Axiomatization of Some Basic and Modal Boolean Connexive Logics

Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses (i) a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and (ii) if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets.

Resurgent Powers and the Failure of Conceptual Analysis

Jennifer McKitrick examines the causes moving many philosophers to pull Aristotelian powers out of history’s dustbin, the failure to reduce or eliminate dispositional ascriptions from philosophical and scientific discourses. Although many see this failure as grounds for rejecting Humeanism and return to Aristotelianism, McKitrick argues that only a more moderate reaction is warranted. She argues that restricting analysis to fundamental dispositions and adding a condition requiring the power ascription be grounded in or made true by the fact that the object possesses that fundamental disposition is the better reaction. McKitrick canvasses the main twentieth-century attempts to reduce or eliminate dispositional talk. She begins with the logical positivists’ attempt to replace dispositional talk with material conditionals. Then, after briefly considering Ryle’s version, she turns to Goodman and the move to replace material conditional analyses with stronger-than-material conditionals, such as causal implication or counterfactual conditionals backed up by natural kinds and laws of nature. Next, she turns to Lewis’s possible worlds semantics and concludes with a presentation of the ‘Simple Counterfactual Analysis’. Despite these problems with providing analyses of dispositional ascriptions in terms of counterfactuals, McKitrick recognizes that there is still an important connection between dispositions and counterfactuals. A thing’s disposition is its property of having a certain kind of counterfactual hold of it. But she advocates restricting counterfactual analyses to fundamental dispositions and powers and requiring that they be made true, or grounded by, the fact that the object has that power.

Truthmaker semantics for natural language: Attitude verbs, modals, and intensional transitive verbs

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. The semantics is applied to factive verbs and response-stance verbs as well as to cases of modal concord. The paper also presents new motivations for ‘object-based truthmaker semantics’ from intensional transitive verbs such as need, look for, own, and buy and gives an outline of their semantics based on a further development of truthmaker semantics.

Perception, memory, and imagination as propositional attitudes

Jaakko Hintikka started in 1969 the study of the logic of perception as a spe- cial case of his more general approach to propositional attitudes by means of the possible worlds semantics. His students and co-workers extended this study to the logic of memory and imagination. The key elements of this approach are the distinction between physical and perspectival cross-identification and the related two kinds of quantifiers, which allow a formulation of the syntax and semantics of various types of statements about perceiving, re- membering and imagining. This paper surveys the main results of these logical investigations.

A study of possible-worlds semantics of relevance-sensitive belief revision

Parikh’s relevance-sensitive axiom (P) for belief revision is open to two different interpretations, i.e. the weak and the strong version of (P), both of which are plausible depending on the context. Given that strong (P) has not received the attention it deserves, in this article, an extended examination of it is conducted. In particular, we point out interesting properties of the semantic characterization of the strong version of (P), as well as a vital feature of it that, potentially, results in a significant drop on the resources required for an implementation of a belief-revision system. Lastly, we shed light on the natural connection between global and local revision functions, via their corresponding semantic characterization, hence, a means for constructing global revision functions from local ones, and vice versa, is provided.

Revisiting McKinsey's 'Syntactical' Construction of Modality

In 1945 J.C.C. McKinsey produced a ‘semantics’ for modal logic based on necessity defined in terms of validity. The present papers looks at how to update F.R. Drake’s completeness proof for McKinsey’s semantics by comparing McKinsey ‘models’ with the now standard Kripke models. It also looks at the motivation behind the system McKinsey called S4.1, but which we now call S4M; and use this motivation to produce a McKinsey semantics for that system. One lesson which emerges from this work is an appreciation of the superiority of the current possible worlds semantics based on frames and models, both in terms of an intuitive understanding of modality, and also in terms of the ease of working with particular systems.

Introduction

More than thirty years ago I wrote a book called Inquiry. This was a great title for a philosophy book, with its allusion (or homage) to classic works in the empiricist tradition, and it was an appropriate title for the aspirations with which the book was written: its topic, I said in the preface, was the abstract structure of inquiry. But it is less clear that this was an appropriate title for what was actually accomplished in the book since it did not get much beyond preliminary setting up of the issues, and some exposition of and motivation for the formal apparatus that I planned to use to talk about the structure of inquiry. Before getting to the main issues, I had to explain and motivate my approach to the problem of intentionality, sketch and motivate the formal apparatus used to represent that approach (possible worlds semantics), and respond to problems that the approach faced. That took up most of the book. The rest of it focused mainly on another piece of apparatus needed to represent the dynamics of belief (a formal semantics for conditionals), and I was able to make only a start on a discussion of the role of this apparatus in forming and refining both rules for revising beliefs, and concepts for giving a theoretical description of the world....