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Switch to: References
Citations of:
Beyond the Limits of Thought
British Journal for the Philosophy of Science 47 (2):331-334 (1996)
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What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) |
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PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...) |
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This article is an inquiry into how the relationship between the principle of non-contradiction and the limits of thought has been understood by thinkers as diverse as Hegel, Heidegger, Levinas, and Graham Priest. While Heidegger and Levinas focus on the question of temporality and Priest takes a formal approach, all these philosophers effectively maintain that the principle of non-contradiction imposes a restriction on thought that disables it from adequately accounting for its own limits and thus what lies beyond those limits, (...) |
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Ultralogic as Universal? is a seminal text in non-classcial logic. Richard Routley presents a hugely ambitious program: to use an 'ultramodal' logic as a universal key, which opens, if rightly operated, all locks. It provides a canon for reasoning in every situation, including illogical, inconsistent and paradoxical ones, realized or not, possible or not. A universal logic, Routley argues, enables us to go where no other logic—especially not classical logic—can. Routley provides an expansive and singular vision of how a universal (...) |
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It has seemed, to many, that there is an important connection between the ways in which some theoretical posits explain our observations, and our reasons for being ontologically committed to those posits. One way to spell out this connection is in terms of what has become known as the explanatory criterion of ontological commitment. This is, roughly, the view that we ought to posit only those entities that are indispensable to our best explanations. Our primary aim is to argue that (...) |
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Tim travels back in time and tries to kill his grandfather before his father was born. Tim fails. But why? Lewis's response was to cite "coincidences": Tim is the unlucky subject of gun jammings, banana peels, sudden changes of heart, and so on. A number of challenges have been raised against Lewis's response. The latest of these focuses on explanation. This paper diagnoses the source of this new disgruntlement and offers an alternative explanation for Tim's failure, one that Lewis would (...) |
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According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty (...) |
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This essay re-examines Kierkegaard's view of Socrates. I consider the problem that arises from Kierkegaard's appeal to Socrates as an exemplar for irony. The problem is that he also appears to think that, as an exemplar for irony, Socrates cannot be represented. And part of the problem is the paradox of self-reference that immediately arises from trying to represent x as unrepresentable. On the solution I propose, Kierkegaard does not hold that, as an exemplar for irony, Socrates is in no (...) |
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Chinese Chan or Zen Buddhism is renowned for its improvisational, atypical, and perplexing use of words. In particular, the tradition’s encounter dialogues, which took place between Chan masters and their interlocutors, abound in puzzling, astonishing, and paradoxical ways of speaking. In this chapter, we are concerned with Chan’s use of paradoxical language. In philosophical parlance, a linguistic paradox comprises the confluence of opposite or incongruent concepts in a way that runs counter to our common sense and ordinary rational thinking. One (...) |
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This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions ), including classical logic as a particular case. In \, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then (...) |
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In Saving Truth from Paradox, Hartry Field presents and defends a theory of truth with a new conditional. In this paper, I present two criticisms of this theory, one concerning its assessments of validity and one concerning its treatment of truth-preservation claims. One way of adjusting the theory adequately responds to the truth-preservation criticism, at the cost of making the validity criticism worse. I show that in a restricted setting, Field has a way to respond to the validity criticism. I (...) |
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The Analytic Tradition in Philosophy is an excellent successor to an excellent book : It is a fine an example of the necromantic style in the history of philosophy where the object of the exercise is to resurrect the mighty dead in order to get into an argument with them, either because we think them importantly right or instructively wrong. However what was a pardonable a simplification and a reasonable omission in the earlier book has now metamorphosed into a sin (...) |
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For logicians and metaphysicians curious about the evolution of Russell's logic from The Principles of Mathematics to Principia Mathematica, no volume of the Collected Papers of Bertr... |
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The state of affairs of some things falling under a predicate is supposedly a single entity that collects these things as its constituents. But whether we think of a state of affairs as a fact, a proposition or a possibility, problems will arise if we adopt a plural logic. For plural logic says that any plurality include themselves, so whenever there are some things, the state of affairs of their plural self-inclusion should be a single thing that collects them all. (...) |
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In this article, I consider the possibility of interpreting Hegel’s dialectic as dialetheism. After a first basic recapitulation about the meaning of the words ‘dialetheism’ and ‘dialectic’ and a consideration of Priest’s own account of the relation between dialectical and dialetheic logic in 1989, I discuss some controversial issues, not directly considered by Priest. As a matter of fact, the reflection on paraconsistent logics and dialetheism has enormously grown in recent years. In addition, the reception of Hegel’s logic and metaphysics (...) |
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This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...) |
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True contradictions are taken increasingly seriously by philosophers and logicians. Yet, the belief that contradictions are always false remains deeply intuitive. This paper confronts this belief head-on by explaining in detail how one specific contradiction is true. The contradiction in question derives from Priest's reworking of Berkeley's argument for idealism. However, technical aspects of the explanation offered here differ considerably from Priest's derivation. The explanation uses novel formal and epistemological tools to guide the reader through a valid argument with, not (...) |
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This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other enigmas of the genre. I (...) |
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My discussion addresses the differences between analytic and continental philosophy concerning the use of logic and exact reasoning in philosophical practice. These differences are mainly examined in the light of the controversial dominance of Hegel's concept of logic in twentieth-century continental philosophy. The inquiry is developed in two parts. In the first, I indicate some aspects of the analytic -continental divide, pointing to the role that the topic 'logic and philosophy' plays in it. In the second part, I give a (...) |
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Online philosophy seminar notes, for virtual conference on the Aristotelian philosophy of mathematics, hosted by University of Geneva (organiser Ryan Miller), June 15, 2023. |
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This paper argues that the traditional characterization of the notion of paradox — an apparently valid argument with apparently true premises and an apparently false conclusion — is too narrow; there are paradoxes that do not satisfy it. After discussing, and discarding, some alternatives, an outline of a new characterization of the notion of paradox is presented. A paradox is found to be an apparently valid argument such that, apparently, it does not present the kind of commitment to the conclusion (...) |
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There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...) |
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This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) |
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This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields — mostly philosophy, mathematics and computer science — and with different backgrounds — from undergraduate students to senior researchers. (...) |
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Buddhist schools of thought share two fundamental assumptions about language. On the one hand, language is identified with conceptual thinking, which according to the Buddhist doctrine separates us from the momentary and fleeting nature of reality. Language is comprised of generally applicable forms, which fuel the reificatory proclivity for clinging to the distorted – and ultimately fictious – belief in substantial existence. On the other hand, the distrust of language is mitigated by the doctrine of ineffability, which although asserts that (...) |
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Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue (...) |
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This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) |
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Although idealism was widely defended in the history of philosophy, it is nowadays almost universally considered a non-starter. This holds in particular for a strong form of idealism, which asserts that not just minds or the mental in general, but our human minds in particular are metaphysically central to reality. Such a view seems to be excessively anthropocentric and contrary to what we by now know about our place in the universe. Nonetheless, there is reason to think that such a (...) |
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In this paper, I introduce and defend a notion of analyticity for formal languages. I first uncover a crucial flaw in Timothy Williamson’s famous argument template against analyticity, when it is applied to sentences of formal mathematical languages. Williamson’s argument targets the popular idea that a necessary condition for analyticity is that whoever understands an analytic sentence assents to it. Williamson argues that for any given candidate analytic sentence, there can be people who understand that sentence and yet who fail (...) |
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Many science teachers are presented with the challenge of characterizing science as a dynamic, human endeavour. Perspectivism, as a hermeneutic philosophy of science, has the potential to be a learning tool for teachers as they elucidate the complex nature of science. Developed earlier by Nietzsche and others, perspectivism has recently re-emerged in the context of the philosophy of science in the work of Ronald Giere. Giere presents a compelling case that scientific theories and scientific observation are perspectival by using science (...) |
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Lately, philosophers of mathematics have been exploring the notion of mathematical explanation within mathematics. This project is supposed to be analogous to the search for the correct analysis of scientific explanation. I argue here that given the way philosophers have been using “ explanation,” the term is not applicable to mathematics as it is in science. |
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This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate about mathematical objects. |
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For Sengzhao (374−414 CE), a leading Sanlun philosopher of Chinese Buddhism, things in the world are ontologically indeterminate in that they are devoid of any determinate form or nature. In his view, we should understand and use words provisionally, so that they are not taken to connote the determinacy of their referents. To echo the notion of ontic indeterminacy and indicate the provisionality of language, his main work, the Zhaolun, abounds in paradoxical expressions. In this essay, I offer a philosophical (...) |
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Religious believers react in one of four ways to apparent contradictions among their beliefs: Redirection, Resistance, Restraint, or Resolution. This paper evaluates positive mysterian Resistance, the view that believers may rationally believe and know apparently contradictory religious doctrines. After locating this theory by comparing and contrasting it with others, I explore the best developed version of it, that of James Anderson’s Paradox in Christian Theology. I argue that it faces steep epistemic problems, and is at best a temporarily reasonable but (...) |
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For scientific essentialists, the only logical possibilities of existence are the real (or metaphysical) ones, and such possibilities, they say, are relative to worlds. They are not a priori, and they cannot just be invented. Rather, they are discoverable only by the a posteriori methods of science. There are, however, many philosophers who think that real possibilities are knowable a priori, or that they can just be invented. Marc Lange [Lange 2004] thinks that they can be invented, and tries to (...) |
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Over the past 25 years, Graham Priest has ably presented and defended dialetheism, the view that certain sentences are properly characterized as true with true negations. Our goal here is neither to quibble with the tenability of true, assertable contradictions nor, really, with the arguments for dialetheism. Rather, we wish to address the dialetheist's treatment of cases of semantic pathology and to pose a worry for dialetheism that has not been adequately considered. The problem that we present seems to have (...) |
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Dialetheism is the view that some contradictions are true. Resorting to either metaphysical dialetheism or semantic dialetheism may seem like an appropriate resolve to certain theological contradictions. At least for those who concede to theological contradictions, and take dialetheism seriously. However, I demonstrate that neither of these types of dialetheism would serve to be amenable in resolving an Islamic theological contradiction. This is a theological contradiction that I refer to as ‘the paradox of an unknowable and ineffable God’. As a (...) |
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Radical glut and gap theorists deny—in opposite ways—that the liar sentence has exactly one of the two values true and not true. I describe a scenario where a signalman finds himself in a situation analogous to the liar paradox: if he lights a fire at a certain time, that is analogous to the liar being true, and if he does not, that is analogous to the liar not being true. It is obvious that he must make exactly one of those (...) |
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At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution of (...) |
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ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines. |
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_ The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi _, by PriestGraham. Oxford: Oxford University Press, 2018. Pp. 208. |
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Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the non-explanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...) |
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The authors consider a recurring objection to fictional realism, the view that fictional characters are objects. The authors call this the counting objection. Russell presses a version of the objection against Meinong’s view. Everett presses a version of the objection against contemporary fictional realist views, as do Nolan and Sandgren. As the authors see it, the objection assumes that the fictional realist must provide criteria of identity for fictional characters, so its force depends on the plausibility of that assumption. Rather (...) |
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Restrictionism is a response to the Liar and other paradoxes concerning truth. Restrictionists—as I will call proponents of the strategy—respond to these paradoxes by giving up instances of the schema -/- <p> is true iff p. -/- My aim is to show that the current unpopularity of restrictionism is undeserved. I will argue that, whilst cautious versions of the strategy may face serious problems, a radical and previously overlooked version of restrictionism provides a strong and defensible response to the paradoxes. |
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The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds. |
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Graham Priest 2002 argues that all logical paradoxes that include set-theoretic paradoxes and semantic paradoxes share a common structure, the Inclosure Schema, so they should be treated as one family. Through a discussion of Berry's Paradox and the semantic notion ?definable?, I argue that (i) the Inclosure Schema is not fine-grained enough to capture the essential features of semantic paradoxes, and (ii) the traditional separation of the two groups of logical paradoxes should be retained. |
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