Fregean Quantification Theory

Frege’s system of first-order logic is presented in a contemporary framework. The system described is distinguished by economy of expression and an unusual syntax.     

Standard Quantification Theory in the Analysis of English

Standard first-order logic plus quantifiers of all finite orders (SFOL) faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOL models. The typed structure of SFOL models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOL type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOL models.     

Unrestricted composition and restricted quantification

Many of those who accept the universalist thesis that mereological composition is unrestricted also maintain that the folk typically restrict their quantifiers in such a way as to exclude strange fusions when they say things that appear to conflict with universalism. Despite its prima facie implausibility, there are powerful arguments for universalism. By contrast, there is remarkably little evidence for the thesis that strange fusions are excluded from the ordinary domain of quantification. Furthermore, this reconciliatory strategy seems hopeless when applied to the more fundamental conflict between universalism and the intuitions that tell against it.

Quantification Theory in *8 of Principia Mathematica and the Empty Domain

The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain.     

Quantification Theory in *9 of Principia Mathematica

This paper examines the quantification theory of *9 of Principia Mathematica. The focus of the discussion is not the philosophical role that section *9 plays in Principia's full ramified type-theory. Rather, the paper assesses the system of *9 as a quantificational theory for the ordinary predicate calculus. The quantifier-free part of the system of *9 is examined and some misunderstandings of it are corrected. A flaw in the system of *9 is discovered, but it is shown that with a minor repair the system is semantically complete. Finally, the system is contrasted with the system of *8 of Principia's second edition.     

语义结构理论与临床推理

临床推理是医生的核心能力之一。临床推理的语义结构理论认为,语义轴由临床意义相反的两个词构成,能精确地表征临床知识并促进医生精确地回忆知识;语义轴是正确临床诊断的必要条件,医生使用语义轴的数量与其临床诊断的正确性呈正相关。应用语义结构理论进行医学教学改革可能有益于医学生临床推理能力的迅速提高。     

A Theory of Social Structure and the Quality of Life

The demographic and social structure of the community/society provide the basis for interactions that lead to satisfactions, subjective well being and the quality of life. Studies are cited that employ elements of social structure in identifying satisfying aspects of the quality of life. Ten propositions are offered that identify theoretical relationships between social structural features and well-being. To improve the quality of life, suggestions for altering the social structure are presented. This essay brings together conceptual positions for an understanding of the exogenous effects upon the quality of life (QOL). References to the literature provide insights to the relationship of social structure to the QOL. The author will appreciate receiving readers' observations and additional references to scholarly works – for there are many – on the subject.     

Asymptotic Densities in Logic and Type Theory

This paper presents a systematic approach for obtaining results from the area of quantitative investigations in logic and type theory. We investigate the proportion between tautologies (inhabited types) of a given length n against the number of all formulas (types) of length n. We investigate an asymptotic behavior of this fraction. Furthermore, we characterize the relation between number of premises of implicational formula (type) and the asymptotic probability of finding such formula among the all ones. We also deal with a distribution of these asymptotic probabilities. Using the same approach we also prove that the probability that randomly chosen fourth order type (or type of the order not greater than 4), which admits decidable lambda definability problem, is zero. Presented by Jacek Malinowski     

Completeness in Hybrid Type Theory

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret \(@_i\) in propositional and first-order hybrid logic. This means: interpret \(@_i\alpha _a\) , where \(\alpha _a\) is an expression of any type \(a\) , as an expression of type \(a\) that rigidly returns the value that \(\alpha_a\) receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic.     

The Art Type Theory of Art

Abstract

The theory I present and defend in this paper—what I term the art type theory— holds that something is a work of art iff it belongs to an established art type. Something is an established art type, in turn, either because its paradigmatic instances standardly satisfy eight art-making conditions, or because the art world has seen fit to enfranchise it as such. It follows that the art status of certain objects is independent of what any individual or culture might say about it, while the art status of others fundamentally depends on the judgment of the art world. Because of the theory's quasi-institutional component, I conclude by defending it against four objections that have been raised against institutional definitions.     

Logic Without Contraction as Based on Inclusion and Unrestricted Abstraction

On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within the framework of a logic based on inclusion and unrestricted abstraction, without any form of extensionality. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Causal Structure of Evolutionary Theory

One contentious debate in the philosophy of biology is that between the statisticalists and causalists. The former understand core evolutionary concepts like fitness and selection to be mere statistical summaries of underlying causal processes. In this view, evolutionary changes cannot be causally explained by selection or fitness. The causalist side, on the other hand, holds that populations can change in response to selection—one can cite fitness differences or driftability in causal explanations of evolutionary change. But, on the causalist side, it is often not clear how, precisely, one should understand these causes. Thus, much more could be said about what sort of causes fitness and driftability are. In this paper, I borrow Dretske's distinction between structuring and triggering causes and I suggest that fitness and driftability are structuring causes of evolution.     

The Logical Structure of Just War Theory

A survey of just war theory literature reveals the existence of quite different lists of principles. This apparent arbitrariness raises a number of questions: What is the relation between ad bellum and in bello principles? Why are there so many of the former and so few of the latter? What order is there among the various principles? To answer these questions, I first draw on some recent work by Jeff McMahan to show that ad bellum and in bello principles are not, as often portrayed, independent—the justice of conduct in war largely presupposes the justice of the recourse to war. Undermining this independence claim is one important step toward revealing the unified logical structure of just war theory. I then argue that we can see the dependence of the jus in bello upon the jus ad bellum, not just in the content of certain principles, but also in the structure of the two sets of principles: I construct a one-to-one mapping between ad bellum and in bello principles. In doing so, I argue also that the shared structure successfully finds place for the questions central to the evaluation of the morality of war: what is a sufficient provocation to use force, what objectives may be sought by force, why or for what ends, who has authority to decide to use force, and when or in what circumstances? Despite variations in expression, the theory allows for a coherent and comprehensive evaluation of morality in warfare.     

耗散结构理论在生理学中的应用

医学与自然科学有着密切的联系.耗散结构理论作为更高层次的研究复杂系统的系统科学的一个分支理论,对复杂的生命系统的研究起着指导作用.它可以用来解释许多生理学方面的基本生命活动现象,因此耗散结构理论对生理学的研究和发展有着重要的作用.     

The Logical Structure of International Trade Theory

In this paper the structuralist approach of theory reconstruction is applied to International Trade Theory. In the basic element the universal laws of the theory are stated and the general concepts are defined in terms of three sets and seven functions. Ricardo’s Theory of Comparative Advantage and the Factor Proportions Theory by Heckscher and Ohlin are reconstructed as specialisations of the basic element. Two intratheoretical constraints are formulated in order to ensure the consistency of the theory. A number of empirical studies are shown to be paradigmatic, successful or questionable applications of International Trade Theory. The reconstruction allows the assessment of the theory from a metatheoretical angle and illuminates the logical interdependencies of its components.

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