What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...) far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

MEANING POSTULATES REINSTATED If I am right in agreeing with Cresswell that the "logicarrlexicaT distinction is one of degree rather than one of kind, that in turn impugns the distinction between the official truth-rules that define logical ...

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

Fragmentalism is the view that reality is not a metaphysically unified place, but fragmented in a certain sense, and constituted by incompatible facts across such fragments. It was introduced by Kit Fine in a discussion of tense realist theories of time. Here I discuss the conceptual foundations of fragmentalism, identify several open questions in Fine’s characterization of the view, and propose an understanding of fragmentalism that addresses these open questions.

The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)

Objects often manifest themselves in incompatible ways across perspectives that are epistemically on a par. The standard response to such cases is to deny that the properties that things appear to have from different perspectives are properties that things really have out there. This type of response seems worrying: too many properties admit of perspectival variance and there are good theoretical reasons to think that such properties are genuinely instantiated. So, we have reason to explore views on which things can (...) have the incompatible properties they appear to have across perspectives. This paper explores the view that things can have incompatible properties if the world is not a metaphysically unified place but is instead fragmented. There is a sensible notion of co-obtainment, on which two facts can each obtain without co-obtaining. Using this notion, we can step back from our embedded perspectives on the world without deeming the contents of those perspectives to be mere appearances. This renders th.. (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argued consequence relation, taking into account the existence of consistent arguments in favour of a conclusion and the absence of consistent arguments in favour of its contrary, is particularly investigated. Flat knowledge bases, i.e., without any priority between their elements, are studied under different inconsistency-tolerant consequence relations, namely the so-called argumentative, free, universal, existential, cardinality-based, and paraconsistent consequence relations. The syntax-sensitivity of these consequence relations is (...) studied. A companion paper is devoted to the case where priorities exist between the pieces of information in the knowledge base. (shrink)

The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) (...) to solve the problems associated with propositional attitude contexts, intentional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphysical theory of such atypical worlds tend to move too quickly from philosophical characterizations to formal semantics. (shrink)

It is shown that the consequence relations defined from theRescher-Manor Mechanism are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics isobtained by applying a suitable adaptive strategy to the paraconsistent logicCLuN.This result provides all those consequence relations with a proof theory and with a static semantics.

This paper argues for a particular view about in what metaphysical equivalence consists: namely, that any two metaphysical theories are metaphysically equivalent if and only if those theories are strongly hyperintensionally equivalent. It is consistent with this characterisation that said theories are weakly hyperintensionally distinct, thus affording us the resources to model the content of propositional attitudes directed towards metaphysically equivalent theories in such a way that non-ideal agents can bear different propositional attitudes towards metaphysically equivalent theories.

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...) some expressions is not uniquely defined. Other strategies for generalizing supervaluations are considered and some comparative facts are discussed. (shrink)

US citizens perceive their society to be one of the most diverse and religiously tolerant in the world today. Yet seemingly intractable religious intolerance and moral conflict abound throughout contemporary US public life - from abortion law battles, same-sex marriage, post-9/11 Islamophobia, public school curriculum controversies, to moral and religious dimensions of the Black Lives Matter and Occupy Wall Street movements, and Tea Party populism. Healthy Conflict in Contemporary American Society develops an approach to democratic discourse and coalition-building across deep (...) moral and religious divisions. Drawing on conflict transformation in peace studies, recent American pragmatist thought, and models of agonistic democracy, Jason Springs argues that, in circumstances riven with conflict between strong religious identities and deep moral and political commitments, productive engagement may depend on thinking creatively about how to constructively utilize conflict and intolerance. The result is an approach oriented by the recognition of conflict as a constituent and life-giving feature of social and political relationships. (shrink)

One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics using non-normal worlds (...) of different kinds. (shrink)

David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false (...) even when both ‘A’ and ‘~A’ are true, just as supervaluational semantics makes a tautology ‘A v ~A’ true even when neither ‘A’ nor ‘~A’ are. Connections with discussive logics and complications of the account are discussed, and some general morals are drawn. (shrink)

This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.

The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a natural solution to the problem of logical omniscience.

In this analysis of one of the most difficult and neglected topics in Hegelian studies, Songsuk Susan Hahn tackles the status of contradiction in Hegel's ...

The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

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)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

John Horty has proposed an approach to reasoning with ought-propositions which stands in contrast to the standard modal approach to deontic logic. Horty’s approach is based on default theories as known from the framework of Default Logic. It is argued that the approach cannot be extended beyond the most simple kinds of default theories and that it fails in particular to account for conditional obligations. The most plausible ways of straightening out the defects of the approach conform to a simple (...) theory of default reasoning in standard deontic language. (shrink)

The book offers a novel approach to the idea of divinity in guise of a philosophical doctrine called 'Logical Pantheism', according to which the only way to establish the existence of God undeniably is by equating God with Logical Space.

The common view has it that there are two families of approaches towards the logical structure of impossible worlds – Australasian and North American. According to the first, impossible worlds are closed under the relation of logical consequence of one of the non-classical logics. The North American approach is more liberal, allowing for impossible worlds where no logic holds. After pointing out the questionable consequences of each view, I propose a third one. While this new perspective allows for worlds where (...) no logical consequence holds, it also imposes some constraints on what worlds are built upon. This renders the proposed view not as restrictive as the Australasian approach and not as liberal as the North American approach. Due to its intermediary nature, I have named this perspective ‘the Pacific’ approach. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy (...) to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a principle of contradiction is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing "space" as the seat of stability, and "time" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion `separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of `non-locality' as related to it, indicating the need to re-think the notions `system', `entity', as well as the implications of the operation `measurement', which is seen here as an application of classical logic on the material world. (shrink)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.

Alexius Meinong developed a notion of defective objects in order to account for various logical and psychological paradoxes. The notion is of historical interest, since it presages recent work on the logical paradoxes by Herzberger and Kripke. But it fails to do the job it was designed for. However, a technique implicit in Meinong's investigation is more successful and can be adapted to resolve a similar paradox discovered by Romane Clark in a revised version of Meinong's Theory of Objects due (...) to Rapaport. One family of paradoxes remains, but it is argued that they are unavoidable and relatively harmless. (shrink)

Truth-relativism is the claim that the truth of statements is dependent on the context in which they are made. In this article, truth-relativism is considered as a way to explain disagreements. Viewpoint relativism, a recent version of truth-relativism, is introduced as a useful framework to analyse how truth-relativism approaches disagreements. Viewpoint relativism is based on contextual semantics and the logic of viewpoint, which is a two-dimensional modal logic. In viewpoint relativism, the central concept is a point of view in relation (...) to which truth claims are evaluated. Viewpoint relativism is compared to the truth-relativism of Peter Lasersohn and John MacFarlane. Finally, truth-relativism is defended against the critique of Paul Boghossian that it represents untenable ‘replacement relativism’. (shrink)

Chomsky’s principle of epistemological tolerance says that in theoretical linguistics contradictions between the data and the hypotheses may be temporarily tolerated in order to protect the explanatory power of the theory. The paper raises the following problem: What kinds of contradictions may be tolerated between the data and the hypotheses in theoretical linguistics? First a model of paraconsistent logic is introduced which differentiates between week and strong contradiction. As a second step, a case study is carried out which exemplifies that (...) the principle of epistemological tolerance may be interpreted as the tolerance of week contradiction. The third step of the argumentation focuses on another case study which exemplifies that the principle of epistemological tolerance must not be interpreted as the tolerance of strong contradiction. The reason for the latter insight is the unreliability and the uncertainty of introspective data. From this finding the author draws the conclusion that it is the integration of different data types that may lead to the improvement of current theoretical linguistics and that the integration of different data types requires a novel methodology which, for the time being, is not available. (shrink)

I argue that a compulsive seeking for just one sense of consistency is hazardous to rationality, and that observing the subtle distinctions of reasonableness between individual and groups may suggest wider, structuralistic notions of consistency, even relevant to re-assessing Gödei's Second Incompleteness Theorem and to science as a whole.

David Lewis (1979) has argued that according to his possible worlds analysis of counterfactuals, “backtracking” counterfactuals of the form “If event A were to happen at tA, then event B would happen at tB” where tB precedes tA, are usually false if B does not actually happen at tB. On the other..

Abstract In this paper I discuss one apparent counterexample to the rationality constraint on belief ascription. The fact that there are inconsistent believers does not seem compatible with the idea that only rational creatures can be ascribed beliefs. I consider Davidson's explanation of the possibility of inconsistent believers and claim that it involves a reformulation of the rationality constraint in terms of the believers' subscription to norms of rationality. I shall argue that Davidson's strategy is partially successful, but that the (...) emphasis on the notion of subscription badly fits with the motivations behind his theory of interpretation. (shrink)

Aim of this paper is to analyse and assess two divergent understandings of metaphysical modality. On one hand, according to the absolutist conception, metaphysical modality is the extreme variety of objective modality and can be characterised in terms of all the varieties of objective modality: for example, p is metaphysically necessary if and only if p is necessary for every variety of objective necessity. The absolutist conception can also be framed in terms of counterfactual inevitability. On the other hand, according (...) to the essentialist conception of metaphysical modality, p is metaphysically necessary if and only if the truth of p is grounded by the essences of some entities. Based on the analysis of these two conceptions, I show that possible worlds are not helpful in characterising metaphysical modality. I finally suggest that in the light of a general principle about philosophical terminology, the essentialist conception has an edge over the absolutist one. (shrink)

"Thinking about thinking", the topic of this section of our volume, leads us into an Escherian web of self-referential interconnections — which nevertheless make sense, at least if we do not shy away at once in the face of paradox, for fear of inconsistency. How do our critical faculties enter the picture? Adding a few conceptual dimensions to the merely linearly causal one may help us to shed light on the issue, and may help us also to understand some of (...) the basic strategies "Western" thought has developed throughout its historical pathway in its conscious dealings with the 'real'. Of course, in a few pages it is impossible to do justice to this complicated subject. But I'll try to give the reader an as clear as possible description of the, in my view, crucial issues, pointing out the ways they resonate into the many fields of interest represented in the intended readership, and leave it to the reader to dig deeper through the given references. (shrink)

In this paper I argue that inconsistencies in scientific theories may arise from the type of causality relation they—tacitly or explicitly—embody. All these seemingly different causality relations can be subsumed under a general strategy developed to defeat the paradoxes which inevitably occur in our experience of the real. With respect to this, scientific theories are just a subclass of the larger class of metaphysical theories, construed as theories that attempt to explain a (part of) the world consistently. All metaphysical theories (...) share a common structural backbone specificially designed to defeat paradoxes, their often wildly diverging ontological claims notwithstanding. This common structure shapes the procedures which govern the invention of ideas in the context of such theories, by codifying some onto-logical a priori assumptions regarding the consistency of reality into its bare conceptual framework. Causality plays a key rôle here, because it implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalising power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of ‘system’ and ‘lawful behaviour’. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. The fundamental backbone’s specific gestalt thus functions as a theory’s individual signature and paves the way to a comparative historical approach towards their study. An important part of my paper therefore explores the strong connections between paradoxes as they appear and are dealt with in ancient philosophy and their re-appearance in early modern natural philosophy and science. This analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results. (shrink)

Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.

In 1947 Quine wrote one of the most important and influential articles in the twentieth century philosophy - "On What There Is". One of the aims of this article was a critique of Meinong's Theory of Object. The critique was especially focused upon nonactual possibilities, which (according to Meinong) are some kinds of nonexistent objects. In my paper I want to present Neo-Meinongian refutations of Quine's critique. In order to do this I discuss: (i) the main thesis of "On What (...) There Is" ,(ii) premises of Meinongian Theory, (iii) views of proponents and opponents of the idea of nonexistent objects, (iv) Quine's critique aimed at nonactual possibilities, (v) Terence Parsons' theory, based on the distinction between nuclear and extranucler properties, and (vi) noneism, defended by Richard Routley. I also try to give a reply to the most popular critiques aimed at both Neo-Meinongian theories. The main conclusion is that Quine's critique and his arguments against nonactual possibilities aren't dangerous for theories endorsing Meinong's Theory of Object. Contrary to what Gilbert Ryle once claimed (If Meinongianism isn't dead, nothing is), Meinongian theories are still alive and doing well. (shrink)

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

This paper was presented at the 26th International Wittgenstein Symposium on “Knowledge and Belief”, Kirchberg am Wechsel, Austria (3rd - 10th August 2003). The focus of study is a dialogue situation in which one party holds that P while the other holds that ~P. A simple way to establish harmony between the parties in dialogue is to insist that each should include the other’s point of view. This is unsatisfactory because it results in an inconsistent set of beliefs. Clarity is (...) essential, therefore, on how to deal with inconsistency. In this paper, I will proceed in two steps. In the first, I will indicate how some attempts at trying to manage contradictions in terms of ontology remain unsatisfactory. In the second step, I will introduce and evaluate another way in terms of belief and acceptance. I make an original application of L.J. Cohen’s distinction between belief and acceptance, the former being a matter of feeling, the latter a matter of policy in reasoning. (shrink)