While the epistemic significance of disagreement has been a popular topic in epistemology for at least a decade, little attention has been paid to logical disagreement. This monograph is meant as a remedy. The text starts with an extensive literature review of the epistemology of (peer) disagreement and sets the stage for an epistemological study of logical disagreement. The guiding thread for the rest of the work is then three distinct readings of the ambiguous term ‘logical disagreement’. Chapters 1 and (...) 2 focus on the Ad Hoc Reading according to which logical disagreements occur when two subjects take incompatible doxastic attitudes toward a specific proposition in or about logic. Chapter 2 presents a new counterexample to the widely discussed Uniqueness Thesis. Chapters 3 and 4 focus on the Theory Choice Reading of ‘logical disagreement’. According to this interpretation, logical disagreements occur at the level of entire logical theories rather than individual entailment-claims. Chapter 4 concerns a key question from the philosophy of logic, viz., how we have epistemic justification for claims about logical consequence. In Chapters 5 and 6 we turn to the Akrasia Reading. On this reading, logical disagreements occur when there is a mismatch between the deductive strength of one’s background logic and the logical theory one prefers (officially). Chapter 6 introduces logical akrasia by analogy to epistemic akrasia and presents a novel dilemma. Chapter 7 revisits the epistemology of peer disagreement and argues that the epistemic significance of central principles from the literature are at best deflated in the context of logical disagreement. The chapter also develops a simple formal model of deep disagreement in Default Logic, relating this to our general discussion of logical disagreement. The monograph ends in an epilogue with some reflections on the potential epistemic significance of convergence in logical theorizing. (shrink)

When do two sentences say the same thing, that is, express the same content? We defend two-component (2C) semantics: the view that propositional contents comprise (at least) two irreducibly distinct constituents: (1) truth-conditions and (2) subject-matter. We contrast 2C with one-component (1C) semantics, focusing on the view that subject-matter is reducible to truth-conditions. We identify exponents of this view and argue in favor of 2C. An appendix proposes a general formal template for propositional 2C semantics.

Las máquinas aceleradas de Turing (ATMs) son dispositivos capaces de ejecutar súper-tareas. Sin embargo, el simple ejercicio de definirlas ha generado varias paradojas. En el presente artículo se definirán las nociones de súper-tarea y ATM de manera exhaustiva y se aclarará qué debe entenderse en un contexto lógico-formal cuando se pregunta por la existencia de un objeto. A partir de la distinción entre posibilidades lógicas y físicas se disolverán las paradojas y se concluirá que las ATMs son posibles y existen (...) como objetos abstractos. (shrink)

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collapsible schemes, in which (...) the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible. (shrink)

Christopher Hookway has been influential in promoting engagement with pragmatist and naturalist perspectives from classical and contemporary American philosophy. This book reflects on Hookway’s work on the American philosophical tradition and its significance for contemporary discussions of the understanding of mind, meaning, knowledge, and value. -/- Hookway’s original and extensive studies of Charles S. Peirce have made him among the most admired and frequently referenced of Peirce’s interpreters. His work on classical American pragmatism has explored the philosophies of William James, (...) John Dewey, and Josiah Royce, and examined the influence of pragmatist ideas outside of the United States. Additionally, Hookway has participated in a number of celebrated exchanges with some of the most high-profile figures of twentieth- and twenty-first-century philosophy, including Karl-Otto Apel, Philip Pettit, Hilary Putnam, and W.V.O. Quine, through which his treatments of a large range of topics in epistemology and the philosophies of mind and language have been developed and promoted. The chapters in this book—which include contributions from several of Hookway’s former students and colleagues—include studies of Hookway’s engagement with the works of Peirce, James, and Dewey, his contributions to virtue epistemology, and his discussions of hope and pragmatist metaphysics. -/- Pragmatic Reason will be of interest to researchers and advanced students working on American philosophy, the history of analytic philosophy, and epistemology. (shrink)

Der Sammelband umfasst Aufsätze zu den Grundfragen, Anwendungen und Grenzen des Unterrichts des Argumentierens, in allen Fächern und mit Fokus auf die Fächer Philosophie und Ethik. Dabei werden Fragen wie diese behandelt: Welchen Zielen dient das Argumentieren und welche verfolgt der Unterricht des Argumentierens? In welchem Verhältnis stehen diese zu anderen Zielen des Unterrichts? Welche Kenntnisse, Fähigkeiten und Tugenden des Argumentierens sollen eingeübt werden und wie? Die vorgeschlagenen Antworten sind nicht nur für Personen aus der Fachdidaktik, sondern auch aus der (...) Philosophie und der Schullehrpraxis aller Fächer interessant. Der Band trägt damit auch zur stärkeren Etablierung des Felds der Argumentationsdidaktik bei. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

In Truth and Objectivity, Crispin Wright argues that because truth is a distinctively normative property, it cannot be as metaphysically insubstantive as deflationists claim. We offer a reconstruction of Wright’s Inflationary Argument that highlights the steps required to establish its inflationary conclusion. We argue that if a certain metaphysical and epistemological view of a given subject matter is accepted, a local counterexample to the Inflationary Argument can be constructed. As a case study we focus on the domain of basic taste. (...) We develop two variants of a subjectivist and relativist metaphysics and epistemology that seem palatable in that domain and we show that the Inflationary Argument doesn’t go through in the domain of basic taste thus construed. We conclude by briefly discussing the significance of this result for the debate on alethic pluralism. (shrink)

Saul Kripke cuestionó el enfoque de la justificación de la lógica provisto por el modelo de Quine de la red de creencias sobre la base de un resultado que Romina Padró llamó “Problema de la adopción”. Sugiero una solución al problema de la adopción y una defensa de la estrategia quineana para la justificación de la lógica.

In this paper we intend to offer a first approach to the incorporation of certain formal tools in the elucidation of some issues discussed in epistemological contexts. The aim is not to offer an exhaustive resolution of these problems but merely to point out the usefulness of modal semantics when applied to different fields. Here we will show how a series of skeptical arguments eventually involve a modal (counterfactual) structure, which we will try to generalise into a useful scheme. -/- (...) . (shrink)

Surface presentism is the combination of a general relativistic physics with a presentist metaphysics. In this paper, we provide an argument against this combination based on black holes. The problem focuses on the notion of an event horizon. We argue that the present locations of event horizons are ontologically dependent on future black hole regions, and that this dependence is incompatible with presentism. We consider five responses to the problem available to the surface presentist, and argue that none succeed. Surface (...) presentism thus faces the prospect of refutation based on evidence that confirms the existence of black holes. (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)

Per il dialeteismo ci sono contraddizioni vere. Questa concezione filosofica ha assunto una forma chiara e definita a partire dal lavoro del filosofo e logico Graham Priest – uno dei suoi padri fondatori, nonché uno dei suoi più strenui difensori. Questo libro intende portare il dialeteismo all’attenzione di un ampio pubblico, che non sia solo quello degli addetti ai lavori. Il volume è suddiviso in due parti. La prima include le cinque lezioni su "Dialeteismo e storia della filosofia" tenute da (...) Priest e Filippo Casati a Padova nel 2016, in occasione del Corso di Eccellenza per il dottorato in filosofia dell’Università di Padova. La seconda contiene quattro contributi sul dialeteismo di autori italiani. (shrink)

Em sua obra, Robert Brandom apresenta uma teoria expressivista da lógica. Segundo o autor, a lógica tem o papel expressivo de tornar explı́citas as relações inferenciais implı́citas em nossas práticas linguı́sticas. Estas relações inferenciais conferem conteúdo aos conceitos. Neste artigo, exploraremos a tese de que o expressivismo lógico de Brandom é uma teoria antirrealista acerca da lógica. Realistas lógicos costumam defender a existência independente de fatos lógicos em relação a nossas práticas cognitivas e linguı́sticas, de modo que a lógica, uma (...) vez que seria capaz de representar estes fatos, descreveria verdadeiramente a estrutura da realidade. Por contraste, antirrealistas lógicos não se comprometem com a existência independente de fatos lógicos para entenderem a natureza da lógica. Em contraste com uma visão realista, mostramos que o antirrealismo de Brandom tem como consequências uma ontologia simples e econômica e a fundação de uma alternativa pragmatista para se examinar a normatividade da lógica, o fenômeno da pluralidade de lógicas rivais e a natureza de nossa racionalidade. (shrink)

What does it mean that some proposition follows from others? The standard way of spelling out the notion proceeds in modal terms: x follows from y iff necessarily, if y is true, so is x. But although this yields a useful and manageable account of consequence, it fails to capture certain aspects of our pre-theoretical understanding of consequence. In this paper, an alternative notion of logical consequence, based on the idea of grounding, is developed.

Entailment is an interesting sigmatoid: It should mean one thing, but it means another, just for starters. When used in Mathematics, it is usually with the sense of saying that something is definitely true. That would be the use in Classical Logic then. When used in Logic, it became something else. Now it was about how the logical system, which can be any nonclassical one, could be making a proposition become true or false. The major issue we found in 2000, (...) when learning from the own nonclassicists what they do, was that they talk about Nonclassical Logic, therefore a way of thinking that is not Cartesian, yet they stick to the notion of entailment we use in Mathematics, and therefore to the Classical Logic ways. We here discuss exactly this. (shrink)

We here propose a solution to the problem we have raised. Basically, the mathematical notion of entailment seems to be connected to the inferential rules from Classical Logic, so that if we have P: x belongs to the reals, and Q: x+2=5 => x=3, P |= Q. Notwithstanding, we would also have that if P: x belongs to the interval (7,10), and Q: x+2=5 => x=3, P |= Q. The second instance of entailment does not seem to be justifiable if (...) our intuition is consulted: Even though we could say that absurdity implies anything in Classical Logic, entailment should be a concept that belongs to the metalogic, not to the logic of the system, so that we should not be inside of the Classical Logic World by the time we assess things in what regards entailment. As another point, our discussions in Entailment led us to choose the sense has as a consequence for entailment, so that it is not really acceptable that we have, as a consequence, using normal language, of x being inside of the real interval (7,10) that if x+2=5, then x=3. If x is in that interval, x+2 should not be 5, unless we are talking about moduli of vectors. However, when we transfer to Classical Logic, in having the antecedent false, and the consequent false as well, we have that the implication, which some call material, is true. We here discuss this sort of matter in detail, and hope to get to the bottom of the issue, and perhaps to a universal solution. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

In this paper I present reasons for us to accept the hypothesis that suspended judgment has correctness conditions, just like beliefs do. Roughly put, the idea is that suspended judgment about p is correct when both p and ¬p might be true in view of certain facts that characterize the subject’s situation. The reasons to accept that hypothesis are broadly theoretical ones: it adds unifying power to our epistemological theories, it delivers good and conservative consequences, and it allows us to (...) assess processes of reasoning involving attitudes of suspended judgment. (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.

The paper tries to demonstrate the validity of Aristotle’s sea-battle argument, which is still considered as invalid by many authors. The first part presents the usual reconstruction of Aristotle’s argument and the reason for its rejection. It presents the late antique adoption of the argument as valid and strong by Ammonios and Boethius as well as its modern defence. In the second part, the elements that together assure the validity of the argument are combined and cast in the form of (...) two premisses, namely fact-correspondence and the unchangeability of facts. It is shown that these two presuppositions together assure the conclusion, i. e. the negation of bivalence for future contingents, and that they are explicitly stated in several of Aristotle’s texts and in Peri Hermeneias 9 in particular. (shrink)

The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any (...) propositional quantifiers. Then, I will show how these systems can be extended by a couple of propositional quantifiers. I will use a kind of TxW semantics to describe the systems semantically and semantic tableaux to describe them syntactically. Every system will include a constant · that stands for The Good. ‘·’ is read as ‘The Good is realised’. All systems that contain the propositional quantifiers will also include a constant '*' that stands for The Moral Law. '*' is read as ‘The Moral Law is fulfilled’. I will prove that all systems (without the propositional quantifiers) are sound and complete with respect to their semantics and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete. (shrink)

This thesis extends Kit Fine's truthmaker semantics for counterfactuals to indicative conditionals. First, I provide Fine's truthmaker semantics and his extension to counterfactuals. Then I introduce a notion of context state into the semantics and provide the verification-conditions for indicative conditionals by employing this notion of context state. Afterwards, I turn to the logic of indicative conditionals under exact semantics and discuss the principles and inference rules which raise disagreements between variably strict and strict conditionals accounts. The account I provide (...) shows its promise by validating a plausible combination of principles and strikes a balance between variably strict and strict conditional theories. I discuss certain principles in logic of indicative conditionals under exact semantics in detail and show how the present account validates the plausible combination of them. In the end, I draw comparisons between the viable theories for indicatives and the present one, and argue that the present account takes the advantage in several respects. (shrink)

In a recent paper, Pruss proves the validity of the rule beta-2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can (...) be formulated. This new transfer rule is immune to the counter-examples involving the actuality operator and rigidified descriptions. However, we show that counter-examples to this new rule can also be generated, demanding that the Lewisian semantics be generalized for higher dimensions where counter-examples can always be generated. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics. This paper offers a detailed assessment of this suggestion. I argue that an interesting version of logical pluralism is hard, if not impossible, to achieve. I first outline an intuitive understanding of the notions of rivalry and correctness. (...) I then discuss a natural account of rivalry in terms of disagreement about validity claims and the argument from meaning variance that has been raised against it. I explore a more refined picture of the meaning of validity claims that makes use of the character-content distinction of classical two dimensional semantics. There are three ways in which pluralists can use that framework to argue for the view that different logics may be rivals but could nevertheless be equally correct. I argue that none of them is convincing. (shrink)

In "Semantic paradoxes and abductive methodology", Williamson presents a new Quinean argument based on central ingredients of common pragmatism about theory choice (including logical theory, as is common). What makes it new is that, in addition to avoiding Quine's unfortunate charge of mere terminological squabble, Williamson's argument explicitly rejects at least for purposes of the argument Quine's key conservatism premise. In this paper I do two things. First, I argue that Williamson's new Quinean argument implicitly relies on Quine's conservatism principle. (...) Second, by way of answering his charges against nonclassical logic I directly defend a particular subclassical account of logical consequence. (shrink)

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (shrink)

There is a strong case to be made for thinking that an obscure logic, KR, is better than classical logic and better than any relevant logic. The argument for KR over relevant logics is that KR counts disjunctive syllogism valid, and this is the biggest complaint about relevant logics. The argument for KR over classical logic depends on the normativity of logic and the paradoxes of implication. The paradoxes of implication are taken by relevant logicians to justify relevant logic, but (...) considerations on the normativity of logic show that only some of the paradoxes of implication are genuine. KR avoids all the genuine paradoxes of implication, unlike classical logic. Overall, KR avoids the genuine paradoxes of implication and avoids the major objection to relevant logics. This combination of features provides strong reason to give KR a place in the conversation about the right logic. (shrink)

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.

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)

The aim of this text is show how Borges, in his story Tigres azules, develops several interesting ideas about logic, language and mathematics. The starting point is Borgesian skepticism about the ability of classical logic to take the problem of truth and impossible worlds. It is defended that inconsistent and even self-contradictory objects do not necessarily give rise to physically or logically impossible worlds. It is suggested that the paradoxes that Borges constructs in the story are not paradoxes of self-reference, (...) but variants of Moore’s paradox and paradoxes of material implication, so to overcome them requires a non-classical approach that neutralizes ECQ, this is, a paraconsistent logic system. (shrink)

In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The (...) systems in this paper can be used to symbolise not only the doxastic states of perfectly rational individuals, but also the beliefs of finite humans. Proof-theoretically, I will use a tableau technique. Every system is combined with predicate logic with necessary identity and ‘possibilist’ quantifiers and modal logic with two kinds of modal operators for relative and absolute necessity. The semantics is a possible world semantics. Finally, I prove that every tableau system in the paper is sound and complete with respect to its semantics. (shrink)

This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council, Grant Number 681404.

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it to (...) intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint. (shrink)

When we forgive, we do so for reasons. One challenge for forgiveness theorists is to explain which reasons are reasons to forgive and which are not. This paper argues that we forgive in response to a perceived change of heart on the part of the offender. The argument proceeds in four steps. First, I show that we forgive for reasons. Second, I argue that forgiveness requires the right kind of reason. Third, I show that these two points explain a common (...) distinction between forgiving and letting go and, in doing so, solve a problem facing many accounts of forgiveness. Finally, I consider candidate reasons to forgive and argue that all of them are either the wrong kind of reason or are instances of a more general reason of the right kind, namely, a perceived change of heart. (shrink)

Berkeley’s ‘master argument’ for idealism has been the subject of extensive criticism. Two of his strongest critics, A.N. Prior and J.L. Mackie, argue that due to various logical confusions on the part of Berkeley, the master argument fails to establish his idealist conclusion. Prior argues that Berkeley’s argument ‘proves too little’ in its conclusion, while Mackie contends that Berkeley confuses two different kinds of self-refutation in his argument. This paper proposes a defence of the master argument based on intuitionistic argument. (...) It begins by giving a brief exposition of the master argument and Prior's and Mackie's criticism. The following section explains why we might read the master argument along intuitionistic lines. The final section demonstrates that, according to intuitionistic logic, Berkeley's argument withstands the criticisms of Prior and Mackie. (shrink)

The Genuine Process Logic described here (abbreviation: GPL) places the object-bound process itself at the center of formalism. It should be suitable for everyday use, i.e. it is not primarily intended for the formalization of computer programs, but instead, as a counter-conception to the classical state logics. The new and central operator of the GPL is an action symbol replacing the classical state symbols, e.g. of equivalence or identity. The complete renunciation of object-language state expressions also results in a completely (...) new metalinguistic framework, both regarding the axioms and the expressive possibilities of this system. A mixture with state logical terms is readily possible. (shrink)

By a pure modal logic of names we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de re and which is an extension of Propositional Logic. For categorical sentences we use two interpretations: a “natural” one; and Johnson and Thomason’s interpretation, which is suitable for some reconstructions of Aristotelian modal syllogistic :271–284, 1989; Thomason in J Philos Logic 22:111–128, 1993 and J Philos Logic 26:129–141, 1997. In both (...) cases we use Johnson-like models. We also analyze different kinds of versions of PMLN, for both general and singular names. We present complete tableau systems for the different versions of PMLN. These systems enable us to present some decidability methods. It yields “strong decidability” in the following sense: for every inference starting with a finite set of premises we can specify a finite number of steps to check whether it is logically valid. This method gives the upper bound of the cardinality of models needed for the examination of the validity of a given inference. (shrink)

The object of this paper is to examine two approaches to giving non-vacuous truth conditions for counterpossibles, counterfactuals with impossible antecedents. I first develop modifications of a Lewis-style sphere semantics with impossible worlds. I argue that this approach sanctions intuitively invalid inferences and is supported by philosophically problematic foundations. I then develop modifications of certain ceteris paribus conditional logics with impossible worlds. Tableaux are given for each of these in an appendix and soundness and completeness results are proved. While certain (...) of the latter systems are shown to have similar problems to logics from the first approach, at least one relatively weak system appears to offer an adequate uniform semantics for counterpossibles and counterfactuals. (shrink)

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment.

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

In Paradoxa Stoicorum, the Roman philosopher Cicero defends six important Stoic theses. Since these theses seem counterintuitive, and it is not likely that the average person would agree with them, they were generally called "paradoxes". According to the third paradox, (P3), (all) transgressions (wrong actions) are equal and (all) right actions are equal. According to one interpretation of this principle, which I will call (P3′), it means that if it is forbidden that A and it is forbidden that B, then (...) not-A is as good as not-B; and if it is permitted that A and it is permitted that B, then A is as good as B. In this paper, I show how it is possible to prove this thesis in dyadic deontic logic. I also try to defend (P3′) against some philosophical counterarguments. Furthermore, I address the claim that (P3′) is not a correct interpretation of Cicero’s third paradox and the assertion that it does not matter whether (P3′) is true or not. I argue that it does matter whether (P3′) is true or not, but acknowledge that (P3′) is perhaps a slightly different principle than Cicero’s thesis. The upshot is that (P3′) seems to be a plausible principle, and that at least one part of paradox III in Cicero’s Paradoxa Stoicorum appears to be defensible. (shrink)

Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with respect to (...) twist structures over modal algebras. Sound and complete tableau calculi are presented as well. Moreover, a number of constructive non-modal logics with strong negation are faithfully embedded into BS4, into its three-valued extension B3S4, or into temporal BS4, BtS4. These logics include David Nelson's three-valued logic N3, the four-valued logic N4 bottom, the connexive logic C, and several extensions of bi-intuitionistic logic by strong negation. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (shrink)

Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios combined with Kleene’s strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three-valued logic, we will show how (...) an agent could solve the initial problem despite the fact that the sub-problems remain unsolved. Thus our model not only indicates missing information but also specifies the contexts in which the problem-solving process may end in success despite the lack of information. We will also show that this model of problem solving may find use in an analysis of natural language dialogues. (shrink)