The book offers a proposal on how to define truth in all its complexity, without reductionism, showing at the same time which questions a theory of truth has to answer and which questions, although related to truth, do not belong within the scope of such a theory. Just like any other theory, a theory of truth has its structure and limits. The semantic core of the position is that truth-ascriptions are pro-forms, i.e. natural language propositional variables. The book also offers (...) an explanation of the syntactic behaviour of truth-terms, and the pragmatic roles of truth-acts. The theory of truth we present is a technical proposal, relatively uncontaminated by radical philosophical discussion. It makes indeed philosophical points, but it is intended to be a conceptual analysis, as neutral as possible, of the aspects that may serve as a point of departure for more philosophically-laden destinations. Like the Fregean account of quantifiers, which is prior to and, to a large extent, independent of the metaphysical debate about existence and its forms, or the Kaplanian view on demonstratives, that is neutral regarding the debate about individuals and the possibilities we have to actually “reach” them in a referring act, we intend our proposal about truth to be a sophisticated and explicative setting that helps to situate other debates about truth accurately, far from the distorted and sometimes strongly ideological discussions that have turned the topic into a paradigm of philosophical impasse. (shrink)

It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can (...) talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched. (shrink)

A number of contemporary philosophers think that the unqualified statement “X is unspeakable” faces the danger of self-referential absurdity: if this statement is true, it must simultaneously be false, given that X is speakable by the predicate word “unspeakable.” This predicament is in this chapter formulated as an argument that I term the “ineffability paradox.” After examining the Buddhist semantic theory of apoha (exclusion) and an apoha solution to the issue, I resort to a few Chinese Buddhist and Hindu philosophical (...) materials to rationally reconstruct a strategy for resolving the paradox. By introducing the mode of expression termed “indication,” together with the relevant notions of superimposition and of gesturing beyond the horizon, I show that expressing the ineffable does not necessarily involve irresoluble contradiction. It is also suggested that philosophers may need to acknowledge the relevance of the notion of ineffability for contemporary philosophizing. (shrink)

The sciences occasionally generate discoveries that undermine their own assumptions. Two such discoveries are characterized here: the discovery of apophenia by cognitive psychology and the discovery that physical systems cannot be locally bounded within quantum theory. It is shown that such discoveries have a common structure and that this common structure is an instance of Priest’s well-known Inclosure Schema. This demonstrates that science itself is dialetheic: it generates limit paradoxes. How science proceeds despite this fact is briefly discussed, as is (...) the connection between our results and the realism-antirealism debate. We conclude by suggesting a position of epistemic modesty. (shrink)

A unified answer is offered to two distinct fundamental questions: whether a nonclassical solution to the semantic paradoxes should be extended to other apparently similar paradoxes and whether a nonclassical logic should be expressed in a nonclassical metalanguage. The paper starts by reviewing a budget of paradoxes involving the logical properties of validity, inconsistency, and compatibility. The author’s favored substructural approach to naive truth is then presented and it is explained how that approach can be extended in a very natural (...) way so as to solve a certain paradox of validity. However, three individually decisive reasons are later provided for thinking that no approach adopting a classical metalanguage can adequately account for all the features involved in the paradoxes of logical properties. Consequently, the paper undertakes the task to do better, and, building on the system already developed, introduces a theory in a nonclassical metalanguage that expresses an adequate logic of naive truth and of some naive logical properties. (shrink)

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.

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 (...) has also impressively improved. So I suggest that the discussion about the binomial dialectic/dialetheism should be reopened, on these new bases. (shrink)

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.

Apophaticism -- the view that God is both indescribable and inconceivable -- is one of the great medieval traditions of philosophical thought about God, but it is largely overlooked by analytic philosophers of religion. This paper attempts to rehabilitate apophaticism as a serious philosophical option. We provide a clear formulation of the position, examine what could appropriately be said and thought about God if apophaticism is true, and consider ways to address the charge that apophaticism is self-defeating. In so doing (...) we draw on recent work in the philosophy of language, touching on issues such as the nature of negation, category mistakes, fictionalism, and reductionism. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

It is commonly assumed that classical logic is the embodiment of a realist ontology. In “Sets and Semantics”, however, Jonathan Lear challenged this assumption in the particular case of set theory, arguing that even if one is a set-theoretic Platonist, due attention to a special feature of set theory leads to the conclusion that the correct logic for it is intuitionistic. The feature of set theory Lear appeals to is the open-endedness of the concept of set. This article advances reasons (...) internal to Lear’s account to show that his argument for intuitionistic set theory is unsuccessful. (shrink)

On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ?definability? (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ?definability?.1 1?Special thanks to (...) Francesco Orilia for criticisms of an early draft of this article. (shrink)

Imagine a sculptor who molds a lump of clay to create a statue. Hylomorphism claims that the statue and the lump of clay are two different colocated objects that have different forms, even though they share the same matter. Recently, there has been some discussion on the requirements of consistency for hylomorphist theories. In this paper, we focus on an argument presented by Maegan Fairchild, according to which a minimal version of hylomorphism is inconsistent. We argue that the argument is (...) unsound or, at best, it just points to a well-known problem for hylmorphist theories. Additionally, we explore some general consequences of this fact. (shrink)

A Curry paradox about truth is generated by the following sentence, written on the board in room 101:If the sentence on the board in room 101 is true then 1 ≠ 1.A Curry paradox about validity is generated by the following argument, written on the board in room 102:The argument on the board in room 102 is valid. Therefore, 1 ≠ 1.Though the sentence and the argument generate Curry paradoxes, they also generate more basic paradoxes, in a sense to be (...) made clear. I argue that if we solve these more basic paradoxes, we have solutions to both kinds of Curry paradox. The positive proposal is in part inspired by a brief remark of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concepts of truth and validity, for example, are everywhere applicable except for certain singular points or singularities. A second central claim is that 'true' and 'valid' are context-sensitive predicates. This contextual-singularity approach to the Curry paradoxes applies also to other paradoxes of truth, validity, denotation, and predicate-extension. So a more general aim of the paper is to provide a unified response to semantic paradox. (shrink)

The view that contradictions cannot be true has been part of accepted philosophical theory since at least the time of Aristotle. In this regard, it is almost unique in the history of philosophy. Only in the last forty years has the view been systematically challenged with the advent of dialetheism. Since Graham Priest introduced dialetheism as a solution to certain self-referential paradoxes, the possibility of true contradictions has been a live issue in the philosophy of logic. Yet, despite the arguments (...) advanced by dialetheists, many logicians and philosophers still hold the opinion that contradictions cannot be true. -/- Rather than advocating the truth of certain contradictions, this thesis offers a different challenge to the classical logician. By showing that it can be philosophically coherent to propose that true contradictions are metaphysically possible, the thesis suggests that the classical logician must do more than she currently has to justify her confidence in the impossibility of true contradictions. Simply fighting off the dialetheist’s putative examples of true contradictions at the actual world isn’t enough to justify the classical logician’s conclusion that true contradictions are impossible. -/- To aid the thesis dialectically, we introduce a new position, absolutism, which hypothesises that it’s metaphysically possible for at least one contradiction to be true, contrasting with the dialetheic hypothesis that some contradictions are true in the actual world. We demonstrate that absolutism can be given a philosophically coherent interpretation, an appropriate logic, and that certain criticisms are completely toothless against absolutism. The challenge put to the classical logician is then: On what logical or philosophical grounds can we rule out the metaphysical possibility of true contradictions? (shrink)

Kant's first antinomy uses a notion of infinity that is tied to the concept of (finitary) successive synthesis. It is commonly objected that (i) this notion is inadequate by modern mathematical standards, and that (ii) it is unable to establish the stark ontological assumption required for the thesis that an infinite series cannot exist. In this paper, I argue that Kant's notion of infinity is adequate for the set-up and the purpose of the antinomy. Regarding (i), I show that contrary (...) to appearance, the Critique can even accommodate a modern notion of infinity without consequences for the antinomy; and regarding (ii), that the ‘ontological’ consequence indeed follows once its covertly epistemic character is adequately understood. (shrink)

Philosophers of language and linguists need to be wary of generalizing from too small a sample of natural languages. They also need to be wary of neglecting possible insights from philosophical traditions that have focused on natural languages other than the most familiar Western ones. Take, for example, classical Indian philosophy, where philosophical concerns with language were very much involved with the early development of Sanskrit linguistics. Indian philosophers and linguists frequently discussed more general issues about semantics, often in ways (...) that are both similar to and interestingly different from Western philosophers.One such issue is the problem of sentential unity: what is the relation of our understanding of the meaning of a sentence to our understanding of the meaning of the words that compose it? If words have meanings, why is the meaning of a sentence not just the meaning of the words that compose it? A challenging Indian response is that of the grammarian and philosopher Bhartṛhari (fifth-century), who advocated for a kind of sentence-holism according to which words are unreal and sentence-meaning is primary. (shrink)

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 (...) that should be implied by an acceptance of the truth of the premises and the validity of the argument. (shrink)

The question of ontological foundation has undergone a noteworthy revival in recent years: metaphysicians today quarrel about how exactly to understand the asymmetrical and hyperintensional relationship of grounding. One of the reasons for this revival is that the old quantificationalist meta-ontology inherited from Quine has been effectively criticised by leading philosophers favourable to a meta-ontology, the aim of which is to come to know “which facts/items ground (constitute the base of) which other facts/items”, thus to examine the relation of ontological (...) dependence between beings (e.g. chemical properties depend on physical properties, the economic situation on the behaviour of individuals etc.), i.e. to explore the hierarchical structure of reality. I shall not discuss here the relationship of grounding in itself, but make some historical-formal remarks on the properties of the ultimate ontological foundational item itself and its aporetic nature. To do so I explore various more or less exotic philosophical ecosystems in the following order: Heidegger (Seyn), Plato (ἕν), Wáng Bi (道, dào). On the way I shall propose a new interpretation both of certain hypotheses in the Parmenides and of the nature of the opposition between Wáng Bì and Guō Xiàng in regard to the logical grammar of the expression “nothing (無, wú)” (transl. J. Dudley). (shrink)

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 (...) this paper, I explore the limits of what a relevant connective is, showing how some basic criteria motivated by the ideology of relevant logicians provide robust limits on potential connectives. These criteria provide some plausible necessary conditions on being a relevant connective. (shrink)

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 (...) result of this, I propose an alternative type of dialetheism which aims to resolve the paradox of an unknowable and ineffable God. I call this type of dialetheism, ‘mystical dialetheism’. (shrink)

Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)

The thesis that nothing is true has long been thought to be a self-refuting position not worthy of serious philosophical consideration. Recently, however, the thesis of alethic nihilism—that nothing is true—has been explicitly defended (notably by David Liggins). Nihilism is also, I argue, a consequence of other views about truth that have recently been advocated, such as fictionalism about truth and the inconsistency account. After offering an account of alethic nihilism, and how it purports to avoid the self-refutation problem, I (...) argue that it avoids the problem at the expense of changing the subject. I then present other arguments against nihilism and responses to the considerations offered in defense of it. The only tenable position is that something is indeed true. (shrink)

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 (...) that, when we make claims about those notations, we inevitably get saddled with bivalent commitments. I present several simple inferences to show this. The argument that results from those examples is ‘pragmatic’, because the inevitability of the principle is revealed in use (not mention); and it is ‘semiotic’, because this revelation happens in the use of signs. (shrink)

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 (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

In the paper two seemingly distinct areas of philosophical investigations are brought together: metaphor and dialetheism. They both turn out to be deeply related, which becomes visible against a background, i.e. the hybrid structure of metaphor delineated in the first part. This network elicits three variations of dissonance subsequently called: (1) phantom-contradiction, which is combined with unconventionality of metaphors; (2) indexed-bound contradiction, bearing some cognitive tension but no real truth value gluts and; (3) logical contradiction “spread” between the two layers (...) of metaphorical structure. Finally, the analysis allows for approaching a theoretically pending question concerning the influence of dialetheic aspects of metaphor upon human cognition and thinking in general. (shrink)

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 (...) all booksellers, including Barnes & Noble, Amazon, and brick-and-mortar bookstores under ISBN 978-0-578-88646-6. ●●●●● In light of the length of this book, readers who would like to have a more detailed description of the book's objectives and method may find it helpful to read the detailed and clearly written Wikipedia entry about this work: From the Wikipedia search page, use the search phrase "Critique of Impure Reason". At least at the time of this writing (11/29/2021), the Wikipedia entry is well-researched and accurate. ●●●●● In addition, a "Primer on Bartlett's CRITIQUE OF IMPURE REASON" has been made available by the author. It is available under its title through PhilPapers and other philosophy online archives. ●●●●● COMMENDATIONS OF THIS WORK, from the back cover of the published edition: ●●●●● “I admire its range of philosophical vision.” – Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh, author of more than 100 books. ●●●●● “Bartlett’s _Critique of Impure Reason_ is an impressive, bold, and ambitious work. Careful scholarship is balanced by original analyses that lead the reader to recognize the limits of meaning, knowledge, and conceptual possibility. The work addresses a host of traditional philosophical problems, among them the nature of space, time, causality, consciousness, the self, other minds, ontology, free will and determinism, and others. The book culminates in a fascinating and profound new understanding of relativity physics and quantum theory.” – Gerhard Preyer, Professor of Philosophy, Goethe-University, Frankfurt am Main, Germany, author of many books including _Concepts of Meaning_, _Beyond Semantics and Pragmatics_, _Intention and Practical Thought_, and _Contextualism in Philosophy_. ●●●●● “[This work’s] goal is of a unique and difficult species: Dr. Bartlett seeks to develop a formal logical calculus on the basis of transcendental philosophical arguments; in fact, he hopes that this calculus will be the formal expression of the transcendental foundation of knowledge.... I consider Dr. Bartlett’s work soundly conceived and executed with great skill.” – C. F. von Weizsäcker, philosopher and physicist, former Director, Max-Planck-Institute, Starnberg, Germany. ●●●●● “Bartlett has written an American “Prolegomena to All Future Metaphysics.” He aims rigorously to eliminate meaningless assertions, reach bedrock, and place philosophy on a firm foundation that will enable it, like science and mathematics, to produce lasting results that generations to come can build on. This is a great book, the fruit of a lifetime of research and reflection, and it deserves serious attention.” — Martin X. Moleski, former Professor, Canisius College, Buffalo, NY, studies of scientific method, the presuppositions of thought, and the self-referential nature of epistemology. ●●●●● “Bartlett has written a book on what might be called the underpinnings of philosophy. It has fascinating depth and breadth, and is all the more striking due to its unifying perspective based on the concepts of reference and self-reference.” – Don Perlis, Professor of Computer Science, University of Maryland, author of numerous publications on self-adjusting autonomous systems and philosophical issues concerning self-reference, mind, and consciousness. ●●●●● ●●●●● The _Critique of Impure Reason: Horizons of Possibility and Meaning_ comprises a major and important contribution to philosophy. Thanks to the generosity of its publisher, this massive 885-page volume has been published as a free open access eBook (3.75MB) as well as an open access printed edition. It inaugurates a revolutionary paradigm shift in philosophical thought by providing compelling and long-sought-for solutions to a wide range of philosophical problems. In the process, the work fundamentally transforms the way in which the concepts of reference, meaning, and possibility are understood. The book includes a Foreword by the celebrated German philosopher and physicist Carl Friedrich von Weizsäcker. ●●●●● In Kant’s _Critique of Pure Reason_ we find an analysis of the preconditions of experience and of knowledge. In contrast, but yet in parallel, the new _Critique_ focuses upon the ways—unfortunately very widespread and often unselfconsciously habitual—in which many of the concepts that we employ _conflict_ with the very preconditions of meaning and of knowledge. ●●●●● This is a book about the boundaries of frameworks and about the unrecognized conceptual confusions in which we become entangled when we attempt to transgress beyond the limits of the possible and meaningful. We tend either not to recognize or not to accept that we all-too-often attempt to trespass beyond the boundaries of the frameworks that make knowledge possible and the world meaningful. ●●●●● The _Critique of Impure Reason_ proposes a bold, ground-breaking, and startling thesis: that a great many of the major philosophical problems of the past can be solved through the recognition of a viciously deceptive form of thinking to which philosophers as well as non-philosophers commonly fall victim. For the first time, the book advances and justifies the criticism that a substantial number of the questions that have occupied philosophers fall into the category of “impure reason,” violating the very conditions of their possible meaningfulness. ●●●●● The purpose of the study is twofold: first, to enable us to recognize the boundaries of what is referentially forbidden—the limits beyond which reference becomes meaningless—and second, to avoid falling victims to a certain broad class of conceptual confusions that lie at the heart of many major philosophical problems. As a consequence, the boundaries of _possible meaning_ are determined. ●●●●● Bartlett, the author or editor of more than 20 books, is responsible for identifying this widespread and delusion-inducing variety of error, _metalogical projection_. It is a previously unrecognized and insidious form of erroneous thinking that undermines its own possibility of meaning. It comes about as a result of the pervasive human compulsion to seek to transcend the limits of possible reference and meaning. ●●●●● Based on original research and rigorous analysis combined with extensive scholarship, the _Critique of Impure Reason_ develops a self-validating method that makes it possible to recognize, correct, and eliminate this major and pervasive form of fallacious thinking. In so doing, the book provides at last provable and constructive solutions to a wide range of major philosophical problems. ●●●●● CONTENTS AT A GLANCE ▪▪▪▪▪ Preface ▪▪▪▪▪ Foreword by Carl Friedrich von Weizsäcker ▪▪▪▪▪ Acknowledgments ▪▪▪▪▪ Avant-propos: A philosopher’s rallying call ▪▪▪▪▪ Introduction ▪▪▪▪▪ A note to the reader ▪▪▪▪▪ A note on conventions ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART I ▪▪▪▪▪ ▪▪▪▪▪ WHY PHILOSOPHY HAS MADE NO PROGRESS AND HOW IT CAN ▪▪▪▪▪ 1 Philosophical-psychological prelude ▪▪▪▪▪ 2 Putting belief in its place: Its psychology and a needed polemic ▪▪▪▪▪ 3 Turning away from the linguistic turn: From theory of reference to metalogic of reference ▪▪▪▪▪ 4 The stepladder to maximum theoretical generality ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART II ▪▪▪▪▪ THE METALOGIC OF REFERENCE ▪▪▪▪▪ A New Approach to Deductive, Transcendental Philosophy ▪▪▪▪▪ 5 Reference, identity, and identification ▪▪▪▪▪ 6 Self-referential argument and the metalogic of reference ▪▪▪▪▪ 7 Possibility theory ▪▪▪▪▪ 8 Presupposition logic, reference, and identification ▪▪▪▪▪ 9 Transcendental argumentation and the metalogic of reference ▪▪▪▪▪ 10 Framework relativity ▪▪▪▪▪ 11 The metalogic of meaning ▪▪▪▪▪ 12 The problem of putative meaning and the logic of meaninglessness ▪▪▪▪▪ 13 Projection ▪▪▪▪▪ 14 Horizons ▪▪▪▪▪ 15 De-projection ▪▪▪▪▪ 16 Self-validation ▪▪▪▪▪ 17 Rationality: Rules of admissibility ▪▪▪▪▪ ▪▪▪▪▪ ▪▪▪▪▪ PART III ▪▪▪▪▪ PHILOSOPHICAL APPLICATIONS OF THE METALOGIC OF REFERENCE ▪▪▪▪▪ Major Problems and Questions of Philosophy and the Philosophy of Science ▪▪▪▪▪ 18 Ontology and the metalogic of reference ▪▪▪▪▪ 19 Discovery or invention in general problem-solving, mathematics, and physics ▪▪▪▪▪ 20 The conceptually unreachable: “The far side” ▪▪▪▪▪ 21 The projections of the external world, things-in-themselves, other minds, realism, and idealism ▪▪▪▪▪ 22 The projections of time, space, and space-time ▪▪▪▪▪ 23 The projections of causality, determinism, and free will ▪▪▪▪▪ 24 Projections of the self and of solipsism ▪▪▪▪▪ 25 Non-relational, agentless reference and referential fields ▪▪▪▪▪ 26 Relativity physics as seen through the lens of the metalogic of reference ▪▪▪▪▪ 27 Quantum theory as seen through the lens of the metalogic of reference ▪▪▪▪▪ 28 Epistemological lessons learned from and applicable to relativity physics and quantum theory ▪▪▪▪▪ ▪▪▪▪▪ PART IV ▪▪▪▪▪ HORIZONS ▪▪▪▪▪ 29 Beyond belief ▪▪▪▪▪ 30 _Critique of Impure Reason_: Its results in retrospect ▪▪▪▪▪ ▪▪▪▪▪ SUPPLEMENT ▪▪▪▪▪ The Formal Structure of the Metalogic of Reference ▪▪▪▪▪ APPENDIX I ▪▪▪▪▪ The Concept of Horizon in the Work of Other Philosophers ▪▪▪▪▪ APPENDIX II ▪▪▪▪▪ Epistemological Intelligence ▪▪▪▪▪ References ▪▪▪▪▪ Index ▪▪▪▪▪ About the author. 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Based on his Inclosure Schema and the Principle of Uniform Solution (PUS), Priest has argued that Curry’s paradox belongs to a different family of paradoxes than the Liar. Pleitz (2015, The Logica Yearbook 2014, pp. 233–248) argued that Curry’s paradox shares the same structure as the other paradoxes and proposed a scheme of which the Inclosure Schema is a particular case and he criticizes Priest’s position by pointing out that applying the PUS implies the use of a paraconsistent logic that (...) does not validate Contraction, but that this can hardly seen as uniform. In this paper, we will develop some further reasons to defend Pleitz’ thesis that Curry’s paradox belongs to the same family as the rest of the self-referential paradoxes & using the idea that conditionals are generalized negations. However, we will not follow Pleitz in considering doubtful that there is a uniform solution for the paradoxes in a paraconsistent spirit. We will argue that the paraconsistent strategies can be seen as special cases of the strategy of restricting Detachment and that the latter uniformly blocks all the connective-involving self-referential paradoxes, including Curry’s. (shrink)

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 (...) states of affairs come about. It is argued that there are no relevant differences between the liar and the signalman’s dilemma, implying that the glut and gap theorists are wrong about the former. A further point is that whether or not the liar is true/the signalman lights the fire, language/the signalman is misleading relative to the conditions under which the liar/the fire “ought” to be true/lit. (shrink)

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, (...) the implication being that the violation of the principle is necessary for such an accounting to take place. However, the ultimate argument here is that, contrary to Priest’s interpretation, Hegel’s philosophy can be convincingly read as supporting the idea that the mind’s ability to go beyond any particular limit of thought can actually be said to involve an adherence to a normative demand to locate and dispel the contradictions that emerge through the very setting of determinative limits. This is a non-formal consistency that evinces a “logic” that is unknowingly followed by the Heideggerian and Levinasian phenomenological philosophies of transcendence. (shrink)

_ The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi _, by PriestGraham. Oxford: Oxford University Press, 2018. Pp. 208.

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 (...) the moral nonnaturalist places herself in an invidious position if she simply accepts that the nonnatural moral facts that she posits are not explanatory. Instead, we offer the nonnaturalist an alternative strategy for dealing with moral explanations. The strategy is to retain the explanatory criterion of ontological commitment and maintain that moral properties are, in fact, explanatory. The explanations they provide are not causal explanations; instead, moral properties make a non-causal difference to the physical facts. (shrink)

According to Fogelin’s account of deep disagreements, disputes caused by a clash in framework propositions are necessarily rationally irresolvable. Fogelin’s thesis is a claim about real-life, and not purely hypothetical, arguments: there are such disagreements, and they are incapable of rational resolution. Surprisingly then, few attempts have been made to find such disputes in order to test Fogelin’s thesis. This paper aims to rectify that failure. Firstly, it clarifies Fogelin’s concept of deep disagreement and shows there are several different breeds (...) of such disagreements. Thus, to fully assess Fogelin’s thesis, it will be necessary to seek out cases of each breed to evaluate their rational irresolvability. Secondly, it begins this task by looking at a significant debate within the logical literature over the truth of contradictions. We demonstrate that, while the debate exemplifies a breed of deep disagreement, the parties involved can supply one another with rationally compelling reasons. (shrink)

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 (...) not have liked. The explanation is an obvious one but controversial, so it is defended against all the objections that can be mustered. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

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 (...) way representable. Rather, he holds that, as an exemplar for irony, Socrates cannot be represented in a purely disinterested way. I show how, in The Concept of Irony, Kierkegaard makes use of 'limiting cases' of representation in order to bring Socrates into view as one who defies purely disinterested representation. I also show how this approach to Socrates connects up with Kierkegaard's more general interest in the problem of ethical exemplarity, where the problem is how ethical exemplars can be given as such, that is, in such a way that purely disinterested contemplation is not the appropriate response to them. (shrink)

This essay offers an account of Kierkegaard’s view of the limits of thought and of what makes this view distinctive. With primary reference to Philosophical Fragments, and its putative representation of Christianity as unthinkable, I situate Kierkegaard’s engagement with the problem of the limits of thought, especially with respect to the views of Kant and Hegel. I argue that Kierkegaard builds in this regard on Hegel’s critique of Kant but that, against Hegel, he develops a radical distinction between two types (...) of thinking and inquiry: the ‘aesthetic-intellectual’ and the ‘ethico-religious’. I clarify this distinction and show how it guides Kierkegaard’s conception of a form of philosophical practice that involves drawing limits to the proper sphere of disinterested contemplation. With reference to two rival interpretations of Kierkegaard’s approach to the limits of thought—which I call ‘bullet-biting’ and ‘relativizing’—I further show how my ‘disambiguating’ account can better explain how, and why, his work courts a form of self-referential incoherence, in which it appears that certain limits of thought are at once affirmed and violated. (shrink)

In this paper I reassess Floridi's solution to the Bar-Hillel-Carnap paradox (the information-yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions), and that unless we accept the additional non-falsity thesis (information cannot be false) there is no reason to presuppose that there is no such thing (...) like contradictory information. (shrink)

The concept of Nothingness—Japanese mu or Chinese wú 無—is central both to the Kyoto School and to important strands of Chinese philosophy. The Kyoto School, which has been active since the 1930s, is arguably modern Japan’s most philosophically sophisticated challenge to Western thought. Further, as contemporary East Asia continues to rise in importance, East Asians and Westerners alike are beginning to consider anew the contemporary philosophical relevance of Confucianism, Daoism, and East-Asian Buddhism. These originally Chinese traditions were certainly important influences (...) directly and indirectly on Kyoto School philosophy itself. At the very least, Kyoto thought and Chinese thought share foundational structural resemblances, especially regarding the concept of Nothingness. This study summarizes the concept of Nothingness in the Kyoto School and in Chinese philosophy, and then offers an evaluation of the contemporary relevance and general coherence of this concept. (shrink)

I have two main objectives. The first is to get a better understanding of what is at issue between friends and foes of higher-order quantification, and of what it would mean to extend a Boolos-style treatment of second-order quantification to third- and higherorder quantification. The second objective is to argue that in the presence of absolutely general quantification, proper semantic theorizing is essentially unstable: it is impossible to provide a suitably general semantics for a given language in a language of (...) the same logical type. I claim that this leads to a trilemma: one must choose between giving up absolutely general quantification, settling for the view that adequate semantic theorizing about certain languages is essentially beyond our reach, and countenancing an open-ended hierarchy of languages of ever ascending logical type. I conclude by suggesting that the hierarchy may be the least unattractive of the options on the table. (shrink)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

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 (...) use his inventions to argue that the essentialist theory of counterfactual conditionals developed in Scientific Essentialism [Ellis 2001, hereafter SE ] is flawed. (shrink)

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 (...) rebut objections that Yablo's paradox is not a genuine liar by constructing a sequence of liars that blend into Yablo's paradox. I rebut objections that Yablo's liar has hidden self-reference with a distinction between attributive and referential self-reference and appeals to Gregory Chaitin's algorithmic information theory. The paper concludes with comments on the mystique of self-reference. (shrink)

The paper is concerned with the development of the paradoxical theme of Daoism. Based on Chad Hansen's interpretation of Daoism and Chinese philosophy in general, it traces the history of Daoism by following their treatment of the limit of language. The Daoists seem to have noticed that there is a limit to what language can do and that the limit of language is paradoxical. The 'theoretical' treatment of the paradox of the limit of language matures as Daoism develops. Yet the (...) Daoists seem to have noticed that the limit of language and its paradoxical nature cannot be overcome. At the end, we are left with the paradoxes of the Daoists. In this paper, we jump into the abyss of the Daoists' paradoxes from which there is no escape. But the Daoists' paradoxes are fun! (shrink)

We present a strategy to dissolve semantic paradoxes which proceeds from an explanation of why paradoxical sentences or their definitions are semantically defective. This explanation is compatible with the acceptability of impredicative definitions, self-referential sentences and semantically closed languages and leaves the status of the so-called truth-teller sentence unaffected. It is based on platitudes which encode innocuous constraints on successful definition and successful expression of propositional content. We show that the construction of liar paradoxes and of certain versions of Curry’s (...) paradox rests on presuppositions that violate these innocuous constraints. Other versions of Curry’s paradox are shown not to be paradoxical at all once their presuppositions are made explicit. Part of what we say rehearses a proposal originally made by Laurence Goldstein in 1985. Like Goldstein we dispose of certain paradoxes by rejecting some of the premises from which they must be taken to proceed. However, we disagree with his more recent view that the premises to be rejected are neither true nor false. (shrink)

Can a theory turn back, as it were, upon itselfand vouch for its own features? That is, canthe derived elements of a theory be the veryprimitive terms that provide thepresuppositions of the theory? This form of anall-embracing feature assumes a totality inwhich there occurs quantification over thattotality, quantification that is defined bythis very totality. I argue that the Machprinciple exhibits such a feature ofall-embracing nature. To clarify the argument,I distinguish between on the one handcompleteness and on the other wholeness andtotality, (...) as different all-embracing features:the former being epistemic while the latter –ontological.I propose an analogy between the Mach principleas a possible selection principle in generalrelativity, and the vicious-circle principle infoundations of mathematics. I finally concludewith a consequence of this analogyvis-à-vis completeness and totality,viz., both should be constrained if they wereto be valid concepts for a physical theory. (shrink)

The central thesis of JC Beall’s paraconsistent Christology is that Christ, being human and divine, is a contradictory being, and a rational Christology can accept it, since logic nowadays does not exclude the possibility of true contradictions. In this paper, I move from Beall’s theory and I present an alternative view. I quote seven statements of the so-called ‘Athanasian Creed’ which synthesizes the results of conciliar Christology. The aim of the Creed is to combat monophysitism by stressing the duplicity and (...) unity of Christ: two (incompatible) natures inseparably joined in only one person. I note that the two-in-one principle, so intended, may be seen as an ancestor of what has been called ‘conjunctive paraconsistency’, whereby there could be true contradictions but contradictories cannot be separately true. I specifically oppose this view to Beall’s idea of Christ’s human divinity (or divine humanity) as a glut, showing that in the conjunctive account, true contradictions do not require any overlapping or joint ascription of truth and falsity. (shrink)