Conditional Excluded Middle in Systems of Consequential Implication

It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius' Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which instances of CEM are derivable. We also investigate the systems CIw and CI of consequential implication, corresponding to the modal logics K and KD respectively, with occasional remarks about stronger systems. While unrestricted CEM produces modal collapse in all these systems, CEM restricted to contingent formulas yields the Alt2 axiom (semantically, each world can see at most two worlds), which corresponds to the symmetry of consequential implication. It is proved that in all the main systems considered, a given instance of CEM is derivable if and only if the result of replacing consequential implication by the material biconditional in one or other of its disjuncts is provable. Several related results are also proved. The methods of the paper are those of propositional modal logic as applied to a special sort of conditional.     

A Dynamic Characterization of the Pure Logic of Relevant Implication

This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual set-theoretical interpretation. (ii) A proof format may display an internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity). (iii) A monotonic logic may have a non-monotonic characterization.     

Two Kinds of Consequential Implication

The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength (symbolized by \(\rightarrow \) and \(\Rightarrow \)). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for \(\Rightarrow \), CI\(\Rightarrow \), is definitionally equivalent to the deontic system KD and is intertranslatable with the minimal consequential system for \(\rightarrow \), CI. The main drawback ot the weaker operator \(\Rightarrow \) is that it lacks unrestricted contraposition, but the final section of the paper argues that \(\Rightarrow \) has some properties which make it a valuable alternative to \(\rightarrow \), turning out especially plausible as a basis for the definition of operators representing synthetic (i.e. context-dependent) conditionals.     

Arrow Logic and Infinite Counting

We consider arrow logics (i.e., propositional multi-modal logics having three -- a dyadic, a monadic, and a constant -- modal operators) augmented with various kinds of infinite counting modalities, such as 'much more', 'of good quantity', 'many times'. It is shown that the addition of these modal operators to weakly associative arrow logic results in finitely axiomatizable and decidable logics, which fail to have the finite base property.     

Computer Implication and the Curry Paradox

There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.     

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.     

Logic and Aggregation

Paraconsistent logic is an area of philosophical logic that has yet to find acceptance from a wider audience. The area remains, in a word, disreputable. In this essay, we try to reassure potential consumers that it is not necessary to become a radical in order to use paraconsistent logic. According to the radicals, the problem is the absurd classical account of contradiction: Classically inconsistent sets explode only because bourgeois classical semantics holds, in the face of overwhelming evidence to the contrary, that both A and A cannot simultaneously be true! We suggest (more modestly) that there is, at least sometimes, something else worth preserving, even in an inconsistent, unsatisfiable premise set. In this paper we present, in a new guise, a very general version of this preservationist approach to paraconsistency.     

生殖器疱疹研究现状及诊疗过程中的伦理问题

生殖器疱疹是单纯疱疹病毒感染生殖器部位皮肤黏膜所引起的炎症性疾病,是常见的性传播性疾病之一.近年来,随着其在人群中的流行率的不断增高,在国内已成为一个令人关注的公共卫生问题.本文就其病原学、流行状况、传播和潜在的危险性作一概述,并分析了在其诊疗过程中的伦理问题及相关的对策.     

The Relevance of a Relevantly Assertable Disjunction for Material Implication

In this paper Grice’s requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz’s conclusion-relevant consequence relation.     

小学儿童CVS策略的发展及其对教育的启示

CVS策略是国外不少研究者正深入研究的一种学习策略,关于它的研究得出了许多有价值的结论。本文首先分析了CVS的概念、研究方法和研究意义,然后对当前的研究结论进行了梳理,从五大方面详细分析了小学儿童CVS策略的发展特点,最后又从四个发面提出了这些研究对当前教育的启示。     

From Necessity to Fate: a Fallacy

Though clearly fallacious, the inference from determinism to fatalism (the ``Lazy Argument') has appealed to such minds as Aristotle and his disciple, Alexander of Aphrodisias. It is argued here (1) that determinism does entail a rather similar position, dubbed ``futilism'; and (2) that distinctively Aristotelian determinism entails fatalism for any event to which it applies. The concept of ``fate' is examined along the way.     

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.     

论廉政的伦理内涵

廉政属于伦理范畴和道德规范。文中从“廉”“政”的语义入手,阐述了“廉政”的伦理内涵,探讨了“廉政”伦理内涵的层次。     

疾病治疗与康复的自我效能模式及其意义

自我效能是指个体对其在特定情境中成功地完成某种活动的能力预期。患者的自我效能预期能以直接或间接的方式影响其行为表现和生理机能,从而影响到疾病治疗与康复效果。患者自我效能的形成与发展既受各种效能信息的影响,也受个体认知加工方式的影响。根据患者自我效能的形成与作用模式,可以采取不同的措施来提高患者的自我效能预期,发挥它在疾病治疗与康复中的作用。     

Cartesian Method and the Aristotelian-Scholastic Method

In book one of the Consolation of Philosophy, Boethius is portrayed as a man who suffers because he forgot philosophy. Scholars have underestimated the significance of this portrayal and considered it a literary device the goal of which is simply to introduce the discussion that follows. In this paper, I show that this view is mistaken since it overlooks that this portrayal of Boethius is the key for the understanding of the whole text. The philosophical therapy that constitutes the core of the ‘Consolation’ can in fact be properly evaluated only if we recognize the condition it is designed to cure. Through the portrayal of Boethius's forgetfulness, the ‘Consolation’ illustrates that it is the very nature of philosophical knowledge that makes it susceptible to being forgotten. Philosophical knowledge can (i) turn into misology, when it appears unable to solve certain problems, and (ii) be overrun by strong emotions. The therapy offered in the ‘Consolation’ is designed to make Boethius aware of the ‘fragility’ of philosophical knowledge and show him how to ‘strengthen’ it. He is taught how to more fully embody philosophy's precepts and that philosophy's inability to solve certain problems reveals not its failures but its limits.     

The Chrysippus intuition and contextual theories of truth

Contextual theories of truth are motivated primarily by the resolution they provide to paradoxical reasoning about truth. The principal argument for contextual theories of truth relies on a key intuition about the truth value of the proposition expressed by a particular utterance made during paradoxical reasoning, which Anil Gupta calls “the Chrysippus intuition.” In this paper, I argue that the principal argument for contextual theories of truth is circular, and that the Chrysippus intuition is false. I conclude that the philosophical motivation for contextual theories of truth fails.

The Relation between Formal and Informal Logic

The issue of the relationship between formal and informal logic depends strongly on how one understands these two designations. While there is very little disagreement about the nature of formal logic, the same is not true regarding informal logic, which is understood in various (often incompatible) ways by various thinkers. After reviewing some of the more prominent conceptions of informal logic, I will present my own, defend it and then show how informal logic, so understood, is complementary to formal logic.     

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].     

Contemplative withdrawal in the Hellenistic age

I reject the traditional picture of philosophical withdrawal in the Hellenistic Age by showing how both Epicureans and Stoics oppose, in different ways, the Platonic and Aristotelian assumption that contemplative activity is the greatest good for a human being. Chrysippus the Stoic agrees with Plato and Aristotle that the greatest good for a human being is virtuous activity, but he denies that contemplation exercises virtue. Epicurus more thoroughly rejects the assumption that the greatest good for a human being is virtuous activity. He maintains that the greatest good for a human being is the tranquility that virtuous activity always and contemplative activity sometimes brings about.

Love and Benevolence in Hutcheson's and Hume's Theories of the Passions

In this paper I consider two related issues raised by Aristotle's treatment of hearing and sounds. The first concerns the kinds of changes Aristotle takes to occur, in both perceptual medium and sense organs, when a perceiver hears a sounding object. The second issue concerns Aristotle's views on the nature and location of the proper objects of auditory perception. I argue that Aristotle's views on these topics are not what they have sometimes been taken to be, and that when rightly understood they compare favourably in many respects with leading contemporary accounts.