Reference and Reinterpretation

Reference is the relation held to obtain between an expression and what a speaker or thinker intends the expression to represent. Reference is a component of interpretation, the process of giving terms, sentences, and thoughts semantic content. An example of reference in a formal context involves the natural numbers, where each one can be taken to have a corresponding set-theoretic counterpart as its referent. In an informal context reference is exemplified by the relation between a name and the specific name-bearer when a speaker or thinker utters or has the name in mind. Recent debates over reference have concerned the mechanism of reference: How is it that we can refer? In informal contexts, externalists see the reference relation as explicable in terms of the salient causal relations involved in the naming of a thing, or a class of things, and the ensuing causal chains leading to a term’s use. Opponents of this view—internalists—see the reference relation as being conceptually direct, and they take the external approach to rely on untenable metaphysical assumptions about the world’s structure. Moreover, some internalists take the permutability—i.e. the consistent reinterpretation—of certain referential schemes to confound the externalist picture of reference. In this thesis I focus on the reference of theoretical terms in science, and I argue for an externalist treatment of natural kinds and other theoretical elements. Along the way I offer a defense of the externalist’s pre-theoretic metaphysical assumptions and emphasize their central role in the interpretation of scientific languages. The externalist approach acknowledges the necessary constraints on reference-fixing that account for the schemes we employ, and this, I argue, confounds the permutation strategy

Impredicativity and turn of the century foundations of mathematics : presupposition in Poincare and Russell

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1993.Includes bibliographical references (leaves 145-158).by Joseph Romeo William Michael PicardPh.D

Metalevel and reflexive extension in mechanical theorem proving

In spite of many years of research into mechanical assistance for mathematics it is still much more difficult to construct a proof on a machine than on paper. Of course this is partly because, unlike a proof on paper, a machine checked proof must be formal in the strictest sense of that word, but it is also because usually the ways of going about building proofs on a machine are limited compared to what a mathematician is used to. This thesis looks at some possible extensions to the range of tools available on a machine that might lend a user more flexibility in proving theorems, complementing whatever is already available.In particular, it examines what is possible in a framework theorem prover. Such a system, if it is configured to prove theorems in a particular logic T, must have a formal description of the proof theory of T written in the framework theory F of the system. So it should be possible to use whatever facilities are available in F not only to prove theorems of T, but also theorems about T that can then be used in their turn to aid the user in building theorems of T.The thesis is divided into three parts. The first describes the theory FS₀, which has been suggested by Feferman as a candidate for a framework theory suitable for doing meta-theory. The second describes some experiments with FS₀, proving meta-theorems. The third describes an experiment in extending the theory PRA, declared in FS₀, with a reflection facility.More precisely, in the second section three theories are formalised: propositional logic, sorted predicate logic, and the lambda calculus (with a deBruijn style binding). For the first two the deduction theorem and the prenex normal form theorem are respectively proven. For the third, a relational definition of beta-reduction is replaced with an explicit function.In the third section, a method is proposed for avoiding the work involved in building a full Godel style proof predicate for a theory. It is suggested that the language be extended with quotation and substitution facilities directly, instead of providing them as definitional extensions. With this, it is possible to exploit an observation of Solovay's that the Lob derivability conditions are sufficient to capture the schematic behaviour of a proof predicate. Combining this with a reflection schema is enough to produce a non-conservative extension of PRA, and this is demonstrated by some experiments

À quoi bon la métaphysique?

La présente thèse a pour objet l'examen de la légitimité de l'entreprise métaphysique, dans ses rapports avec le réalisme métaphysique scientifique. La tâche de fournir une description véridique de la nature, de la structure et de la composition ultimes du monde tel qu'il est en réalité semble désormais (depuis l'avènement de la modernité, en fait) l'apanage de la science plutôt que de la métaphysique. Le problème est donc le suivant : quelle place pour la métaphysique? La métaphysique n'est plus depuis belle lurette la « reine de toutes les sciences ». Doit-elle être « éliminée » comme le recommandait Carnap? Ma thèse sera guidée par trois grandes questions. Premièrement, étant donné que l'aspiration de connaître le « monde tel qu'il est » présuppose l'adoption du réalisme, la question se posera de la définition et de la défense d'une telle conception. Nous verrons dans le premier chapitre qu'un réalisme robuste requiert un engagement ontologique ferme envers une métaphysique réaliste comprenant à la fois les objets du sens commun et les entités théoriques postulées par la science. Je me demanderai en deuxième lieu s'il est nécessaire, ou du moins, s'il vaut la peine d'admettre, en sus de ces entités physiques, des entités proprement « métaphysiques », comme les universaux ou les tropes, postulées par la métaphysique. Et même si la réponse à cette deuxième question m'apparaît devoir être assez négative, je me demanderai en troisième lieu s'il pourrait y avoir néanmoins un avantage ou une utilité, sur le plan explicatif, heuristique, ou même seulement à titre illustratif, à postuler de telles entités et à tenir un tel discours.\ud ______________________________________________________________________________ \ud MOTS-CLÉS DE L’AUTEUR : métaphysique, réalisme, métamétaphysique, philosophie analytique, philosophie des sciences, philosophie de la connaissance, tropes, universaux

A source modelling system and its use for uncertainty management

Human agents have to deal with a considerable amount of information from their environment and are also continuously faced with the need to take actions. As that information is largely of an uncertain nature, human agents have to decide whether, or how much, to believe individual pieces of information. To enable a reasoning system to deal in general with the demands of a real environment, and with information from human sources in particular, requires tools for uncertainty management and belief formation. This thesis presents a model for the management of uncertain information from human sources. Dealing, more specifically, with information which has been pre-processed by a natural language processor and transformed into an event-based representation, the model assesses information, forms beliefs and resolves conflicts between them in order to maintain a consistent world model. The approach is built on the fundamental principle that the uncertainty of information from people can, in the majority of situations, successfully be assessed through source models which record factors concerning the source's abilities and trustworthiness. These models are adjusted to reflect changes in the behaviour of the source. A mechanism is presented together with the underlying principles to reproduce such a behaviour. A high-level design is also given to make the proposed model reconstructible, and the successful operation of the model is demonstrated on two detailed examples