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In this paper I respond to Jacquette’s criticisms, in (Jacquette, 2008), of my (Barker, 2008). In so doing, I argue that the Liar paradox is in fact a problem about the disquotational schema, and that nothing in Jacquette’s paper undermines this diagnosis. 

A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: nonparadoxical character of discourses, admissibility of arguments in argumentation (...) 



The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories meets the correspondence (...) 

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “formseries” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. / There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...) 

This is part two of a twopart paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truthpredicates and principles about the interaction of partial ground and truth. We show that our theory is (...) 

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I argue that the interaction between the multidimensional intensional framework and intensional plural quantification enables epistemic possibilities to target the haecceitistic properties of individuals. I outline the elements of plural logic, and I specify, then, a multidimensional intensional formula encoding the relation between the epistemic possibility of haecceity comprehension and its metaphysical possibility. I conclude by addressing objections from the indeterminacy (...) 

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I (...) 

We show how removing faithbased beliefs in current philosophies of classical and constructive mathematics admits formal, evidencebased, definitions of constructive mathematics; of a constructively welldefined logic of a formal mathematical language; and of a constructively welldefined model of such a language. / We argue that, from an evidencebased perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. / We then adopt what may (...) 



In this paper I consider two paradoxes that arise in connection with the concept of demonstrability, or absolute provability. I assume—for the sake of the argument—that there is an intuitive notion of demonstrability, which should not be conflated with the concept of formal deducibility in a (formal) system or the relativized concept of provability from certain axioms. Demonstrability is an epistemic concept: the rough idea is that a sentence is demonstrable if it is provable from knowable basic (“selfevident”) premises by (...) 

This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possibleworlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) 

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is noncircular. Just like that, Priest (1997) has argued that such formalization (...) 

Having, as it is generally agreed, failed to destroy the computational conception of mind with the G\"{o}delian attack he articulated in his {\em The Emperor's New Mind}, Penrose has returned, armed with a more elaborate and more fastidious G\"{o}delian case, expressed in and 3 of his {\em Shadows of the Mind}. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is (...) 

This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology. Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there (...) 

There are two paradoxes of satisfaction, and they are of different kinds. The classic satisfaction paradox is a version of Grelling’s: does ‘does not satisfy itself’ satisfy itself? The Unsatisfied paradox finds a predicate, P, such that Px if and only if x does not satisfy that predicate: paradox results for any x. The two are intuitively different as their predicates have different paradoxical extensions. Analysis reduces each paradoxical argument to differing rule sets, wherein their respective pathologies lie. Having different (...) 

Many philosophers recognize that, as a matter of psychological fact, one can believe something valuable without valuing it. I argue that it is also possible to value something without believing it valuable. Agents can genuinely value things that they neither believe disvaluable nor believe valuable along a scale of impersonal value. 



The Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will (...) 

The goal of this paper is to present Yabloesque versions of Grelling’s and Zwicker’s paradoxes concerning the notions of “heterological” and “hypergame” respectively. We will offer counterparts of these paradoxes that do not seem to involve selfreference or vicious circularity.El objetivo de este artículo es ofrecer versiones de las paradojas de Grelling y de Zwicker inspiradas en la paradoja de Yablo. Nuestras versiones de estas paradojas no parecen involucrar ni autorreferencia ni circularidad viciosa. 



To borrow a colorful phrase from Kant, this dissertation offers a prolegomenon to any future semantic theory. The dissertation investigates Yablo's omegaliar paradox and draws the following consequence. Any semantic theory that accepts the existence of semantic objects must face Yablo's paradox. The dissertation endeavors to position Yablo's omegaliar in a role analogous to that which Russell's paradox has for the foundations of mathematics. Russell's paradox showed that if we wed mathematics to sets, then because of the many different possible (...) 

It seems that the Truthteller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truthteller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...) 

I will argue that Roy Cook’s (forthcoming) reformulation of Yablo’s Paradox in the infinitary system D is a genuinely noncircular paradox, but for different reasons than the ones he sustained. In fact, the first part of the job will be to show that his argument regarding the absence of fixed points in the construction is insufficient to prove the noncircularity of it; at much it proves its nonself referentiality. The second is to reconsider the structural collapse approach Cook rejects, and (...) 

We investigate the properties of Yablo sentences and for mulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered. 

Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally classified (...) 

The semantic paradoxes are often associated with selfreference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...) 

Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glutbased approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, this (...) 

Ebbhinghaus, H., J. Flum, and W. Thomas. 1984. Mathematical Logic. New York, NY: SpringerVerlag. Forster, T. Typescript. The significance of Yablo’s paradox without selfreference. Available from http://www.dpmms.cam.ac.uk. Gold, M. 1965. Limiting recursion. Journal of Symbolic Logic 30: 28–47. Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam. 





We prove Yablo’s paradox without the diagonal lemma or the recursion theorem. Only a disquotation schema and axioms for a serial and transitive ordering are used in the proof. The consequences for the discussion on whether Yablo’s paradox is circular or involves selfreference are evaluated. 













I use the principle of truthmaker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the Tschema's validity, or obvious (...) 



I present a problem for a prominent kind of conservatism, viz., the combination of traditional moral & religious values, patriotic nationalism, and libertarian capitalism. The problem is that these elements sometimes conflict. In particular, I show how libertarian capitalism and patriotic nationalism conflict via a scenario in which the thing that libertarian capitalists love – unregulated market activity – threatens what American patriots love – a strong, independent America. Unrestricted libertarian rights to buy and sell land would permit the sale (...) 

The Liar paradox is the directly selfreferential Liar statement: This statement is false.or : " Λ: ∼ T 1" The argument that proceeds from the Liar statement and the relevant instance of the Tschema: " T ↔ Λ" to a contradiction is familiar. In recent years, a number of variations on the Liar paradox have arisen in the literature on semantic paradox. The two that will concern us here are the Curry paradox, 2 and the Yablo paradox. 3The Curry paradox (...) 

Two periods in the history of logic and philosophy are characterized notably by vivid interest in selfreferential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...) 

The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...) 



The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless stepbystep determination processes can be used to provoke antinomies, more concretely, to make our logical and our ontological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a stepbystep determination process. As a consequence, the paradoxical nature of beginningless stepbystep determination processes concerns time and causality as usually (...) 

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The aim of this paper is to provide a minimalist axiomatic theory of truth based on the notion of reference. To do this, we first give sound and arithmetically simple notions of reference, selfreference, and wellfoundedness for the language of firstorder arithmetic extended with a truth predicate; a task that has been so far elusive in the literature. Then, we use the new notions to restrict the Tschema to sentences that exhibit "safe" reference patterns, confirming the widely accepted but never (...) 

This paper gives a definition of selfreference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about selfreference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...) 