A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force of the model (...) is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...) the concepts of science through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap's understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap's logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap's program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts. The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language, and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap's entire program. My third chapter argues that this reading makes Carnap's program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap's program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful. (shrink)

A version of intuitionistic type theory is presented here in which all logical symbols are defined in terms of equality. This language is used to construct the so-called free topos with natural number object. It is argued that the free topos may be regarded as the universe of mathematics from an intuitionist's point of view.

The theory New Foundations of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [8] and [9], have models in ZF. Very little is known about subsystems of NF satisfying typical properties of ZF; for example in [11] it is shown that the existence of some sets which appear naturally in ZF is an axiom (...) independent from NF . Here we discuss a model of subsystems of NF in which there is a set which is a model of ZF. MSC: 03E70. (shrink)

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.

Cet article s'ajoute à la liste déjà longue de ceux qui traitent des rapports entre la théorie russellienne des descriptions définies et la théorie ramifiée des types. Seule la prétention d'aborder cette question dans une perspective nouvelle justifie ici sa présence: d'une part, la théorie des descriptions définies sera resituée dans le contexte initial et souvent méconnu de la théorie des expressions dénotantes et d'autre part, c'est à la logique intensionnelle de Russell, objet d'une méconnaissance au moins égale, que nous (...) nous intéresserons. De plus, c'est du point de vue de la théorie de la signification et non pas du point de vue ontologique, génético-historique ou logico-mathematique que nous nous proposons de traiter de ces rapports. (shrink)