En este artículo discutimos la tesis de Jc Beall según la cual no hay negación lógica. Evaluamos la solidez del argumento con el que defiende su tesis y presentamos dos razones para rechazar una de sus premisas: que la negación tiene que ser excluyente o exhaustiva. La primera razón involucra una presentación alternativa de las reglas de la negación en sistemas de secuentes diferentes al que Beall presupone. La segunda razón establece que la negación no tiene que ser excluyente o (...) exhaustiva. (shrink)

Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...) which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...) is to respond to Field’s objections and to point to a coherent notion of validity which underwrites a coherent reading of Beall and Murzi’s principles: grounded validity. The notion, first introduced by Nicolai and Rossi, is a generalisation of Kripke’s notion of grounded truth, and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic, we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches. (shrink)

Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.

We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in such a (...) language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438–445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one’s theory a shrieking rule of the form A & ~A |- \bot, where \bot entails triviality. We argue, however, that the proposal doesn’t work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists—an extension of the logic commonly called LP. (shrink)

A principle of continuity due to Leibniz has recently been revived by Graham Priest in arguing for an inconsistent account of motion. This paper argues that the Leibniz Continuity Condition has a reasonable interpretation in a different, though still inconsistent, class of dynamical systems. The account is then applied to the quantum mechanical description of the hydrogen atom.

Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...) “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

Priest and others have presented their “most telling” argument for paraconsistent logic: that only paraconsistent logics allow non-trivial inconsistent theories. This is a very prevalent argument; occurring as it does in the work of many relevant and more generally paraconsistent logicians. However this argument can be shown to be unsuccessful. There is a crucial ambiguity in the notion of non-triviality. Disambiguated the most telling reason for paraconsistent logics is either question-begging or mistaken. This highlights an important confusion about the role (...) of logic in our development of our theories of the world. Does logic chart good reasoning or our commitments? We also consider another abductive argument for paraconsistent logics which also is shown to fail. (shrink)

My purpose in this paper is to argue that the classical notion of entailment is not suitable for non-bivalent logics, to propose an appropriate alternative and to suggest a generalized entailment notion suitable to bivalent and non-bivalent logics alike. In classical two valued logic, one can not infer a false statement from one that is not false, any more than one can infer from a true statement a statement that is not true. In classical logic in fact preserving truth and (...) preserving non-falsity are one and the same thing. They are not the same in non-bivalent logics however and I will argue that the classical notion of entailment that preserves only truth is not strong enough for such a logic. I will show that if we retain the classical notion of entailment in a logic that has three values, true, false and a third value in between, an inconsistency can be derived that can be resolved only by measures that seriously disable the logic. I will show this for a logic designed to allow for semantic presuppositions, then I will show that we get the same result in any three valued logic with the same value ordering. I will finally suggest how the notion of entailment should be generalized so that this problem may be avoided. The strengthened notion of entailment I am proposing is a conservative extension of the classical notion that preserves not only truth but the order of all values in a logic, so that the value of an entailed statement must alway be at least as great as the value of the sequence of statements entailing it. A notion of entailment this strong or stronger will, I believe, be found to be applicable to non-classical logics generally. In the opinion of Dana Scott, no really workable three valued logic has yet been developed. It is hard to disagree with this. A workable three valued logic however could perhaps be developed however, if we had a notion of entailment suitable to non-bivalent logics. (shrink)

Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on Priest and attempts some fixes and alternative construals to get (...) around some elementary problems. Despite these efforts, the argument remains unconvincing. (shrink)

Philosophers of science often assume that logically equivalent theories are theoretically equivalent. I argue that two theses, anti-exceptionalism about logic (which says, roughly, that logic is not a priori, that it is revisable, and that it is not special or set apart from other human inquiry) and logical realism (which says, roughly, that differences in logic reflect genuine metaphysical differences in the world), make trouble for both this commitment and the closely related commitment to theories being closed under logical consequence. (...) I provide three arguments. The first two show that anti-exceptionalism about logic provides an epistemic challenge to both the closure and the equivalence claims; the third shows that logical realism provides a metaphysical challenge to both the closure and the equivalence claims. Along the way, I show that there are important methodological upshots for metaphysicians and philosophers of logic. In particular, there are lessons to be drawn about certain conceptions of naturalism as constraining the possibilities for metaphysics and the philosophy of logic. (shrink)

This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.

Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived. Strikingly these logics have found a wide range of application, despite the misgivings of philosophers as prominent as Lewis and Putnam. Such applications, I will argue, are of significant philosophical interest. They suggest ways to employ these logics in philosophical and scientific theories. To this end I will sketch out a ‘naturalized semantic dialetheism’ following Priest’s early (...) suggestion that the principles governing human natural language may well be inconsistent. There will be a significant deviation from Priest’s work, namely, the assumption of a broadly Chomskyan picture of semantics. This allows us to explain natural language inconsistency tolerance without commitment to contentious views in formal logic. (shrink)

Trope theory is the view that the world is a world of abstract particular qualities. But if all there is are tropes, how do we account for the truth of propositions ostensibly made true by some concrete particular? A common answer is that concrete particulars are nothing but tropes in compresence. This answer seems vulnerable to an argument (first presented by F. H. Bradley) according to which any attempt to account for the nature of relations will end up either in (...) contradiction, nonsense, or will lead to a vicious infinite regress. I investigate Bradley’s argument and claim that it fails to prove what it sets out to. It fails, I argue, because it does not take all the different ways in which relation and relata may depend on one another into account. If relations are entities that are distinct from yet essentially dependent upon their relata, the Bradleyan problem is solved. We are then free to say that tropes in compresence are what make true propositions ostensibly made true by concrete particulars. (shrink)

Inconsistency toleration is the phenomenon of working with inconsistent information without threatening one’s rationality. Here I address the role that ignorance plays for the tolerance of contradictions in the empirical sciences. In particular, I contend that there are two types of ignorance that, when present, can make epistemic agents to be rationally inclined to tolerate a contradiction. The first is factual ignorance, understood as temporary undecidability of the truth values of the conflicting propositions. The second is what I call “ignorance (...) of theoretical structure”, which is lack of knowledge of relevant inference patterns within a specific theory. I argue that these two types of ignorance can be explanatory of the scientists’ rational disposition to be tolerant towards contradictions, and I illustrate this with a case study from neutrino physics. (shrink)

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

This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate about mathematical objects.

Rejectivism is one of the most influential embodiments of pragmatism within contemporary philosophy of logic, advancing an explanation of the meaning of a logical notion, negation, in terms of the speech act of denial. This paper offers a challenge to rejectivism by proposing that in virtue of explaining negation in terms of denial, the rejectivist ought to be able to explain the concept of contradiction partially in terms of denial. It is argued that any failure to achieve this constitutes an (...) explanatory failure on the part of rejectivism, and reasons are then provided to doubt that the challenge can be successfully met. (shrink)

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic, that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two (...) uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...) and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

Given the plethora of competing logical theories of validity available, it’s understandable that there has been a marked increase in interest in logical epistemology within the literature. If we are to choose between these logical theories, we require a good understanding of the suitable criteria we ought to judge according to. However, so far there’s been a lack of appreciation of how logical practice could support an epistemology of logic. This paper aims to correct that error, by arguing for a (...) practice-based approach to logical epistemology. By looking at the types of evidence logicians actually appeal to in attempting to support their theories, we can provide a more detailed and realistic picture of logical epistemology. To demonstrate the fruitfulness of a practice-based approach, we look to a particular case of logical argumentation—the dialetheist’s arguments based upon the self-referential paradoxes—and show that the evidence appealed to support a particular theory of logical epistemology, logical abductivism. (shrink)

It is often held that identity properties like the property of being identical to Paris are intrinsic. It is also often held that, while some logically uninstantiable properties are intrinsic, some logically uninstantiable properties are non-intrinsic. The combination of these views, however, raises a problem, since virtually every existing account of intrinsicality fails to analyse a notion of intrinsicality on which both these views are true. In this paper, I argue that, given the orthodox theory of counterlogicals, there is no (...) notion of intrinsicality on which both these views are true. If this argument is sucessful, then, at least given orthodoxy about counterlogicals, we face no challenge in analysing a notion of intrinsicality on which both these views are true, since there is no such notion. In addition, if we are also convinced that there is a notion of intrinsicality on which one of these views is true and a notion of intrinsicality on which the other of these views is true, we should hold that there is more than one notion of intrinsicality. (shrink)

This paper first offers a standard modal extension of dialetheic logics that respect the normal semantics for negation and conjunction, in an attempt to adequately model absolutism, the thesis that there are true contradictions at metaphysically possible worlds. It is shown, however, that the modal extension has unsavoury consequences for both absolutism and dialetheism. While the logic commits the absolutist to dialetheism, it commits the dialetheist to the impossibility of the actual world. A new modal logic AV is then proposed (...) which avoids these unsavoury consequences by invalidating the interdefinability rules for the modal operators with the use of two valuation relations. However, while using AV carries no significant cost for the absolutist, the same isn't true for the dialetheist. Although using AV allows her to avoid the consequence that the actual world is an impossible world, it does so only on the condition that the dialetheist admits that she cannot give a dialetheic solution to all self-refe.. (shrink)

This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional (...) properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together. (shrink)

(No abstract is available for this citation).

We sketch an account according to which the semantic concepts themselves are not pathological and the pathologies that attend the semantic predicates arise because of the intention to impose on them a role they cannot fulfill, that of expressing semantic concepts for a language that includes them. We provide a simplified model of the account and argue in its light that (i) a consequence is that our meaning intentions are unsuccessful, and such semantic predicates fail to express any concept, and (...) that (ii) in light of this it is incorrect to characterize the pathology simply as semantic inconsistency; a more nuanced view of the problem is needed. We also show that the defects of the semantic predicates need not undercut the use of a truth theory in a compositional semantics for a language containing them because the meaning theory per se need not involve commitment to the axioms of the truth theory it exploits. (shrink)

There is a strong intuition that for a change to occur, there must be a moment at which the change is taking place. It will be demonstrated that there are no such moments of change, since no state the changing thing could be in at any moment would suffice to make that moment a moment of change. A moment in which the changing thing is simply in the state changed from or the state changed to cannot be the moment of (...) change, since these states are respectively before and after the change; moreover, to select one of these moments over the other as the moment of change would be arbitrary. A moment in which the changing thing is neither in the state changed from nor in the state changed to cannot be the moment of change, since there are changes for which it is impossible for something to be in neither state. Finally, the moment of change cannot be a moment in which the changing thing is in both the state changed from and the state changed to, as suggested by Graham Priest and others. Even if, like proponents of this view, we are willing to accept the contradictions that the account entails, it is demonstrated that on such a model, every change would require an infinite number of other changes, every change would take an infinite amount of time, and some changes would occur without occurring at any time. Further, the model is grossly counterintuitive, with the exact nature of the counterintuitive element depending on what model of time and space one endorses. Finally, it is demonstrated that this model is incompatible with the Leibniz Continuity Condition. (shrink)

I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.

Perhaps the real paradox of Zeno's Arrow is that, although entirely stationary, it has, against all odds, successfully traversed over two millennia of human thought to trouble successive generations of philosophers. The prospects were not good: few original Zenonian fragments survive, and our access to the paradoxes has been for the most part through unsympathetic commentaries. Moreover, like its sister paradoxes of motion, the Arrow has repeatedly been dismissed as specious and easily dissolved. Even those commentators who have taken it (...) seriously have propounded solutions with which they profess themselves to be perfectly satisfied. So my question is: will Zeno's Arrow survive into the millennium just begun? (shrink)

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)

Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, we also compare various dynamical rules of the two frameworks, all seen as (...) generalizations of classic Bayes’ conditioning. (shrink)

A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.

In this paper, I investigate how far we can use stories to learn about logic. How can we engage with fiction in order to come to find out what logical principles are actually valid? Is that possible at all? I claim that it is, and I propose two case studies to make the point.

According to one prominent strand of mainstream logic and metaphysics, identity is indistinguishability. Priest has recently argued that this permits counterexamples to the transitivity and substitutivity of identity within dialetheic metaphysics, even in paradigmatically extensional contexts. This paper investigates two alternative regimentations of indistinguishability. Although classically equivalent to the standard regimentation on which Priest focuses, these alternatives are strictly stronger than it in dialetheic settings. Both regimentations are transitive, and one satisfies substitutivity. It is argued that both regimentations provide better (...) candidates to occupy the core theoretical role of numerical identity than does the standard regimentation. (shrink)

First paragraph: This paper seeks to understand various paradoxes as cases of conflicting rules. In particular, the ambition is to outline a new perspective on and response to the Liar -- though it will take us a while to get that far. We begin in Section 1 with an account of simple rule confliction. Section 2 then brings this account to bear on a paradox, the Secretary Liberation Paradox, which is readily seen to involve conflicting rules. Finally in Section 3 (...) I suggest that the Liar can also be seen as a case of rule confliction, and outline briefly how that perspective provides for Liar arguments to be blocked. (shrink)

In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.

I present a paradoxical combination of desires. I show why it's paradoxical, and consider ways of responding. The paradox saddles us with an unappealing trilemma: either we reject the possibility of the case by placing surprising restrictions on what we can desire, or we deny plausibly constitutive principles linking desires to the conditions under which they are satisfied, or we revise some bit of classical logic. I argue that denying the possibility of the case is unmotivated on any reasonable way (...) of thinking about mental content, and rejecting those desire-satisfaction principles leads to revenge paradoxes. So the best response is a non-classical one, according to which certain desires are neither determinately satisfied nor determinately not satisfied. Thus, theorizing about paradoxical propositional attitudes helps constrain the space of possibilities for adequate solutions to semantic paradoxes more generally. (shrink)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating (...) all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

Are there dispositions which not only do not manifest, but which could not manifest? We argue that there are dispositions to Ф in circumstances C where C is impossible, and some where Ф is impossible. Furthermore, postulating these dispositions does useful theoretical work. This paper describes a number of cases of dispositions had by objects even though those dispositions are not possibly manifest, and argues for the importance of these dispositions.

The paper focuses on Nāgārjuna, the founder of the middle way school of Mahāyāna Buddhism. It argues that while Nāgārjuna’s rejection of the notion of ontological independence is justified and corr...

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)

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well (...) as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources. (shrink)

You and I can differ in what we say, or believe, even though the things we say, or believe, are logically equivalent. Discussing what is said, or believed, requires notions of content which are finer-grained than sets of (metaphysically or logically) possible worlds. In this paper, I develop the approach to fine-grained content in terms of a space of possible and impossible worlds. I give a method for constructing ersatz worlds based on theory of substantial facts. I show how this (...) theory overcomes an objection to actualist constructions of ersatz worlds and argue that it naturally gives rise to useful notions of fine-grained content. (shrink)