Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters-one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Anti-realism and logic

The Oxford handbook of philosophy of mathematics and logic

There are many different accounts of the distinction between primary quality and secondary quality concepts. But one thing is generally agreed. Secondary quality concepts implicate subjects in a way primary quality concepts do not. Consider the concepts of smoothness, blandness, and redness. They are tailor-made for creatures like us who are capable, as many intelligences may not be, of certain responses: capable of finding things smooth to the touch, bland to the taste, red to the eye. The concepts, as we may say, are response-dependent. i They are fashioned for beings with a capacity for certain responses and it is hard to see how creatures which lacked that capacity could get a proper, first-hand grasp of the concepts. The notion of response-dependence requires further definition, and this will be provided in ?2.2 But however it is understood, it enables us to identify a certain sort of doctrine about any range of concepts. This is the claim that the concepts in question, objective though they may at first seem, are really response-dependent notions: they conform in relevant respects to the general image of secondary quality concepts. That claim is meant to be descriptive of the concepts in question: to provide an analytical characterisation of how they function. (A variant on such a doctrine would argue, not that the concepts in ordinary use are responsedependent, but that the ordinary concepts should be given up in favour of response-dependent surrogates. The variant is a revisionary doctrine, where the original claim is descriptive.3) Most philosophers will acknowledge that some concepts are response-dependent: most will go along with the general view and think of secondary quality concepts in that way; and many will add apparently more objective concepts to the response-dependent camp. These philosophers all make a distinction between response-independent concepts that have a tenure in nature and response-dependent concepts whose tenure is tied to our interests or sensibilities; they differ only in where they draw the line between tenured and non-tenured concepts. Other philosophers reject that distinction, or at least this way of making it, and hold that

Realism and response-dependence

In the view of many, perhaps most, economists, to state a theory in terms of a formal model is an unambiguous improvement, rather than, as we see it, a matter of costs and benefits. The benefits (greater rigour, more precision, demonstrable results) are widely understood, while the costs are underexplored. The costs are associated with the way in which formalising an argument can change its meaning, i.e., with its non-neutrality. This paper will focus on the particular costs of formalism, associated with the obstacles formal ism poses for translating from (formalist) theory to practical application.

Formalism, logic and reality: a Keynesian analysis

Logic deals with the inevitable - those consequences which follow inescapably from a given set of premisses. This fact has caused it to be seen as different from other more self-questioning branches of philosophy. In this book, Stephen Read sets out to rescue logic from its undeserved reputation as an inflexible, dogmatic discipline by demonstrating that its technicalities and processes are founded on assumptions which are themselves amenable to philosophical investigation. He examines the fundamental principles of consequence, logical truth and correct inference within the context of logic, and shows that the principles by which we delineate consequences are themselves not guaranteed free from error. Central to the notion of truth is the beguiling issue of paradox. Its philosophical value, Read shows, lies in exposing the invalid assumption on which the paradox is built. Thinking About Logic also discusses logical puzzles which introduce questions relating to language, the world, and their relationship. While formal logic often employs its own esoteric language, the achievement of this book is to focus on those issues which raise exciting philosophical questions, and to make them intelligible to readers with no previous knowledge of logic.

Thinking about logic : an introduction to the philosophy of logic

The standard approach to what I call “proof-theoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of proof-theoretic semantics, this paper investigates in detail various notions of proof-theoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It is argued that these two sorts of concepts must be kept strictly apart.

/pdf/validity-concepts-in-proof-theoretic-semantics-1wxikmtmc6.pdf

Anti-realism and logic

Citations

The Oxford handbook of philosophy of mathematics and logic

Realism and response-dependence

Formalism, logic and reality: a Keynesian analysis

Thinking about logic : an introduction to the philosophy of logic

Validity Concepts in Proof-theoretic Semantics

Related Papers (5)

The logical basis of metaphysics

Truth and other enigmas

Frege: Philosophy of Language

The Runabout Inference-Ticket

Truth and Objectivity