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This paper discusses a novel response to two closely related regress arguments from Bolzano’s Theory of Science and Carroll’s What the Tortoise Said to Achilles. Bolzano’s argument aims to refute the thesis that full grounds must include propositions involving notions such as entailment, grounding or lawhood which link the respective grounds to their groundee. This thesis is motivated, Bolzano’s argument is reconstructed, and a response based on self-referential linking propositions is developed and defended against objections concerning self-reference and Curry’s paradox. Finally, the idea is applied to a reading of Carroll’s dialogue and a corresponding solution to the so-called infinite regress problem of inference is proposed. [ABSTRACT FROM AUTHOR]

Justified belief is a core concept in epistemology and there has been an increasing interest in its logic over the last years. While many logical investigations consider justified belief as an operator, in this paper, we propose a logic for justified belief in which the relevant notion is treated as a predicate instead. Although this gives rise to the possibility of liar-like paradoxes, a predicate treatment allows for a rich and highly expressive framework, which lives up to the universal ambitions of investigating epistemological concepts. We start with a base theory for justified belief, and then systematically present putative additional axioms for justified belief. We provide an overview of (in)consistency results when the additional principles are added to the base theory, and discuss their philosophical plausibility. [ABSTRACT FROM AUTHOR]

I argue that there are living and everyday case in which rationality requires you, as a non-idealized human thinker, to have inconsistent beliefs while recognizing the inconsistency. I defend my argument against classical and insightful objections by Doris Olin, as well as others. I consider three versions of the preface paradox as candidate cases, including Makinson's original version. None is free from objection. However, there is a fourth version, Modesty, that supposes that you believe that at least one of your beliefs (excluding this) is false. I argue that this version escapes all the objections that could trouble the other versions, including the objection that given certain closure principles for justified belief, justified inconsistent beliefs saddle you with a pair of justified beliefs that are in explicit contradiction (their contents being syntactic negations). I also argue more tentatively for the same verdict for Modesty*, a version that supposes that you believe that at least one of your beliefs (including this) is false. In that case, your belief guarantees that its content is true, in which case your beliefs are inconsistent, because at least one of them must be false. Once you think you're wrong, you must be right! Crucial to my argument is a distinction between explicitly contradictory beliefs and three forms of inconsistency in belief. In the first of these, you believe contingent propositions each of which is logically independent of the others, yet you also believe the syntactic negation of their conjunction. In the second, your beliefs are inconsistent because of the rigid designation of demonstratives such as 'this' embedded in their contents. In the third, as in Modesty and Modesty* your beliefs are inconsistent because of self-reference. [ABSTRACT FROM AUTHOR]

It has been argued recently (Beall in Spandrels of truth, Oxford University Press, Oxford, 2009; Beall and Murzi J Philos 110:143–165, 2013) that dialetheist theories are unable to express the concept of naive validity. In this paper, we will show that LP can be non-trivially expanded with a naive validity predicate. The resulting theory, LP Val reaches this goal by adopting a weak self-referential procedure. We show that LP Val is sound and complete with respect to the three-sided sequent calculus SLP Val . Moreover, LP Val can be safely expanded with a transparent truth predicate. We will also present an alternative theory LP Val ∗ , which includes a non-deterministic validity predicate. [ABSTRACT FROM AUTHOR]

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (J Philos Logic 34(2):155–192, 2005), and the dependence digraph by Beringer and Schindler (Reference graphs and semantic paradox, 2015. https://www.academia.edu/19234872/Reference%5fGraphs%5fand%5fSemantic%5fParadox). Unlike the usual discussion about self-reference 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 that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (Logic J IGPL 22(1):24–38, 2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its ∀ ∃ -unwinding variant are non-self-referential, and neither McGee's paradox nor the ω -cycle liar has circularity dependence. [ABSTRACT FROM AUTHOR]

Graham Priest (Analysis 57:236-242, 1997) has argued that Yablo’s paradox (Analysis 53:251-252, 1993) involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve satisfaction conditions that are not recursively specifiable, and hence not recognizable in the sense required for Priest’s argument. In this paper I provide a general recipe for constructing infinitely many (in fact, continuum-many) such noncircular Yabloesque paradoxes, and conclude by drawing some more general lessons regarding our ability to identify conditions that are necessary and sufficient for paradoxically more generally. [ABSTRACT FROM AUTHOR]

I discuss an aspect of the relation between accounts of de se thought and the phenomenon of immunity to error through misidentification. I will argue that a deflationary account of the latter—the Simple Account, due to Evans (The varieties of reference, 1982)—will not do; a more robust one based on an account of de se thoughts is required. I will then sketch such an alternative account, based on a more general view on singular thoughts, and show how it can deal with the problems I raise for the Simple Account. [ABSTRACT FROM AUTHOR]

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones. [ABSTRACT FROM AUTHOR]