What Is an Inconsistent Truth Table?

Do truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions.     

Yes,Virginia, there Really are Paraconsistent Logics

B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever negation symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics — the preservationist logics — are not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations — even those that emerge from dialetheic approaches — does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism.     

Atheism and Dialetheism; or, ‘Why I Am Not a (Paraconsistent) Christian’

In ‘Theism and Dialetheism’, Cotnoir explores the idea that dialetheism (true contradictions) can help with some puzzles about omnipotence in theology. In this note, I delineate another aspect of this project. Dialetheism cannot help with one big puzzle about another classic ‘omni’ property, omnibenevolence—the famous problem of evil. For someone (including a dialetheist) who thinks that the existence of evil is a knock-down argument against traditional theism, it is a knock-down argument against dialetheic theism, too.     

Dialetheism and the Impossibility of the World

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-referential semantic paradoxes. Thus, unless there are any further available modal logics that don't commit her to the impossibility of the actual world, the dialetheist is faced with a dilemma. Either admit that the actual world is an impossible world, or admit that her research programme cannot give a comprehensive solution to the self-referential paradoxes.     

Are there True Contradictions? A Critical Discussion of Graham Priest's, Beyond the limits of thought

The present article critically examines three aspects of Graham Priest's dialetheic analysis of very important kinds of limitations (the limit of what can be expressed, described, conceived, known, or the limit of some operation or other). First, it is shown that Priest's considerations focusing on Hegel's account of the infinite cannot be sustained, mainly because Priest seems to rely on a too restrictive notion of object. Second, we discuss Priest's treatment of the paradoxes in Cantorian set-theory. It is shown that Priest does not address the issue in full generality; rather, he relies on a reading of Cantor which implicitly attributes a very strong principle concerning quantification over arbitrary domains to Cantor. Third, the main piece of Priest's work, the so-called “inclosure schema”, is investigated. This schema is supposed to formalize the core of many well-known paradoxes. We claim, however, that formally the schema is not sound. This revised version was published online in August 2006 with corrections to the Cover Date.     

Chunk and Permeate,a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus

In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind – specifically concerning the preservation of the consistency of each chunk – and concludes with some other possible applications and technical questions.     

Negative Equivalence of Extensions of Minimal Logic

Two logics L₁ and L₂ are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L₁ if and only if it can be done in L₂. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.The author acknowledges support by the Alexander von Humboldt-StiftungPresented by Jacek Malinowski     

Non-Adjunctive Inference and Classical Modalities

The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A∧B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski.     

Filtering Theories of Truth: Compositionality as a Criterion

The traditional way to filter out the implausible candidate solutions to the semantic paradoxes is to appeal to the so-called “cost/benefit analyses.” Yet it is often tedious and controversial to carry out such analyses in detail. Facing this, it would be helpful for us to rely upon some principles to filter out at least something, if not everything, from them. The proposal in this paper is thereby rather simple: We may use principles of compositionality as a “filter” for this purpose. The paper has four sections. In Section 2, the author uses the filter to examine Kripke’s fixed-point theory and to thereby show how it works. In Section 3, the author gives more examples from the classical theories of truth to demonstrate the power of the filter. In Section 4, the author addresses the skepticism concerning whether there is any consistent or non-trivial theory of truth that can survive this filtering procedure. A “nearly sufficient” condition for a theory of truth to survive this test is discussed in order to show that at least some consistent or non-trivial theories of truth do indeed survive the filtering procedure.     

Diamonds are a Philosopher's Best Friends

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.     

A Note on Priest's Finite Inconsistent Arithmetics

We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.     

On what will be: reply to Westphal

Jonathan Westphal’s recent paper attempts to reconcile the view that propositions about the future can be true or false now with the idea that the future cannot now be real. I attempt to show that Westphal’s proposal is either unoriginal or unsatisfying. It is unoriginal if it is just the well-known eternalist solution. It is unsatisfying if it is instead making use of a peculiar, tensed truthmaking principle.

Socratic Proofs and Paraconsistency: A Case Study

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φ_v. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.     

The Logic of Pragmatic Truth

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.     

未来心理时间的新取向：集体未来思考

集体未来思考是指想象一个尚未发生的群体事件,其与集体记忆之间存在着复杂的相互作用。目前对集体未来思考的研究发现它的记忆基础更多为语义记忆。而有关集体未来思考的脑机制研究则相对较少,但在遗忘症患者中发现个体未来思考和集体未来思考是可分离的,并且非海马依赖的未来场景构建与集体未来思考可能存在重要联系。未来研究应该注重不同文化背景下的集体未来思考,探讨其产生条件及影响因素,并加强在正常人群中神经机制的研究,以更好地揭示集体未来思考的实质。     

未来取向研究概述

未来取向是指个人的思想和行为偏好未来的方向, 同时也是个体对于未来的思考和规划过程。未来取向心理结构的代表性观点有要素观、过程观和动机认知行为观。主要测量方式包括问卷法、投射法、圆环测验、讲故事技术和完成故事技术。个体的年龄、性别、人格和情绪等是未来取向的主要影响因素。未来取向在健康行为、物质滥用和学业成绩等方面起着积极作用。明确未来取向的功能机制、完善测量工具、采用精巧的实验设计并进一步探讨未来取向的脑机制是未来研究的方向。     

Apocalyptic relevance

In their book, Relevance, Sperber and Wilson make an important contribution towards constructing a credible theory of this unforthcoming notion. All is not clear sailing, however. If it is accepted as a condition on the adequacy of any account of relevance that it not be derivable either that nothing is relevant to anything or that everything is relevant to everything, it can be shown that Sperber and Wilson come close to violating the condition.     

Expansion and Contraction of Finite States

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.     

情节式未来思考的年龄差异及其脑机制

情节式未来思考是将自我投射到未来以预先经历某事件的能力。本文探讨情节式未来思考的年龄差异及其脑机制,重点阐述情节式未来思考的个体发生发展及其现象学特征的年龄差异,探究其年龄差异的脑机制主要涉及颞叶及楔前叶、海马以及额叶等脑区。未来研究应扩大正常人与特殊群体的年龄范围,关注情节式未来思考年龄差异的研究角度及纵向交叉方法,同时需结合内外部影响因素进行研究,这在认知老化中有重要的社会应用价值。