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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. Ernest W. Adams (1998). Idealization in Applied First-Order Logic. 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 (...)
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  2. Kazimierz Ajdukiewicz (1966). The Logical Concept of Proof. Studia Logica 19 (1):12-45.
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  3. Kazimierz Ajdukiewicz (1966). A Definition of the Logical Concept of Proof. Studia Logica 19 (1):46 -.
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  4. Kazimierz Ajdukiewicz (1955). Classification of Reasonings. Studia Logica 2 (1):300-300.
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  5. Ben Baker (2012). Boghossian's Implicit Definition Template. In Piotr Stalmaszczyk (ed.), Philosophical and Formal Approaches to Linguistic Analysis. Ontos-Verlag. 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 (...)
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  6. Corine Besson (2012). Logical Knowledge and Ordinary Reasoning. 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.
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  7. Corine Besson (2010). Propositions, Dispositions and Logical Knolwedge. 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 (...)
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  8. Corine Besson, Understanding the Logical Constants and Dispositions. The Baltic International Yearbook of Cognition, Logic and Communication (2010).
    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 (...)
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  9. Paul Boghossian (2012). Inferentialism and the Epistemology of Logic: Reflections on Casalegno and Williamson. 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.
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  10. Paul Boghossian (2003). Blind Reasoning. 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.
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  11. Paul Boghossian (2000). Knowledge of Logic. In Paul Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori.
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  12. Manuel Bremer (2008). Transcendental Logic Redefined. 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 (...)
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  13. Selmer Bringsjord, The Impact of Computing on Epistemology: Knowing Gödel's Mind Through Computation.
    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).
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  14. Tyler Burge (2003). Logic and Analyticity. 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 (...)
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  15. Walter Carnielli & Rodrigues Abilio, On the Philosophical Motivations for the Logics of Formal Consistency and Inconsistency.
    We present a philosophical motivation for the logics of formal inconsistency (LFIs), a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency (and inconsistency as well) 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 (...)
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  16. Patrizio Contu (2006). The Justification of the Logical Laws Revisited. 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 (...)
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  17. A. C. Cotter (1938). Logic and Epistemology. Boston, Mass.,The Stratford Company.
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  18. Cesare Cozzo (forthcoming). Inference and Compulsion. In E. Moriconi (ed.), Second Pisa Colloquium in Logic,Language and Epistemology. ETS.
    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.
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  19. Florian Demont (2008). Reconsidering the Epistemology of Deductive-Inferential Validity. Abstracta--Linguagem, Mente e Ação 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 (...)
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  20. Sinan Dogramaci (2010). Knowledge of Validity. 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 (...)
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  21. Philip A. Ebert (2005). Transmission of Warrant-Failure and the Notion of Epistemic Analyticity. Australasian Journal of Philosophy 83 (4):505 – 521.
    In this paper I will argue that Boghossian's explanation of how we can acquire a priori knowledge of logical principles through implicit definitions commits a transmission of warrant-failure. To this end, I will briefly outline Boghossian's account, followed by an explanation of what a transmission of warrant-failure consists in. I will also show that this charge is independent of the worry of rule-circularity which has been raised concerning the justification of logical principles and of which Boghossian is fully aware. My (...)
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  22. Danny Frederick (2011). Deduction and Novelty. The Reasoner 5 (4):56-57.
    It is often claimed that the conclusion of a deductively valid argument is contained in its premises. Popper refuted this claim when he showed that an empirical theory can be expected always to have logical consequences that transcend the current understanding of the theory. This implies that no formalisation of an empirical theory will enable the derivation of all its logical consequences. I call this result ‘Popper-incompleteness.’ This result appears to be consistent with the view of deductive reasoning as a (...)
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  23. James Gasser (1999). Logic and Metaphor. History and Philosophy of Logic 20 (3-4):227-238.
    In this work, attention is drawn to the abundant use of metaphor and analogy in works of logic. I argue that pervasiveness of figurative language is to be counted among the features that characterize logic and distinguish it from other sciences. This characteristic feature reflects the creativity that is inherent in logic and indeed has been demonstrated to be a necessary part of logic. The goal of this paper, in short, is to provide specific examples of figurative language used in (...)
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  24. Mikkel Gerken (2011). Conceptual Equivocation and Warrant by Reasoning. Australasian Journal of Philosophy 89 (3):381-400.
    In this paper, I challenge a widely presupposed principle in the epistemology of inference. The principle, (Validity Requirement), is this: S’s (purportedly deductive) reasoning, R, from warranted premise-beliefs provides (conditional) warrant for S’s belief in its conclusion only if R is valid. I argue against (Validity Requirement) from two prominent assumptions in the philosophy of mind: that the cognitive competencies that constitute reasoning are fallible, and that the attitudes operative in reasoning are anti-individualistically individuated. Indeed, my discussion will amount to (...)
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  25. Kathrin Glüer (2003). Analyticity and Implicit Definition. Grazer Philosophische Studien 66 (1):37-60.
    Paul Boghossian advocates a version of the analytic theory of a priori knowledge. His defense of an "epistemic" notion of analyticity is based on an implicit definition account ofthe meaning of the logical constants. Boghossian underestimates the power of the classical Quinean criticisms, however; the challenge to substantiate the distinction between empirical and non-empirical sentences, as forcefully presented in Two Dogmas, still stands, and the regress from Truth by Convention still needs to be avoided. Here, Quine also showed that there (...)
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  26. Ebba Gullberg & Sten Lindström, Semantics and the Justification of Deductive Inference. Hommage à Wlodek: Philosophical Papers Dedicated to Wlodek Rabinowicz.
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  27. Susan Haack (1982). Dummett's Justification of Deduction. Mind 91 (362):216-239.
  28. William H. Hanson (2003). Logic, the a Priori, and the Empirical. Theoria 18 (2):171-177.
    The time-honored view that logic is a non-empirical enterprise is still widely accepted, but it is not always recognized that there are (at least) two distinct ways in which this view can be made precise. One way focuses on the knowledge we can have of logical matters, the other on the nature of the logical consequence relation itself. More specifically; the first way embodies the claim that knowledge of whether the logical consequence relation holds in a particular case is knowledge (...)
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  29. Charles A. Hart (1931). Review of Logic and Epistemology and A Modern Introduction to Logic. New Scholasticism 5 (2):179-181.
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  30. Jaakko Hintikka (1973). Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. Oxford,Clarendon Press.
    I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...
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  31. Mark Jago (2012). The Content of Deduction. Journal of Philosophical Logic 42 (2):317-334.
    For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...)
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  32. Thomas Kroedel (2012). Implicit Definition and the Application of Logic. Philosophical Studies 158 (1):131-148.
    The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that fully (...)
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  33. Paul F. Linke (1926). The Present Status of Logic and Epistemology in Germany. The Monist 36 (2):222-255.
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  34. Conor Mayo-Wilson (2011). Russell on Logicism and Coherence. Journal of Bertrand Russell Studies 31 (1).
    According to Quine, Charles Parsons, Mark Steiner, and others, Russell's logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as a prioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell's explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent (...)
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  35. Susana Nuccetelli & Gary Seay (2012). Reasoning, Normativity, and Experimental Philosophy. American Philosophical Quarterly 49 (2):151 - 163.
    The development of modern science, as everybody knows, has come largely through naturalizing domains of inquiry that were historically parts of philosophy. Theories based on mere speculation about matters empirical, such as Aristotle‟s view about teleology in nature, were replaced with law-based, predictive explanatory theories that invoked empirical data as supporting evidence. Although philosophers have, by and large, applauded such developments, inquiry into normative domains presents a different set of problems, and there is no consensus about whether such an inquiry (...)
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  36. Jaroslav Peregrin, Logic and Reasoning.
    Logic, it is often held, is primarily concerned with reasoning; and the conviction that logic and reasoning are two sides of the same coin nowadays usually equates with the conviction that logic spells out some directives for the "right" management of beliefs. In this paper I put forward an alternative view, based on seeing rules of logic rules as constitutive rules, not instructing us how to reason, but rather providing us with certain vehicles or in terms of which to reason. (...)
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  37. Jaroslav Peregrin (2007). Logical Rules and the a Priori: Good and Bad Questions. In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic. 111--122.
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  38. Patrice Philie (2007). Carroll's Regress and the Epistemology of Logic. Philosophical Studies 134 (2):183 - 210.
    On an internalist account of logical inference, we are warranted in drawing conclusions from accepted premises on the basis of our knowledge of logical laws. Lewis Carroll’s regress challenges internalism by purporting to show that this kind of warrant cannot ground the move from premises to conclusion. Carroll’s regress vindicates a repudiation of internalism and leads to the espousal of a standpoint that regards our inferential practice as not being grounded on our knowledge of logical laws. Such a standpoint can (...)
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  39. Hilary Putnam (1968). Is Logic Empirical? Boston Studies in the Philosophy of Science 5.
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  40. Vladimir G. Red'ko (2000). Evolution of Cognition: Towards the Theory of Origin of Human Logic. [REVIEW] Foundations of Science 5 (3):323-338.
    The main problem discussed in this paper is: Why and how did animal cognition abilities arise? It is argued that investigations of the evolution of animal cognition abilities are very important from an epistemological point of view. A new direction for interdisciplinary researches – the creation and development of the theory of human logic origin – is proposed. The approaches to the origination of such a theory (mathematical models of ``intelligent invention'' of biological evolution, the cybernetic schemes of evolutionary progress (...)
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  41. Penelope Rush (ed.) (forthcoming). The Metaphysics of Logic: Logical Realism, Logical Anti-Realism and All Things In Between. Cambridge University Press.
  42. Gillian K. Russell (2013). Metaphysical Analyticity and the Epistemology of Logic. Philosophical Studies:1-15.
    Recent work on analyticity distinguishes two kinds, metaphysical and epistemic. This paper argues that the distinction allows for a new view in the philosophy of logic according to which the claims of logic are metaphysically analytic and have distinctive modal profiles, even though their epistemology is holist and in many ways rather Quinean. It is argued that such a view combines some of the more attractive aspects of the Carnapian and Quinean approaches to logic, whilst avoiding some famous problems.
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  43. Joshua Schechter (2013). Could Evolution Explain Our Reliability About Logic? In Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology 4. 214.
    We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection (or to a related mechanism). The central idea is that being able to (...)
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  44. Joshua Schechter (2010). The Reliability Challenge and the Epistemology of Logic. Philosophical Perspectives 24 (1):437-464.
    We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...)
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  45. Michael J. Shaffer (2013). Epistemic Paradox and the Logic of Acceptance. Journal of Experimental and Theoretical Artificial Intelligence 25:337-353.
    Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. (...)
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  46. Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
    The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...)
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  47. Manley Thompson (1981). On a Priori Truth. Journal of Philosophy 78 (8):458-482.
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  48. Clinton Tolley (2011). Frege's Elucidatory Holism. Inquiry 54 (3):226-251.
    Abstract I argue against the two most influential readings of Frege's methodology in the philosophy of logic. Dummett's ?semanticist? reading sees Frege as taking notions associated with semantical content?and in particular, the semantical notion of truth?as primitive and as intelligible independently of their connection to the activity of judgment, inference, and assertion. Against this, the ?pragmaticist? reading proposed by Brandom and Ricketts sees Frege as beginning instead from the independent and intuitive grasp that we allegedly have on the latter activity (...)
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  49. Lisa Warenski (2012). Erratum To: Naturalism, Fallibilism, and the a Priori. Philosophical Studies 159 (2):321-321.
    Erratum to: Naturalism, fallibilism, and the a priori Content Type Journal Article Category Erratum Pages 1-1 DOI 10.1007/s11098-012-9889-4 Authors Lisa Warenski, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.
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  50. Lisa Warenski (2009). Naturalism, Fallibilism, and the a Priori. Philosophical Studies 142 (3):403 - 426.
    This paper argues that a priori justification is, in principle, compatible with naturalism—if the a priori is understood in a way that is free of the inessential properties that, historically, have been associated with the concept. I argue that empirical indefeasibility is essential to the primary notion of the a priori; however, the indefeasibility requirement should be interpreted in such a way that we can be fallibilist about apriori-justified claims. This fallibilist notion of the a priori accords with the naturalist’s (...)
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