Note on the Scope of Truth-functional Logic

A plausible and popular rule governing the scope of truth-functional logic is shown to be indequate. The argument appeals to the existence of truth-functional paraphrases which are logically independent of their natural language counterparts. A more adequate rule is proposed.     

Substructural Implicational Logics Including the Relevant Logic E

We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic logic. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Extensions of Intermediate Logics by Strong Negation

In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC).     

Meme Pools, World 3, and Averroës's Vision of Immortality

Dawkins's concept of the meme pool, essentially equivalent to Popper's World 3, is considered as an expression in modern terms for what Averroës knew as the active intellect , an immortal entity feeding into, or even creating, the passive intellect of consciousness. A means is thus provided for reconciling a materialist Darwinian view of the universe with a conception of nonpersonal immortality. The meme pool/active intellect correspondence provides a strong basis for regarding science as a communal enterprise producing enrichment of the meme pool and expansion of consciousness. It also emphasizes the virtues of memetic conservation in relation to vanishing cultures.     

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.     

Moral Responses and Moral Theory: Socially-based Externalist Ethics

The paper outlines a view called social (or two-level) response-dependency as an addition to standard alternatives in metaethics that allows for a position intermediate between standard versions of internalism and externalism on the question of motivational force. Instead of taking psychological responses as either directly supplying the content of ethics (as on emotivist or sentimentalist accounts) or as irrelevant to its content (as in classical versions of Kantian or utilitarian ethics), the view allows them an indirect role, as motivational props to moral teaching and thus to the general institution of moral discourse. However, they are not implied by any particular moral judgment (or speaker), so that amoralism comes out as possible. The response that defines the distinctively moral notion of wrong on this account is the second-level (social) response of forbidding some behavior; but this is ultimately to be understood in terms of (variable) individual reactions. Natural human emotion tendencies thereby constrain the content of ethics, while allowing for some degree of social variation in moral codes.