A Unified Logic for Contingency and Accident

Journal of Philosophical Logic - As shown in Fan (Journal of Philosophical Logic, 48, 425–445, 2019), there are some similarities/resemblances between contingency and accident. Given this,...     

"Articulation"与后马克思主义的偶然性逻辑--从拉克劳和墨菲的"articulation"谈起

该文认为,“articulation”是拉克劳、墨菲的后马克思主义的一个核心概念,它的基本意思是“链结”。该文从词源上考察了“articulation”一词的意义及其历史演变,并对其基本含义和特征做了深入的分析。该文认为,链接是理解后马克思主义的偶然性逻辑的核心概念。链接是发生在主体身份之间的,话语性的,偶然性的建构实践活动。但拉克劳、墨菲的链接虽然力图避免近代哲学的本质主义和还原主义,但却仍然避免不了其精致的“唯心”倾向和向上的还原论的嫌疑。我们对此要有清晰的认识。     

On the Logic of Classes as Many

The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.     

Mass Nouns in a Logic of Classes as Many

A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation can also be given for mass nouns.     

Contingency contracting with school problems

Contingency contracting procedures used in managing problems with school-age children involved analyzing teacher and/or parental reports of behavior problem situations, isolating the most probable contingencies then in effect, the range of reinforcers presently available, and the ways in which they were obtained. The authors prepared written contracts delineating remediative changes in reinforcement contingencies. These contracts specified ways in which the child could obtain existing individualized reinforcers contingent upon approximations to desired appropriate behaviors chosen as incompatible with the referral problem behaviors. Contract procedures were administered by the natural contingency managers, parents and/or teachers, who kept daily records of contracted behaviors and reinforcers. These records were sent to the authors and provided feedback on the progress of the case. Initial results of this procedure have been sufficiently encouraging to warrant recommending an experimental analysis of contingency contracting as a clinical method.     

Dynamic Modalities

A new modal logic containing four dynamic modalities with the following informal reading is introduced: ${\square^\forall}$ – always necessary, ${\square^\exists}$ – sometimes necessary, and their duals – ${\diamondsuit^\forall}$ – always possibly, and ${\diamondsuit^\exists}$ – sometimes possibly. We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp.     

Bimodal Logics with Contingency and Accident

Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this logic over various classes of frames, whose completeness proofs are shown with the help of a crucial schema. The interactions between contingency and accident can sharpen our understanding of both notions. Then we extend the logic to a dynamic case: public announcements. By finding the required reduction axioms, we obtain a complete axiomatization, which gives us a good application to Moore sentences.

     

Contingency effects with maintained instrumental reinforcement

In three experiments we investigated the effect on the performance of thirsty rats of varying the instrumental contingency between lever pressing and the delivery of a saccharin reinforcer. In Experiment 1, the subjects performed more slowly in a non-contingent condition, in which the momentary probability of reinforcement was unaffected by whether or not the animals pressed, than in a contingent condition in which the reinforcer was never presented except following a lever press. This was true of performance under both random ratio and interval schedules in which the function determining the probability of reinforcement following a lever press remained the same across the contingent and non-contingent conditions. Experiment 2 demonstrated that instrumental performance was less affected when the contingency was degraded by the introduction of free reinforcers if these reinforcers were signalled. In Experiment 3, lever pressing was reinstated to some degree after non-contingent training by giving non-reinforced exposure to the operant chamber in the absence of the lever. These results suggest that free reinforcers depress instrumental behaviour through a performance mechanism engaged by their ability to support conditioning of the contextual cues.     

On Provability Logics with Linearly Ordered Modalities

We introduce the logics GLP _Λ, a generalization of Japaridze’s polymodal provability logic GLP _ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP _ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP _Λ and the decidability of GLP _Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment of GLP _Λ.     

Historical Contingency

The paper provides a new characterization of the concepts of necessity and contingency as they should be used in the historical context. The idea is that contingency (necessity) increases in direct (reverse) proportion to sensitivity to initial conditions. The merits of this suggestion are that it avoids the conflation of causality and necessity (or contingency and chance), that it enables the bracketing of the problem of free will while maintaining the concept of human action making a difference, that it sanctions tendencies without recourse to teleology, and that it recasts the controversy between historicists and anti-historicists in less dogmatic language.     

The Agentive Modalities

A number of philosophical projects require a proper understanding of the modal aspects of agency, or of what I call ‘the agentive modalities.’ I propose a general account of the agentive modalities, one which takes as its primitive the decision‐theoretic notion of an option. I relate this account to the standard semantics for ‘can’ and to the viability of some positions in the free will debates.     

Kant's Modalities of Judgment

Abstract: This paper proposes a way to understand Kant's modalities of judgment—problematic, assertoric, and apodeictic—in terms of the location of a judgment in an inference. Other interpretations have tended to understand these modalities of judgment in terms of one or other conventional notion of modality. For example, Mattey (1986) argues that we should take them to be connected to notions of epistemic or doxastic modality. I shall argue that this is wrong, and that these kinds of interpretation of the modality of judgments cannot be reconciled with a key claim made by Kant, namely, that the modality of a judgment does not contribute to its content, and has nothing to do with the matter that is judged. I offer an alternative interpretation based upon Kant's explicating these modalities in terms of the location of a judgment in an inference, whereby the modality of a judgment is determined by the role a judgment plays in a given course of reasoning. If I am right, then Kant in fact presents an intriguing thesis pertaining to the inferential status and potential of all our judgments.     

Contingency in Nature

Contingencies in Nature may be explained, but such explanations refer to other contingencies (pt. I). Is there a way to “explain away” all contingencies? The first physical theory of modern times, Newton’s theory of gravitation, was received in a way that leaves this question open (pt. II), while Kepler’s theory of cosmological harmony arrived at a positive solution (pt. III). However, later developments in science outdated Kepler’s approach (pt. IV).     

Projection across Sensory Modalities

Question is raised as to whether we are not setting our sights too high in trying to understand personality. Difficulty of understanding the “whole” personality is related to the fact that half of what is determining it at any given time is situationally defined and the other half is tied up with almost invisible inner processes. Homage is paid to Henry Murray for having put us on the right path.     

Logic with numbers

Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”.