern and contemporary age Descartes, Locke, Berkeley, Hume, Kant, Mill, Gentzen gave alternative solutions of the universal generalization problem. In this paper I consider Locke’s, Berkeley’s and Gentzen’s solutions and argue that they are problematic. Then I consider (...)
  24. Debunking Arguments: Mathematics, Logic, and Modal Security.Justin Clarke-Doane - forthcoming - In Robert Richards and Michael Ruse (ed.), Cambridge Handbook of Evolutionary Ethics. Cambridge University Press.
    I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...)
  25. The Justification of the Logical Laws Revisited.Patrizio Contu - 2006 - Synthese 148 (3):573-588.
    The proof-theoretic analysis of logical semantics undermines the received view of proof theory as being concerned with symbols devoid of meaning, and of model theory as the sole branch of logical theory entitled to access the realm of semantics. The basic tenet of proof-theoretic semantics is that meaning is given by some rules of proofs, in terms of which all logical laws can be justified and the notion of logical consequence explained. In this paper an attempt will be made to (...)
  26. Counterexamples and Proexamples.J. Corcoran - 2005 - Bulletin of Symbolic Logic 11:460.
    Corcoran, J. 2005. Counterexamples and proexamples. Bulletin of Symbolic Logic 11(2005) 460. -/- John Corcoran, Counterexamples and Proexamples. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: corcoran@buffalo.edu Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even. Conversely, every counterexample for the proposition “every perfect number is even” is a perfect number that is not even. Every perfect number that is odd is a proexample for the existential proposition that some (...)
  27. Significados de la implicación.J. Corcoran - 1985 - Agora 5:279.
    John Corcoran ’s “Meanings of Implication” outlines and discusses 12 distinct uses of the term “implies” while also commenting on the ways in which these different notions of implication might be confused or conflated. Readers may take special note of Corcoran ’s analysis of Russell’s truth-functional account of “implication” and its historical function as logical consequence, as well as Corcoran ’s discussion of Bolzano’s previously obscure and rarely mentioned notion of “relative implication.”.
  28. Contra-Argumento/Contraejemplo.John Corcoran - 2011 - In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 137--141.
    A universal proposition is shown false by a known counterexample. A premise-conclusion argument is shown invalid by a known counterargument. The failure to distinguish counterexample from counterargument is like the failure to distinguish falsehood from invalidity.
  29. Forma lógica/Formalización.John Corcoran - 2011 - In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 257--258.
    The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...)
  30. Review of Striker Translation of Aristotle's PRIOR ANALYTICS. [REVIEW]John Corcoran - 2010 - Notre Dame Philosophical Reviews:1-13.
    This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...)
  31. Peter Hare on the Proposition.John Corcoran - 2010 - Transactions of the Charles S. Peirce Society 46 (1):21-34.
    Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department in (...)
  32. Schema.John Corcoran - 2008 - Stanford Encyclopedia of Philosophy.
    -/- A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema. Schemas are used in logic to specify rules of inference, in mathematics to describe theories with infinitely many axioms, and in semantics to give adequacy conditions for definitions of truth. -/- 1. What is a Schema? (...)
  33. Information-Theoretic Logic and Transformation-Theoretic Logic,.John Corcoran - 1999 - In R. A. M. M. (ed.), Fragments in Science,. World Scientific Publishing Company,. pp. 25-35.
    Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...)
  34. Ancient Logic and its Modern Interpretations.John Corcoran (ed.) - 1974 - Boston: Reidel.
    This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...)
  35. A Mathematical Model of Aristotle's Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
  36. Three Logical Theories.John Corcoran - 1969 - Philosophy of Science 36 (2):153-177.
    This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical (...)
  37. Review: The Contemporary Relevance of Ancient Logical Theory. [REVIEW]John Corcoran & Michael Scanlan - 1982 - Philosophical Quarterly 32 (126):76 - 86.
    This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...)
  38. Logic and Epistemology.A. C. Cotter - 1938 - Boston: Mass., The Stratford Company.
  39. Is Induction Epistemologically Prior to Deduction?George Couvalis - 2004 - Ratio 17 (1):28–44.
    Most philosophers hold that the use of our deductive powers confers an especially strong warrant on some of our mathematical and logical beliefs. By contrast, many of the same philosophers hold that it is a matter of serious debate whether any inductive inferences are cogent. That is, they hold that we might well have no warrant for inductively licensed beliefs, such as generalizations. I argue that we cannot know that we know logical and mathemati- cal truths unless we use induction. (...)
  40. Cogency and Context.Cesare Cozzo - forthcoming - Topoi:1-12.
    The problem I address is: how are cogent inferences possible? In § 1 I distinguish three senses in which we say that one is “compelled” by an inference: automatic, seductive-rhetorical and epistemic compulsion. Cogency is epistemic compulsion: a cogent inference compels us to accept its conclusion, if we accept its premises and we aim at truth. In §§ 2–3 I argue that cogency is intelligible if we consider an inference as a compound linguistic act in which several component acts are (...)
  41. Inference and Compulsion.Cesare Cozzo - 2014 - In E. Moriconi (ed.), Second Pisa Colloquium in Logic,Language and Epistemology. ETS. pp. 162-180.
    What is an inference? Logicians and philosophers have proposed various conceptions of inference. I shall first highlight seven features that contribute to distinguish these conceptions. I shall then compare three conceptions to see which of them best explains the special force that compels us to accept the conclusion of an inference, if we accept its premises.
  42. Reconsidering the Epistemology of Deductive-Inferential Validity.Florian Demont - 2008 - Abstracta 4 (1):44-56.
    Until quite recently, the epistemology of logical laws has not been much discussed and neither has how one can be justified in claiming that a particular inference is valid. The transfer of warrant from premises to conclusion(s) in modus ponens will be examined in the paper through assessing Paul Boghossian's inferentialist proposal of assuming 'blind reasoning'. It will be argued that merely being justified in inferring according to a logical law a priori is worthless un-less one can also be justified (...)
  43. Essay Review.M. Detlefsen - 1988 - History and Philosophy of Logic 9 (1):93-105.
    S. SHAPIRO (ed.), Intensional Mathematics (Studies in Logic and the Foundations of Mathematics, vol. 11 3). Amsterdam: North-Holland, 1985. v + 230 pp. $38.50/100Df.
  44. Löb's Theorem as a Limitation on Mechanism.Michael Detlefsen - 2002 - Minds and Machines 12 (3):353-381.
    We argue that Löb's Theorem implies a limitation on mechanism. Specifically, we argue, via an application of a generalized version of Löb's Theorem, that any particular device known by an observer to be mechanical cannot be used as an epistemic authority (of a particular type) by that observer: either the belief-set of such an authority is not mechanizable or, if it is, there is no identifiable formal system of which the observer can know (or truly believe) it to be the (...)
  45. Why Is a Valid Inference a Good Inference?Sinan Dogramaci - 2017 - Philosophy and Phenomenological Research 94 (1):61-96.
    True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...)
  46. Knowledge of Validity.Sinan Dogramaci - 2010 - Noûs 44 (3):403-432.
    What accounts for how we know that certain rules of reasoning, such as reasoning by Modus Ponens, are valid? If our knowledge of validity must be based on some reasoning, then we seem to be committed to the legitimacy of rule-circular arguments for validity. This paper raises a new difficulty for the rule-circular account of our knowledge of validity. The source of the problem is that, contrary to traditional wisdom, a universal generalization cannot be inferred just on the basis of (...)
  47. The Logic of Forbidden Colours.Elena Dragalina-Chernaya - 2013 - Epistemology and Philosophy of Science 38 (4):136-149.
    The purpose of this paper is twofold: to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that“there can be a bluish green but not a reddish green”, to compare model-theoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects.
  48. Feasibility in Logic.Jacques Dubucs - 2002 - Synthese 132 (3):213 - 237.
  49. Logique, Effectivité Et Faisabilité.Jacques Dubucs - 1997 - Dialogue 36 (01):45-.
    This paper can be read as an attempt at providing philosophical foundations to linear logic. The only plausible form of philosophical antirealism deals with practical feasibility rather than with effectivity in principle. The very notion of recognizability is ambiguous, audit has to be considered from a stricter perspective than currently done. The intuitionistic assertability conditions are to be reinforced. This change requires a move towards a frame in which the circumstances of the application of a logical rule can be specified. (...)
  50. Les Arguments Défaisables.Jacques Dubucs - 1995 - Hermes 15:271.
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