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)

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)

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.

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)

The aim of this paper is to point out the limitations of Hybrid Modal Realism as a general theory of modalities, i.e. one that gives an analysis of possibilities as well as impossibilities. To do so we will firstly sketch the goals that theories of impossible worlds should achieve. Secondly we will briefly present the two most popular accounts of impossibilities—Extended Modal Realism and Extended Ersatzism. We will focus on the aspects of both theories which became the motivation for a (...) hybrid view. In the last part of this paper we will analyze Francesco Berto’s Hybrid Modal Realism and present reasons why this account is an insufficient tool for analyzing impossibilities. (shrink)

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.

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.

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

This multifaceted essay emerges from a host of sources within diverse academic settings. Its central thesis is guided by physicist John A. Wheeler's thoughts on the quantum enigma. Wheeler concludes, following Niels Bohr, that we are co-participants within the universal self-organizing process. This notion merges with concepts from Peirce's process philosophy, Eastern thought, issues of topology, and border theory in cultural studies and social science, while surrounding itself with such key terms as complementarity, interdependence, interrelatedness, vagueness, generality, incompleteness, inconsistency, and (...) mestizaje. Ultimately, a sense of semiosic process pervades in light of combined homogenous and hetergenous tendencies. (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.

In this paper, I argue for a particular conception of impossible worlds. Possible worlds, as traditionally understood, can be used in the analysis of propositions, the content of belief, the truth of counterfactuals, and so on. Yet possible worlds are not capable of differentiating propositions that are necessarily equivalent, making sense of the beliefs of agents who are not ideally rational, or giving truth values to counterfactuals with necessarily false antecedents. The addition of impossible worlds addresses these issues. The kinds (...) of impossible worlds capable of performing this task are not mysterious sui generis entities, but sets of structured propositions that are themselves constructed out of possible worlds and relations. I also respond to a worry that these impossible worlds are unable to represent claims about the shape of modal space itself. (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)

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.

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)

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?

Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)

It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (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)