Author: J. Franklin
Release Date: 2014-04-09
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Author: James Franklin
Publisher: Palgrave Macmillan
Release Date: 2014-04-08
An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.
Author: James Franklin
Publisher: JHU Press
Release Date: 2015-07-09
How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk. -- Giora Hon
Author: Stewart Shapiro
Publisher: Oxford University Press
Release Date: 1997-08-07
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter
Author: James Franklin
Publisher: Encounter Books
Release Date: 2009-11-01
To scientists, the tsunami of relativism, scepticism, and postmodernism that washed through the humanities in the twentieth century was all water off a duck’s back. Science remained committed to objectivity and continued to deliver remarkable discoveries and improvements in technology. In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. He begins with an account of the nature of evidence, where science imitates but extends commonsense and legal reasoning in basing conclusions solidly on inductive reasoning from facts. After a brief survey of the furniture of the world as science sees it—including causes, laws, dispositions and force fields as well as material things—Franklin describes colorful examples of discoveries in the natural, mathematical, and social sciences and the reasons for believing them. He examines the limits of science, giving special attention both to mysteries that may be solved by science, such as the origin of life, and those that may in principle be beyond the reach of science, such as the meaning of ethics. What Science Knows will appeal to anyone who wants a sound, readable, and well-paced introduction to the intellectual edifice that is science. On the other hand it will not please the enemies of science, whose willful misunderstandings of scientific method and the relation of evidence to conclusions Franklin mercilessly exposes.
This volume breaks new ground by investigating the ethics of vulnerability. Drawing on various ethical traditions, the contributors explore the nature of vulnerability, the responsibilities owed to the vulnerable, and by whom.
Author: Thomas S. Kuhn
Publisher: University of Chicago Press
Release Date: 2012-04-18
A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.
Author: Charles S. Peirce
Publisher: Indiana University Press
Release Date: 2010-08-19
The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.
"Theology and the Cartesian Doctrine of Freedom, now for the first time available in English,was Étienne Gilson's doctoral thesis and part of a larger project to show the medieval roots of Descartes at a time when the very existence of medieval philosophy was often ignored. Young Descartes was sent to La Flèche, one of the Jesuits schools that offered a complete philosophical program, and Descartes would have had the same philosophical training as a Jesuit. There is some controversy about the exact dates of Descartes's stay at La Flèche and consequently about his philosophy instructor. By Gilson's calculations François Véron taught Descartes for three years. Véron eventually left the Jesuits to be free to engage in extraordinarily aggressive anti-Calvinist polemics. If anything, Véron's overbearing manner may have contributed to Descartes antipathy toward Scholastic philosophy. (Whatever Descartes's objections to its philosophy curriculum, later in life he recommended la Flèche as the best school in France.) Descartes,s great intellectual mission in life was not his mathematics but his physics, which was understood as a part of philosophy. We see him navigate the shoals of heated theological and religious strife in his attempt to articulate the metaphysical foundations(and in particular a philosophical vision of God) for his physics or theory of nature. As a layman, he always pleaded ignorance in technically theological matters. He presented himself as a loyal Catholic, quite sincerely in the portrait Gilson paints."--
Author: H. F. Cohen
Publisher: Amsterdam University Press
Release Date: 2010
Once upon a time 'The Scientific Revolution of the 17th century' was an innovative concept that inspired a stimulating narrative of how modern science came into the world. Half a century later, what we now know as 'the master narrative' serves rather as a strait-jacket - so often events and contexts just fail to fit in. No attempt has been made so far to replace the master narrative. H. Floris Cohen now comes up with precisely such a replacement. Key to his path-breaking analysis-cum-narrative is a vision of the Scientific Revolution as made up of six distinct yet narrowly interconnected, revolutionary transformations, each of some twenty-five to thirty years' duration. This vision enables him to explain how modern science could come about in Europe rather than in Greece, China, or the Islamic world. It also enables him to explain how half-way into the 17th century a vast crisis of legitimacy could arise and, in the end, be overcome.