Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication

In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We then show that for most of the systems under consideration the labelling mechanism can be avoided by choosing an appropriate way of structuring theories. One peculiar feature of our proof systems is the use of restart rules which allow to re-ask the original goal of a deduction. In case of K, K4, S4 and G, we can eliminate such a rule, without loosing completeness. In all the other cases, by dropping such a rule, we get an intuitionistic variant of each system. The present results are part of a larger project of a goal directed proof theory for non-classical logics; the purpose of this project is to show that most implicational logics stem from slight variations of a unique deduction method, and from different ways of structuring theories. Moreover, the proof systems we present follow the logic programming style of deduction and seem promising for proof search [Gabbay and Reyle 84, Miller et al. 91].     

The Patriarchal Mind as the Ignored Root of Interpersonal and Social Pathologies

The article begins with an integrative theory of neurosis and with the notion of the “patriarchal mind,” which I conceive as the psycho-social foundation of what we call “civilisation” and proceed to characterize as a despotic and repressive activity of the father on the mother and on the child in the family, and also of an analogous relation between the intellect on the emotional and on the instinctual sub-selves in the individual mind. Next, I propose that patriarchy entails four interrelated problems: (1) violent authority; (2) the eclipse of caring; (3) the repression of instinct; and (4) the invalidation of intuition; and point out that since these are evident in our well-recognized social problems, these may be traced down to the “patriarchal complex” that in turn defines patriarchal society. Finally, I develop the idea that not only is the patriarchal mind is embodied in each of the known interpersonal or character pathologies, but that each of these pathologies contributes to the systemic and cultural presence of the patriarchal mind. The corollary of this analysis is that the healing of both our interpersonal and social pathologies will depend on the healing of the patriarchal mind, which is conceivably possible to bring about through a specially designed education oriented to the balanced development of “three-brained beings,” in whom a balance has been achieved between the intellectual, emotional, and instinctive sub-selves that constitute our mind.     

Taking Religious Pluralism Seriously. Arguing for an Institutional Turn. Introduction

Discussions of the relations between religions, society, politics, and the state in recent political philosophy are characterized, firstly, by a strong US American bias focusing on limitations of religious arguments in public debate. Even if the restriction or radical exclusion of religious reasons from public debate has recently been extensively criticized, secularist interpretations of liberal-democratic constitutions still prevail. Here it is argued that both strong secularism and weak or second order secularism are counterproductive for many reasons. Secondly, separationist interpretations of state-church relations are predominant, even if the severe wall of separation is criticized more often nowadays. Here it is argued that there are more and more interesting options than either separationism or accommodationism, that we should not exclusively focus at the constitutional relations between state and churches but address the full reciprocal relationship between society, culture, politics, nation, state and (organized) religions, and that we need more historical and comparative perspectives for the required institutionalist turn in political theory in order to overcome the obstacles inherent in predominant American political philosophy. The articles included in this volume are first, modest steps in this new direction.     

Priorean Strict Implication, Q and Related Systems

We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.     

Sequent Calculi for Some Strict Implication Logics

We introduce various sequent systems for propositional logicshaving strict implication, and prove the completeness theoremsand the finite model properties of these systems.The cut-eliminationtheorems or the (modified) subformula properties are provedsemantically.     

Responsibility and Obligation: Some Kantian Directions

Abstract

This paper asks how we should conceptualize the relationship between responsibility and obligation. Its central concern is the relevance of considerations of obligation to the attribution of responsibility for what we do or bring about. The paper approaches this issue through an examination of Kant’s complex, challenging and instructive theory of responsibility, in which strict obligation plays a pivotal role in attributions of responsibility for the outcomes of our actions. Even if we do not accept Kant’s strongly juridical concept of responsibility, his theory provides insight into the way in which we should see the connection between responsibility and obligation.     

Conceptual Analysis and Philosophical Naturalism

Entitlement is conceived as a kind of positive epistemic status, attaching to certain propositions, that involves no cognitive or intellectual accomplishment on the part of the beneficiary—a status that is in place by default. In this paper I will argue that the notion of entitlement—or something very like it—falls out of an idea that may at first blush seem rather disparate: that the evidential support relation can be understood as a kind of variably strict conditional (in the sense of Lewis 1973). Lewis provided a general recipe for deriving what he termed inner modalities from any variably strict conditional governed by a logic meeting certain constraints. On my proposal, entitlement need be nothing more exotic than the inner necessity associated with evidential support. Understanding entitlement in this way helps to answer some common concerns—in particular, the concern that entitlement could only be a pragmatic, and not genuinely epistemic, status.     

Strict and random alternation in concurrent variable-interval schedules

Six pigeons responded on pairs of concurrent variable-interval schedules with, in different parts, four different arrangements of alternation between schedules. Following a single switching-key response, alternation was either strict or random, and the alternative presented after a switch (the postswitch alternative) was either signaled by the location of the switching key or unsignaled. Generalized-matching analyses showed little difference in behavior among the different alternation arrangements, except the usual finding of lower sensitivity of response allocation than time allocation was eliminated by arranging random alternation. Patterns of interchangeover times were similar for all arrangements except signaled random alternation. Differences in behavior preceding the different postswitch alternatives were found in the signaled random alternation procedure. Preference was biased towards the color of the signaled postswitch alternative and showed increased sensitivity when the postswitch alternative was to be the one with the higher reinforcer rate. Interchangeover times were substantially shorter when the postswitch alternative was signaled to be different from the current alternative than when it was signaled to be the same. However, when separate reinforcer ratios were calculated for the different postswitch alternatives, those effects were eliminated or greatly reduced. We suggest that, although behavior is indeed influenced by the postswitch alternative, the mechanism is indirect. That is, the distributions of reinforcers between alternatives obtained before each postswitch alternative differ when those alternatives are signaled, and those distributions are discriminated, but the same relations between choice and relative reinforcement hold irrespective of which postswitch alternative is signaled.     

The Smith-Walley Interpretation of Subjective Probability: An Appreciation

The right interpretation of subjective probability is implicit in the theories of upper and lower odds, and upper and lower previsions, developed, respectively, by Cedric Smith (1961) and Peter Walley (1991). On this interpretation you are free to assign contingent events the probability 1 (and thus to employ conditionalization as a method of probability revision) without becoming vulnerable to a weak Dutch book. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Physicalism and our knowledge of intrinsic properties

This paper examines recent arguments by Rae Langton and David Lewis intended to prove Humility: the thesis that we have no knowledge of the intrinsic properties of substances. I argue that at best, these arguments are internally incoherent. They at once presuppose a strong version of physicalism according to which physical science is in a position to give a complete list of the fundamental properties of reality, and at the same time various metaphysical principles which in actuality challenge the completeness of the list of properties given by science. Although these arguments are unsound, their consideration enables us to draw important conclusions regarding the tension between the metaphysician's practice of positing intrinsic properties that give colour to the world, and the scientific attempt at giving a complete account of all phenomena.