Theodore Sider’s puzzle in Hell and Vagueness has generated some interesting responses in the past few years. In this paper, I explore yet another possible solution out of the conundrum. This solution implies three ways of denying a binary conception of the afterlife. I argue that while these solutions might first seem tenable, they might still succumb to a Sideresque revenge puzzle.

In ‘Currying omnipotence: A reply to Beall and Cotnoir’, Andrew Tedder and Guillermo Badia argue that Jc Beall and A. J. Cotnoir’s gappy solution to the traditional paradox of unrestricted omnipotence does not extend to a Curry-like version of the paradox. In this paper, we show that it does extend to it.

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

This paper surveys important work done in relevant logic in the past 10 years.

After some generalities about connections between functions and relations in Sections 1 and 2 recalls the possibility of taking the semantic values of ‐ary Boolean connectives as ‐ary relations among truth‐values rather than as ‐ary truth functions. Section 3, the bulk of the paper, looks at correlates of these truth‐value relations as applied to formulas, and explores in a preliminary way how their properties are related to the properties of “logical relations” among formulas such as equivalence, implication (entailment) and contrariety (...) (logical incompatibility), concentrating for illustrative purposes on binary logical relations such as those just listed. To avoid an excess of footnotes, some points have been deferred to an Appendix as “Longer Notes”. (shrink)

The unwinding that Cook, 767–774 2004) proposed is a simple but powerful method of generating new paradoxes from known ones. This paper extends Cook’s unwinding to a larger class of paradoxes and studies further the basic properties of the unwinding. The unwinding we study is a procedure, by which when inputting a Boolean modal net together with a definable digraph, we get a set of sentences in which we have a ‘counterpart’ for each sentence of the Boolean modal net and (...) each point of the digraph. What is more, whenever a sentence of the Boolean modal net says another sentence is necessary, then the counterpart of the first sentence at a point correspondingly says the counterparts of the second one at all accessible points of that point are all true. The output of the procedure is called ‘the unwinding of a Boolean modal net on a definable digraph’. We prove that the unwinding procedure preserves paradoxicality: a Boolean modal net is paradoxical on a definable digraph, iff the unwinding of it on this digraph is also paradoxical. Besides, the dependence digraph for the unwinding of a Boolean modal net on a definable digraph is proved to be isomorphic to the unwinding of the dependence digraph for the Boolean modal net on the previous definable digraph. So the unwinding of a Boolean modal net on a digraph is self-referential, iff the Boolean modal net is self-referential and the digraph is cyclic. Thus, on the one hand, the unwinding of any Boolean modal net on an acyclic digraph is non-self-referential. In particular, the unwinding of any Boolean modal net on \ is non-self-referential. On the other hand, if a Boolean modal net is paradoxical on a locally finite digraph, the unwinding of it on that digraph must be self-referential. Hence, starting from a Boolean modal paradox, the unwinding can output a non-self-referential paradox only if the digraph is not locally finite. (shrink)

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive (...) argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic. (shrink)

Many medieval philosophers and logicians regarded modal logic as a model for epistemic, normative and optative concepts on the basis of their apparent similarities to modal concepts. These interpretations of modal logic led to critical studies of the applicability of modal principles to deontic concepts. Some philosophers presented apparent counterexamples to the deontic interpretation of the Consequence Principle, according to which the consequences of what is obligatory (or permitted) are also obligatory (permitted). These examples are variants of Lennart Åqvist's paradox (...) of the Good Samaritan. In this article it is argued that the examples involve a confusion between the compounded and the divided senses of deontic propositions, and are not genuine counterexamples to the Consequence Principle. If the concept of knowledge is analysed as epistemically satisfactory belief, the paradox of epistemic obligation can be solved in a similar way. (shrink)

There is a widely extended viewpoint about physical possibility, what we will call Standard Approach, which holds that the physically possible is delimited by the nomological structure of physical theories: to be physically possible is to be in accordance with the physical laws, to be physically impossible is to be prohibited by physical laws and to be physically necessary is to be demanded by the physical laws. However, it is possible to show that this approach is too relaxed and permissive (...) when it comes to collecting and systematizing many of the modal intuitions present in the physical community. In this work we will argue, on the one hand, that the notion of physical possibility is more complex and richer than suggested by the standard approach and, on the other hand, that it is necessary to add some extra elements to the characterization of physical possibility in order to that it is adequate in scientific contexts. (shrink)

Meta-ethical realism faces the serious epistemological problem of how to explain our epistemic access to moral reality. In the face of this challenge many are sceptical about non-naturalist realism. Nonetheless, there is good reason to acknowledge moral objectivity: morality shows all the signs of a truth-apt discourse but doesn’t exhibit the typical relativity inducing features. This suggests a middle-ground position, a theory that embraces the virtues of realism but does avoid its vices: objectivist antirealism. In this paper, I’ll discuss, mainly (...) following Crispin Wright’s account of moral truth as superassertibility, a promising version of objectivist antirealism and show how to cope with notorious problems, notably those arising from the thought that moral disagreement might be possible in which nobody is guilty of a cognitive shortcoming, which contradicts the antirealist claim that moral truth is not beyond our epistemic reach. The solution is to deny the possibility of cognitively faultless moral disagreement by arguing that cognitively blameless thinkers either agree or stay agnostic and, therefore, never disagree about any moral proposition. Since assuming an agnostic stance on the part of such thinkers contradicts the antirealist’s conception of truth—even within the limits of intuitionistic logic—I’ll propose an alternative logical revision for the moral discourse: a three-valued logic with epistemically construed truth-values. (shrink)

Meta-ethical realism faces the serious epistemological problem of how to explain our epistemic access to moral reality. In the face of this challenge many are sceptical about non-naturalist realism. Nonetheless, there is good reason to acknowledge moral objectivity: morality shows all the signs of a truth-apt discourse but doesn’t exhibit the typical relativity inducing features. This suggests a middle-ground position, a theory that embraces the virtues of realism but does avoid its vices: objectivist antirealism. In this paper, I’ll discuss, mainly (...) following Crispin Wright’s account of moral truth as superassertibility, a promising version of objectivist antirealism and show how to cope with notorious problems, notably those arising from the thought that moral disagreement might be possible in which nobody is guilty of a cognitive shortcoming, which contradicts the antirealist claim that moral truth is not beyond our epistemic reach. The solution is to deny the possibility of cognitively faultless moral disagreement by arguing that cognitively blameless thinkers either agree or stay agnostic and, therefore, never disagree about any moral proposition. Since assuming an agnostic stance on the part of such thinkers contradicts the antirealist’s conception of truth—even within the limits of intuitionistic logic—I’ll propose an alternative logical revision for the moral discourse: a three-valued logic with epistemically construed truth-values. (shrink)

Classical logic is based on an underlying view of the world, according to which there are elementary facts and compound facts, which are logical combinations of these elementary facts. Sentences are true if they correspond to, in last instance, the elementary facts in the world. This world view has no place for rules, which exist as individuals in the world, and which create relations between the most elementary facts. As a result, classical logic is not suitable to deal with rules, (...) and is therefore unsuitable to deal with legal reasoning. A logic that is more suitable should take into account that law is a part of social reality, in particular a part that consists of constructivist facts, and that rules play a central role in law. This article gives a superficial description of how social reality exists and of the place of law and legal rules in it. It uses this description to argue that traditional techniques to reason with and about legal rules provide a better logic for law than classical logic. These techniques can be accommodated in a logic that treats rules as logical individuals. (shrink)

Jaina philosophy provides a very distinctive account of logic, based on the theory of ?sevenfold predication?. This paper provides a modern formalisation of the logic, using the techniques of many-valued and modal logic. The formalisation is applied, in turn, to some of the more problematic aspects of Jaina philosophy, especially its relativism.

In this paper we deal with a classical question of western philosophy: Is it possible to know that there are things which do not exist? We begin with a brief analysis of some fragments of Parmenides, and later we study whether these arguments are valid using three kinds of epistemic logic: a classical style epistemic logic, where axiom holds, a free epistemic logic, where this axiom does not hold, and finally, we study Lenzen's proposal of using two kinds of quantifiers: (...) possibilistic and realistic quantifiers. We conclude that the last last one is the closest to our intuition and a good way to deal with this kind of problem. (shrink)

In this paper, I respond to what I have called an epistemological objection to a dialetheist approach to the doctrine of the Incarnation, of which one example is Beall’s contradictory Christ. I discuss Anderson’s book Paradox in Christian theology, in which the author claims to account for the rationality of the doctrine of the Incarnation as a merely apparently contradictory doctrine, and I present my model, based on Anderson’s model, according to which the doctrine has the possibility to be rational (...) by understanding it as genuinely contradictory. I show that this model fits perfectly well with the criteria that, according to Anderson, any model for the rationality of a paradoxical doctrine should meet. Beall does not address the problem of the rationality of the doctrine in his works about the contradictory Christ, and he asserts that he is not interested in it. However, I think that if he wants to make his theory more robust, less suspicious, and more convincing for theologians, philosophers, and ordinary people, he should consider this problem. (shrink)

The semantics for counterfactuals due to David Lewis has been challenged by appealing to miracles. Miracles may skew a given similarity order in favour of those possible worlds which exhibit them. Lewis responded with a system of priorities that mitigates the significance of miracles when constructing similarity relations. We propose a prioritised ceteris paribus analysis of counterfactuals inspired by Lewis’ system of priorities. By analysing the couterfactuals with a ceteris paribus clause one forces out, in a natural manner, those possible (...) worlds which do not satisfy the requirements of the clause, thus excluding miracles. If no world can satisfy the ceteris paribus clause in its entirety, then prioritisation is triggered to select worlds that maximise agreement on those things which are favoured most. (shrink)

The idea of relevant logic—that irrelevant inferences are invalid—is appealing. But the standard semantics for relevant logics involve baroque metaphysics: a three-place accessibility relation, a star operator, and ‘bad’ worlds. In this article we propose that these oddities express a mismatch between non-classical object theory and classical metatheory. A uniformly relevant semantics for relevant logic is a better fit.

Priest argued in Fusion and Confusion (Priest in Topoi 34(1):55–61, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of (...) consequence. Unlike the latter, however, Priest’s consequence relation does not satisfy a variant of the variable sharing property. This paper shows that how it can be modified so as to do so. Priest’s consequence relation turns out to be surprisingly weak in some respects. The prospects of strengthening it is raised and discussed in a broader philosophical context. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

What does it take for two logics to be mere notational variants? The present paper proposes a variety of different ways of cashing out notational variance, in particular isolating a constraint on any reasonable account of notational variance which makes plausible that the only kinds of translations which can witness notational variance are what are sometimes called definitional translations.

We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...) LEM is intrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

This contributed volume includes both theoretical research on philosophical logic and its applications in artificial intelligence, mostly employing the concepts and techniques of modal logic. It collects selected papers presented at the Second Asia Workshop on Philosophical Logic, held in Guangzhou, China in 2014, as well as a number of invited papers by specialists in related fields. The contributions represent pioneering philosophical logic research in Asia.

In this dissertation I provide a novel logic of the ordinary-language conditional. First, however, I endeavor to make clearer and more precise just what the objects of the study of the conditional are, as a lack of clarity as to what counts as an instance of a given category of conditional has resulted in deep and significant confusions in subsequent analysis. I motivate for a factual/counterfactual distinction, though not at the level of particular instances of the conditional. Instead, I argue (...) that each individual instance of the conditional may be interpreted either factually or counterfactually, rather than these instances dividing into distinct types. I examine the classic Oswald–Kennedy pair of sentences, typically taken to be the quintessential example of how conditionals must be split into two different categories, to show that they in fact do not demonstrate this. I then present my account of the logic underlying the ordinary-language conditional, the system C3, and a justification of the form it takes. This logic provides distinct interpretations of the conditional as it concerns what is factual or what is counterfactual, respectively. The factual interpretation is true when both antecedent and consequent are true at the actual world, false when the antecedent is true and consequent false, and not truth-apt otherwise. The counterfactual interpretation incorporates a ceteris paribus clause, ensuring that it is not falsified by extraordinary, unforeseeable occurrences, and is true when, at all worlds at which the antecedent is ceteris paribus true, the consequent too is true. It is false when, at any of these worlds the consequent is false; and not truth-apt otherwise. I go on to examine alternative theories of the conditional—from the suppositionalist approach to evaluating the putative indicative conditional, to Stalnaker’s combined indicative and counterfactual account, and Lewis’s analysis of the counterfactual; among a number of others—and offer comparison to my own theory. Finally, I look at various challenges to my account of the conditional. Being a strict conditional (albeit variably so), that of C3 is open to the objection that it fails to match ordinary speakers’ intuitions as regards its truth-value assignments to, for instance, conditionals with necessarily true consequents. I address these so- called paradoxes of the strict conditional, and also discussion the question of truth-preservation in the C3 system in the case of such inferences as those relying on transitivity and that of modus ponens. I maintain that these inferences are indeed truth-preserving under certain, specifiable, conditions, and I close by offering possible avenues for further research. (shrink)

Is there only one logic? Or are there several equally adequate logics? What does it mean, after all, that different logics can be equally adequate? And they would be adequate with respect to what?This article intends to analyze the different answers to these questions, that is, we will evaluate the central arguments of the debate between pluralism, relativism and logical monism. We will explain,on the one hand, the main assumptions of this discussion and, on the other hand, its philosophical ramifications. (...) We will end by indica-ting the development of a possible logical pluralism using the notion of paraconsistentization of logics, which will be explained afterward.We do not intend to refute, once and for all, logical monism. We will show that the main arguments put forward by a monist against logical pluralism are unsound and therefore the existence of some form of logical pluralism remains possible. (shrink)

Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we (...) propose a very general and powerful framework based on quantifier-free predicate language extended by a new modality, which packs exactly ∃x◻ together. We show that the resulting language, though much more expressive, shares many good properties of the basic propositional modal logic over arbitrary models, such as finite-tree-model property and van Benthem-like characterization w.r.t.\ first-order modal logic. We axiomatize the logic over S5 frames with intuitive axioms to capture the interaction between the new modality and know-that operator in an epistemic setting. (shrink)

This paper presents the first compositional semantics for if then conditionals. The semantics of each element are first examined separately. The meaning of if is modeled according to a possible worlds semantics. The particle then is analyzed as an anaphoric word that places its focused element inside the context settled by a previous element. Their meanings are subsequently combined in order to provide a formal semantics of if A then C conditionals, which differs from the simple if A, C form. (...) This semantics has the particularity of validating contraposition for the first type but invalidating it for the second type. Finally, a detailed examination of the sentences presented in the literature opposing this schema of reasoning shows that these counterexamples do not generally concern if then conditionals but, rather, even if conditionals and that contraposition is therefore a valid means of reasoning with regard to if then conditionals in natural language, as this system predicts. (shrink)

This paper presents the first possible world semantics for concessive conditionals (i.e., even if A, C conditionals) constructed in a compositional way. First, the meaning of if is formalized through a semantics that builds on the proposal given by Stalnaker (1968). A major difference from Stalnaker’s approach is that irrelevant conditionals (i.e., conditionals where the antecedent and the consequent have no connection) are false in this new setting. Second, the meaning of even is analyzed through a formal semantics based on (...) the notion of scale. This analysis overcomes the problems arising in standard approaches, in which even is analyzed with the help of pragmatic presuppositions. Finally, the two particles are combined in order to provide a formal analysis of even if. This theory predicts the major phenomena concerning the behavior of concessive conditionals and without any call to pragmatic explanations. More generally, this approach creates the possibility of a compositional analysis of other conditionals such as if then or only if forms. (shrink)

This article defends the principle of sufficient reason (PSR) from a simple and direct valid argument according to which PSR implies that there is a truth that explains every truth, namely an omni-explainer. Many proponents of PSR may be willing to bite the bullet and maintain that, if PSR is true, then there is an omni-explainer. I object to this strategy by defending the principle that explanation is irreflexive. Then I argue that proponents of PSR can resist the conclusion that (...) there is an omni-explainer by denying that explanation distributes over conjunction. In the final section, I consider a plausible revision of this assumption. I argue there that, given the revised assumption, PSR seems to yield a striking picture of the explanatory structure of the universe. I explain why the resulting model does not appear utterly implausible to me. (shrink)

In [5], Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract “core” of logics in general, where logical syntax and semantics are “two sides of the same coin”. The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic. (...) However, the reduction to bivaluation may be a side effect of the architecture of ordinary sequents, which is both overly restrictive, and entails certain expressive restrictions over the language. This paper provides an expansion of Béziau’s completeness results for logics, by showing that there is a natural extension of that line of thinking to n-sided sequent constructions. Through analogical techniques to Béziau’s construction, it is possible, in this setting, to construct abstract soundness and completeness results for n-valued logics. (shrink)

In this paper, we deal with the problem of putting together modal worlds that operate in different logic systems. When evaluating a modal sentence $\Box \varphi $, we argue that it is not sufficient to inspect the truth of $\varphi $ in accessed worlds (possibly in different logics). Instead, ways of transferring more subtle semantic information between logical systems must be established. Thus, we will introduce modal structures that accommodate communication between logic systems by fixing a common lattice $L$ that (...) contains as sublattices the semantics operating in each world. The value of a formula $\Box \varphi $ in a world with lattice $L^{\prime}$ will be defined in terms of the values of $\varphi $ in accessible worlds relativized to $L^{\prime}$ using the common order of $L$. We will investigate natural instances where formulas $\varphi $ can be said to be necessary/possible even though all the accessible world falsify $\varphi $. Further, we will discuss frames that characterize dynamic relations between logic systems: classically increasing, classically decreasing and dialectic frames. Finally, we formalize the semantics of considering worlds operating in classical logic or logic of paradox, exemplifying the kind of issue one should face in this kind of formalization. (shrink)

forall x: Dortmund is an adaptation and German translation of forall x: Calgary. As such, it is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity, the syntax of truth-functional (propositional) logic and truth-table semantics, the syntax of first-order (predicate) logic with identity and first-order interpretations, formalizing German in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as the (...) syntax and (Kripke-)semantics of modal logic. The book is provided in PDF and in LaTeX source code. A booklet with solutions for the exercises in the book is available. (shrink)

There is a phenomenon that often arises when a philosophy argues that there are limits to thought/language, and tries to justify this view by giving reasons as to why there are things about which one cannot think/talk---in the process appearing to give the lie to the claim. I will be concerned with that phenomenon. We will look at some of philosophies that fall into this camp (those of Wittgenstein, Heidegger, and Mahayana Buddhism). We will then see that Buddhist philosophy has (...) resources to address this kind of issue not present in Western traditions, namely the catuskoti and its developments. The catuskoti is a principle to the effect that claims can be true, false, both, or neither. Later developments add a fifth possibility: ineffability. Of course, one might be skeptical that such ideas can be made logically respectable. I will show how to do so with some simple tools from contemporary non-classical logic. (shrink)

Our beliefs utilize various sources: perception, memory, induction, etc. We trust these sources to provide reliable information about the world around us. My dissertation investigates how this trust could be justified. Chapter one introduces background material. I argue that justification rather than knowledge is of primary epistemological importance, discuss the internalism/externalism debate, and introduce an evidentialist thesis that provides a starting point/framework for epistemological theorizing. Chapter two introduces a puzzle concerning justification. Can a belief source provide justification absent prior justification (...) for believing it's reliable? Any answer appears to either make justifying the reliability of a source intellectually unsatisfying or all together impossible. Chapter three considers and rejects a plethora of proposed solutions to our puzzle. Investigating these solutions illustrates the need to further investigate evidence, evidence possession, and evidential support. Chapter four discusses the metaphysics of evidence. I argue that evidence always consists of a set of facts and that fact-proposition pairs stand in confirmation relations isomorphic to those holding between pairs of propositions. Chapter five argues that justification requires what I call actually connected possession of supporting evidence: a subject must be aware of supporting evidence and of the support relation itself. Chapter six argues that the relation constitutive of a set of facts being justificatory evidence is a sui generis and irreducible relation that is knowable a priori. Chapter seven begins by showing how Richard Fumerton's acquaintance theory meets the constraints on a theory of justification laid down in previous chapters. I modify the theory so as to: make room for fallible foundational justification, and allow inferential justification absent higher-order beliefs about evidential connections. Chapter eight applies the developed theory of justification to our initial puzzle. I show how my modified acquaintance theory is in a unique position to vindicate the idea that necessarily a source provides a person with justification only if she is aware of evidence for the reliability of that source. However, this awareness of evidence for a source's reliability falls short of a justified belief and thereby avoids impalement from our dilemma's skeptical horn. (shrink)

Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".

This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truth-predicate to motivate an intermediate speech-act. On this approach, a liar-like sentence should be “weakly asserted”, involving a commitment to the sentence (...) and its negation, without rejecting the sentence. From this, I develop a proof-theory, which both determines a typical paraconsistent model theory, and also gives us a nice way to understand classical recapture. (shrink)

It has been argued that alethic pluralists -- who hold that there are several distinct truth properties -- face a problem when it comes to defining validity. Via consideration of the classical concept of logical consequence, and of strategies for defining validity in many-valued logics, this paper proposes two new kinds of solution to the problem.

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...) the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne. (shrink)

In his second period of logical research, which includes several books and treatises, Athir al-Din al-Abhari is the only Avicennan logician who vindicated as invalid one of the two most important Avicennan novelties: iqtirani conditional syllogism. His exposition and reasons for this invalidity in these books and treatises are various and rooted in numerous kinds of conditionals and their truth-conditions and their developments in the books and treatises. His most important reason to deny conditional syllogism is notice to the manifold (...) assumptions used to prove the syllogisms. In this paper, we deal with the main reason, studying the mentioned differences and developments. Citing successor logicians’ points of views on Abhari’s claim and assessment of all of them is out of the purposes of this paper and in need to other researches. (shrink)

Dialetheic accounts of the liar paradox hold that liar sentences are both true and false. One problem that besets accounts of the liar paradox is that of “revenge liars”. A revenge liar is a liar sentence which, while being of the same kind as the liar sentences an account attempts to handle, cannot be handled in the same way they are without generating contradictions that the account in question is powerless to resolve. It might be thought that dialetheic accounts are (...) immune to revenge problems: If one can intelligibly hold that standard liars are both true and false, why not revenge liars as well? However, in this paper it is argued that dialetheism faces a dilemma: Either it cannot express the distinction between those sentences which are both true and false and those which are not, or else it too suffers from revenge problems. I explore a few different ways in which a dialetheist might try to avoid this dilemma. First, I present a variant of the logic called LP, and show both that it is subject to revenge problems and that it is not well suited to a dialetheic interpretation. Second, I develop a means of expressing the exclusive truth or falsity of sentences which can be utilized by any language that has certain features. Unfortunately, it leads straight to trivialism. Finally, I examine the claim that dialetheists can express the exclusive truth or falsity of sentences in the same way a non-dialetheist can, and conclude that they cannot do so. In the end, it seems that dialetheism’s dilemma is inescapable. (shrink)