Completeness Theorems via the Double Dual Functor

The aim of this paper is to apply properties of the double dual endofunctor on the category of bounded distributive lattices and some extensions thereof to obtain completeness of certain non-classical propositional logics in a unified way. In particular, we obtain completeness theorems for Moisil calculus, n-valued Łukasiewicz calculus and Nelson calculus. Furthermore we show some conservativeness results by these methods. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Complete and Consistent Formal System for Sortals

A formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. The absolute consistency of the system is proved. A completeness proof for the system is also constructed. This proof is relative to a concept of logical validity provided by a semantics, which assumes as its philosophical background an approach to sortals from a modern form of conceptualism.     

From IF to BI

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle.     

Ontogenesis and Phylogenesis in the Analysis of Chinese Classifiers： Remarks on Philosophical Method

Philosophical analysis is commonly assumed to involve decomposing the meaning of a sentence or an expression into a set of conceptually basic constituent parts. This essay challenges this traditional view by examining the potential semantic roles that classifier phrases play in Chinese. It is suggested that the conceptual resources necessary for justifying claims about the semantical status of natural language classifier phrases should be informed in part by methods that accommodate ontogenic and evolutionary contexts. Evidence is provided for the view that many Chinese classifiers （but not all） are features regimented in the grammar of Chinese that have no functional role in normal adult communication, but which play an ontogenetic role in the child＇s development of linguistic competency. Furthermore, it is suggested that this ontogenetic role has features in common with the phylogenetic processes by which Chinese or its classical variants came about, as a later product of mechanisms that evolved in the species in accordance with varying demands for successful communication.     

Semantic and Syntactic Associations During Word Search Modulate the Relationship Between Attention and Subsequent Memory

Two experiments were conducted to investigate how linguistic information influences attention allocation in visual search and memory for words. In Experiment 1, participants searched for the synonym of a cue word among five words. The distractors included one antonym and three unrelated words. In Experiment 2, participants were asked to judge whether the five words presented on the screen comprise a valid sentence. The relationships among words were sentential, semantically related or unrelated. A memory recognition task followed. Results in both experiments showed that linguistically related words produced better memory performance. We also found that there were significant interactions between linguistic relation conditions and memorization on eye-movement measures, indicating that good memory for words relied on frequent and long fixations during search in the unrelated condition but to a much lesser extent in linguistically related conditions. We conclude that semantic and syntactic associations attenuate the link between overt attention allocation and subsequent memory performance, suggesting that linguistic relatedness can somewhat compensate for a relative lack of attention during word search.     

TRUTH AS AN EPISTEMIC IDEAL

Several philosophers—including C. S. Peirce, William James, Hilary Putnam and Crispin Wright—have proposed various versions of the notion that truth is an epistemic ideal. More specifically, they have held that a proposition is true if and only if it can be fixedly warranted by human inquirers, given certain ideal epistemic conditions. This paper offers a general critique of that idea, modeling conceptions of ideality and fixed warrant within the semantics that Kripke developed for intuitionistic logic. It is shown that each of the two plausible notions of fixed warrant faces difficulties and that, moreover, “truth” defined in terms of either of them is distressingly dependent upon one’s conception of idealized inquiry and perhaps also upon one’s standards of warrant.     

Why Propositions Cannot be Sets of Truth-supporting Circumstances

No semantic theory satisfying certain natural constraints can identify the semantic contents of sentences (the propositions they express), with sets of circumstances in which the sentences are true–no matter how fine-grained the circumstances are taken to be. An objection to the proof is shown to fail by virtue of conflating model-theoretic consequence between sentences with truth-conditional consequence between the semantic contents of sentences. The error underlines the impotence of distinguishing semantics, in the sense of a truth-based theory of logical consequence, and semantics, in the sense of a theory of meaning.     

An Approach to Glivenko’s Theorem in Algebraizable Logics

In a classical paper [15] V. Glivenko showed that a proposition is classically demonstrable if and only if its double negation is intuitionistically demonstrable. This result has an algebraic formulation: the double negation is a homomorphism from each Heyting algebra onto the Boolean algebra of its regular elements. Versions of both the logical and algebraic formulations of Glivenko’s theorem, adapted to other systems of logics and to algebras not necessarily related to logic can be found in the literature (see [2, 9, 8, 14] and [13, 7, 14]). The aim of this paper is to offer a general frame for studying both logical and algebraic generalizations of Glivenko’s theorem. We give abstract formulations for quasivarieties of algebras and for equivalential and algebraizable deductive systems and both formulations are compared when the quasivariety and the deductive system are related. We also analyse Glivenko’s theorem for compatible expansions of both cases. Presented by Jacek Malinowski     

Grades of meaning

In this paper, I lend novel support to H. P. Grice’s account of speaker meaning (GASM) by blunting the force of a significant objection. Stephen Schiffer has argued that in order to make GASM sufficient, one must add restrictions that are psychologically impossible to fulfill, thereby making GASM untenable. In what follows, I explain the elements of GASM that require it to invoke these psychologically unrealizable restrictions. I then accept Schiffer’s criticism, but modify its significance to GASM. I argue that the problem that Schiffer notes is not a reason to reject GASM, but a reason to embrace it. GASM shows that meaning is best understood as an absolute concept—an unrealizable ideal limit. Taking some inspiration from contextualist theories of knowledge attribution, I argue that my version of GASM offers a useful contextualist account of meaning attribution. Hence, pragmatic theories of meaning and communication should not wholly exclude GASM from their theorizing, at least not for the reasons that are commonly given.