The Process-Product Distinction and the Normative Implications of Logic (original) (raw)

Mathematics, Logic, and their Philosophies

Springer eBooks, 2021

Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal frameworks, for example, constructive type theory, deontic logics, dialogical logics, epistemic logics, modal logics, and proof-theoretical semantics, have the potential to cast new light on basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific systematic and historic insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity. This book series is indexed in SCOPUS.

Corcoran and Shapiro review “What is Mathematical Logic?” updated PDF.

Corcoran and Shapiro review “What is Mathematical Logic?” updated PDF. 1976. Crossley, J. N. What is Mathematical Logic? OxfordUP 1972. Philosophy of Science 43, 301–302 (Co-author: S. Shapiro). J This book—still in print—pretends to tell the clueless neophyte what mathematical logic is—and in 82 small pages. The idea, we do not say fact, that someone knowledgeable in the subject thinks this possible is astounding. As we show in this review and in another much longer review, it is unlikely that Oxford University Press even copy-edited the book much less had it vetted by a competent logician. People who think that Oxford University Press has recently lowered its standards should read this book—or at least the reviews. 1978. Crossley on Mathematical Logic (essay review, Co-author: Stewart Shapiro), Philosophia 8, 79–94. 1988. Ensayo-Resenas: Introduciendo La Logica Matematica, Mathesis X, 133–150. Spanish translation by A. Garciadiego of revised version of “Crossley on Mathematical Logic”, Philosophia 8 (1978) 79–94. Co-author: S. Shapiro.

Reasoning in Mathematics and Machines: The Place of Mathematical Logic in Mathematical Understanding

Mathematical logic and mechanical reasoning have turned out to be largely irrelevant to the practice of mathematics, and to our philosophical understanding of the nature of that practice. My aim is to understand how this can be. We will see that the problem is not merely that the logician formalizes. Nor even is it, as Poincare argues, that logicians replace all distinctively mathematical steps of reasoning with strictly logical ones. Instead, as will be shown by way of a variety of examples, the problem lies in the way the symbolic language of mathematical logic has been read.

The emergence of logic in mathematics and its influence on learners' cognition and way of thinking

This article sheds light on the single phrase, logical thinking, which came to be understood in so many diverse ways. To assist explain the many distinct meanings, how they arose, and how they are connected, we trace the emergence and evolution of logical thinking in mathematics. This article is also, to some extent, a description of a movement that arose outside of philosophy's mainstream, and whose beginnings lay in a desire to make logic practical and an essential part of learners' lives.

Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method

Springer, Cham, 2013

Despite strenuous efforts by its proponents, the contemporary form of logic, mathematical logic, has generally failed to convince mathematicians, natural scientists and human scientists of its relevance to their work, increasingly so in the last few decades. This contrasts with the reputation logic enjoyed in antiquity, not only as one of the main parts of philosophy, but also as a supplier of instruments for the sciences. The purpose of this book is to explain how the present condition of logic came about and to propose an alternative to it. To this end, the book first gives an overview of how logic and its relation to the scientific method have been conceived in antiquity and in the modern age, because this provides indications for a new approach to the subject. Then the book proposes a new view of logic and its relation to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also proposes a new view of philosophy and its relation to knowledge, because seeing logic in a wider context helps to place it on a more satisfactory basis. In terms of the proposed new view, logic is primarily a logic of discovery. Accordingly, the book deals with the rules of discovery.

Logic as reasoning: On the government of logic and mathematics

It is a widespread thought that the usefulness of Logic and Mathematics in natural sciences portends something about the material world—that materiality, on this view, is structured by (or anyway compliant with strictures or constraints laid down by) these formal disciplines. Contrary to that thought, this paper argues that Logic (and by extension mathematics too) has no import whatsoever for the material world. Equally, the material world is neutral vis-à-vis matters of logic and mathematics. The fundamental connection is merely that logic (and mathematics too) render thought about the material world possible. The arguments of this essay will be directly opposed to those of Gila Sher, although there is much to agree with in her views. Built upon principles of Phenomenology, the analysis of Logical truth that will emerge here will be analogous to H.L.A. Hart’s analysis of legal authority; it too will invoke the idea of a rule of recognition.

Perspectives On Mathematical Practices

Springer eBooks, 2007

Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light no basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.

Against the Judgment-Dependence of Mathematics and Logic

Erkenntnis, 2012

Although the case for the judgment-dependence of many other domains has been pored over, surprisingly little attention has been paid to mathematics and logic. This paper presents two dilemmas for a judgment-dependent account of these areas. First, the extensionality-substantiality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the substantiality condition (roughly: non-vacuous specification). Second, the extensionality-extremality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the extremality condition (roughly: absence of independent explanation). The paper concludes with a moral concerning the judgment-dependence of a posteriori areas of discourse that emerges from consideration of these two a priori cases. A. Paseau (&)