Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools (...) to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science. (shrink)

Rudolf Carnap is widely regarded as one of the most important philosophers of the twentieth century. Born in Germany and later a US citizen, he was a founder of the philosophical movement known as Logical Empiricism. He was strongly influenced by a number of different philosophical traditions, and also by the German Youth Movement, the First World War, and radical socialism. This book places his central ideas in a broad cultural, political and intellectual context, showing how he synthesised many different (...) currents of thought to achieve a philosophical perspective that remains strikingly relevant in the twenty-first century. Its rich account of a philosopher's response to his times will appeal to all who are interested in the development of philosophy in the twentieth century. (shrink)

Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s one familiar example. When we start learning computability theory, we are introduced to the idea of an algorithmically computable function (...) (from numbers to numbers) – i.e. one whose value for any given input can be determined by a step-by-step calculating procedure, where each step is fully determined by some antecedently given finite set of calculating rules. We are told that we are to abstract from practical considerations of how many steps will be needed and how much ink will be spilt in the process, so long as everything remains finite. We are also told that each step is to be ‘small’ and the rules governing it must be ‘simple’, available to a cognitively limited calculating agent: for we want an algorithmic procedure, step-by-minimal-step, to be idiot-proof. For a classic elucidation of this kind, see e.g. Rogers (1967, pp. 1–5). Church’s Thesis, in one form, then claims this informally explicated concept in fact has a perfectly precise extension, the set of recursive functions. Church’s Thesis can be supported in a quasi-empirical way, by the failure of our searches for counterexamples. It can be supported too in a more principled way, by the observation that different appealing ways of sharpening up the informal chararacterization of algorithmic computability end up specifying the same set of recursive functions. But such considerations fall short of a demonstration of the Thesis. So is there a different argumentative strategy we could use, one that could lead to a proof? Sometimes it is claimed that there just can’t be, because you can never really prove results involving an informal concept like algorithmic computability.. (shrink)

In this collection of previously published essays, Sally Haslanger draws on insights from feminist and critical race theory and on the resources of contemporary analytic philosophy to develop the idea that gender and race are positions ...

Bishop and Trout here present a unique and provocative new approach to epistemology. Their approach aims to liberate epistemology from the scholastic debates of standard analytic epistemology, and treat it as a branch of the philosophy of science. The approach is novel in its use of cost-benefit analysis to guide people facing real reasoning problems and in its framework for resolving normative disputes in psychology. Based on empirical data, Bishop and Trout show how people can improve their reasoning by relying (...) on Statistical Prediction Rules. They then develop and articulate the positive core of the book. Their view, Strategic Reliabilism, claims that epistemic excellence consists in the efficient allocation of cognitive resources to reliable reasoning strategies, applied to significant problems. The last third of the book develops the implications of this view for standard analytic epistemology; for resolving normative disputes in psychology; and for offering practical, concrete advice on how this theory can improve real people's reasoning. This is a truly distinctive and controversial work that spans many disciplines and will speak to an unusually diverse group, including people in epistemology, philosophy of science, decision theory, cognitive and clinical psychology, and ethics and public policy. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

Analysis has always been at the heart of philosophical method, but it has been understood and practised in many different ways. Perhaps, in its broadest sense, it might be defined as a process of isolating or working back to what is more fundamental by means of which something, initially taken as given, can be explained or reconstructed. The explanation or reconstruction is often then exhibited in a corresponding process of synthesis. This allows great variation in specific method, however. The aim (...) may be to get back to basics, but there may be all sorts of ways of doing this, each of which might be called ‘analysis’. The dominance of ‘analytic’ philosophy in the Englishspeaking world, and increasingly now in the rest of the world, might suggest that a consensus has formed concerning the role and importance of analysis. This assumes, though, that there is agreement on what ‘analysis’ means, and this is far from clear. On the other hand, Wittgenstein's later critique of analysis in the early (logical atomist) period of analytic philosophy, and Quine's attack on the analytic-synthetic distinction, for example, have led some to claim that we are now in a ‘post-analytic’ age. Such criticisms, however, are only directed at particular conceptions of analysis. If we look at the history of philosophy, and even if we just look at the history of analytic philosophy, we find a rich and extensive repertoire of conceptions of analysis which philosophers have continually drawn upon and reconfigured in different ways. Analytic philosophy is alive and well precisely because of the range of conceptions of analysis that it involves. It may have fragmented into various interlocking subtraditions, but those subtraditions are held together by both their shared history and their methodological interconnections. It is the aim of this article to indicate something of.. (shrink)

Abstract Recent criticisms of intuition from experimental philosophy and elsewhere have helped undermine the authority of traditional conceptual analysis. As the product of more empirically informed philosophical methodology, this result is compelling and philosophically salutary. But the negative critiques rarely suggest a positive alternative. In particular, a normative account of concept determination—how concepts should be characterized—is strikingly absent from such work. Carnap's underappreciated theory of explication provides such a theory. Analyses of complex concepts in empirical sciences illustrates and supports this (...) claim, and counteracts the charge explication is only suitable for highly mathematical, axiomatic contexts. Explication is also defended against the influential criticism it is “philosophically unilluminating”. Content Type Journal Article Category Original paper in Philosophy of Science Pages 1-19 DOI 10.1007/s13194-011-0027-5 Authors James Justus, Philosophy Department, Florida State University and University of Sydney, Tallahassee, FL 32306, USA Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912. (shrink)

Our aim in this paper is to bring the woefully neglected literature on predictive modeling to bear on some central questions in the philosophy of science. The lesson of this literature is straightforward: For a very wide range of prediction problems, statistical prediction rules (SPRs), often rules that are very easy to implement, make predictions than are as reliable as, and typically more reliable than, human experts. We will argue that the success of SPRs forces us to reconsider our views (...) about what is involved in understanding, explanation, good reasoning, and about how we ought to do philosophy of science. (shrink)

How can formal methods be applied to philosophical problems that involve informal concepts of ordinary language? Carnap answered this question by describing a methodology that he called “explication." Strawson objected that explication changes the subject and does not address the original philosophical problem; this paper shows that Carnap’s response to that objection was inadequate and offers a better response. More recent criticisms of explication by Boniolo and Eagle are shown to rest on misunderstandings of the nature of explication. It is (...) concluded that explication is an appropriate methodology for formal philosophy. (shrink)

This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...) so as to shed new light on the relevant strengths and limits of higher-order logic. (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)