Theism and Dialetheism

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against the divine attributes.     

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.     

Quine and Slater on Paraconsistency and Deviance

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant ^*c^* in a given logic: its operational meaning, given by the operational rules for ^*c^* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing ^*c^* which can be proved in the same calculus. Subsequently, we use the same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics ^*L^* and ^*L^* is possible whenever each constant in ^*L^* has the same operational meaning as its counterpart in ^*L^* although differences in global meaning arise in at least one case.     

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.     

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.     

Properties,laws, and worlds

Jonathan Schaffer argues against a necessary connection between properties and laws. He takes this to be a question of what possible worlds we ought to countenance in our best theories of modality, counterfactuals, etc. In doing so, he unfairly rigs the game in favor of contingentism. I argue that the necessitarian can resist Schaffer’s conclusion while accepting his key premise that our best theories of modality, counterfactuals, etc. require a very wide range of things called ‘possible worlds’. However, the necessitarian can and should insist that, in many cases, these worlds are not metaphysically possible. I will further argue that, having taken such a stance, the necessitarian has additional resources to respond to Schaffer’s other arguments against the view.     

Future Contradictions

A common and much-explored thought is ?ukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present.

The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3.     

The Class of Extensions of Nelson's Paraconsistent Logic

The article is devoted to the systematic study of the lattice εN4_⊥ consisting of logics extending N4_⊥. The logic N4_⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4_⊥ and the lattice of superintuitionistic logics. Distinguish in εN4_⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate. The author acknowledges support by the Alexander von Humboldt-Stiftung and by Counsil for Grants under RF President, project NSh - 2112.2003.1.     

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.     

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.     

Possible Worlds Semantics and Fiction

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.     

Truth in Fiction,Impossible Worlds,and Belief Revision

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

Heidegger and the contradiction of Being: a dialetheic interpretation of the late Heidegger

ABSTRACT

It is well known that, from the beginning to the end of his philosophical trajectory, Martin Heidegger tries to develop a fundamental ontology which aims at answering the so-called question of Being: what does Being mean? Unfortunately, in trying to answer this question, Heidegger faces a predicament: given his own premises, speaking about Being leads to a contradiction. Moreover, according to the majority, if not all, of the interpreters who admit the existence of such a predicament, Heidegger tries to avoid the contradiction in question. But is this the only way Heidegger tries to solve the predicament? In this paper, I argue that, in some of his late works and, in particular, in the Contributions to Philosophy, Heidegger also takes into serious consideration the possibility of accepting the contradiction he faces in speaking about Being as true. If this is correct, Heidegger endorses what nowadays analytic philosophers call dialetheism, namely the metaphysical position according to which some (but not all) contradictions are true.     

Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics.     

Equivalential and algebraizable logics

The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the theory of equivalential logics in the sense of Prucnal and Wroski [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable.Most of the results of the present and a forthcoming paper originally appeared in [13].Presented by Wolfgang Rautenberg     

On the Impossibility of Epistemology

Philosophical Studies -     

On the Impossibility of Amalgamating Evidence

It is argued in this paper that amalgamating confirmation from various sources is relevantly different from social-choice contexts, and that proving an impossibility theorem for aggregating confirmation measures directs attention to irrelevant issues.     

Augustine on the Impossibility of Teaching

The information-transference account of teaching takes it to be a process in which information is transferred from one person's mind to another's. Augustine argues that this is impossible, since in order to understand something the person who understands must come to see why it is so, and that is an internal episode of awareness that isn't caused by an outside source. Augustine's insight here is contrasted with the contemporary view, following Wittgenstein, that learning is a matter of conformity to rules (public norms). The case is made that teaching and learning pose philosophical problems that contemporary theories don't address, and a brief examination of Searle's Chinese Room example suggests that its plausibility derives from Augustine's insight that mere rule-following behavior isn't enough to explain the phenomenon of understanding at the heart of knowledge. A reconstruction of Augustine's epistemological claims, divorced from his discredited views in the philosophy of language, is also provided.     

Special issue: Combining probability and logic

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.