On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that (...) nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken. (shrink)

On the dominant view of vagueness, if it is vague whether Harry is bald, then it is unsettled, not merely epistemically, but metaphysically, whether Harry is bald. In other words, vagueness is a type of indeterminacy. On the standard alternative, vagueness is a type of ignorance: if it is vague whether Harry is bald, then, even though it is metaphysically settled whether Harry is bald, we cannot know whether Harry is bald. On my view, vagueness is neither a type of (...) indeterminacy nor a type of ignorance. Rather, it is sui generis. (shrink)

Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.

Les questions qui ont suscité le présent texte concernent la relation entre la théorie et le réel empirique: comment peut-on identifier le contenu empirique d'une théorie? Dans quelle mesure sa prétention à révéler le réel estelle justifiée? La première tâche que ces interrogations commandent est celle d'exposer les conceptions de la structure des théories scientifiques les plus marquantes de ce siècle. Dans cette période la philosophie des sciences a d'abord été dominée par l'empirisme logique et son approche formelle de la (...) structure des théories scientifiques. L'empirisme logique est certes un mouvement qui a eu une histoire mouvementée et qui a été le théâtre de nombreuses modifications, mais une de ses thèses les plus persistantes peut le caractériser de façon générale: sa représentation de la théorie sous la forme d'un système d'énoncés. Pour désigner cette position, nous utiliserons l'expression «conception assertive» comme traduction de statement view. L'approche sémantique est une conception plus récente de la structure de la théorie qui semble peu à peu vouloir prendre la place de la conception assertive. Nous décrirons donc dans un premier temps ces deux approches afin de déterminer chaque fois la fagon dont le rapport de la théorie au réel est envisagé. (shrink)

In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this (...) paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections. (shrink)

In this paper Rudolf Carnap's definition of 'analytic truth' based upon a meaning postulate At, for theoretical predicates of a given scientific theory is subjected to critique. It is argued that this definition is both too exclusive and too inclusive. Assuming that the preceding is correct, At is subjected to further scrutiny to determine how to interpret it and whether, and under what conditions, it need even be true. It is argued that a given At need not be true as (...) a sentence in a scientific theory and that it must be regarded as a confusedly presented rule for the same. It is then argued that even as a semantical rule for the theory, At cannot provide a guarantee of truth for some meaning postulate similar to At in the theory itself. It is thus argued that Carnap's definition of 'analytic truth' for theoretical predicates is unsatisfactory. (shrink)