Mary Tiles (born 1946 [1] ) is a philosopher and historian of mathematics and science. From 2006 until 2009, she served as chair of the philosophy department of the University of Hawaii at Manoa. [2] She retired in 2009. [3]
At Bristol University, Tiles obtained her B.A. in philosophy and mathematics in 1967, and her Ph.D. in philosophy in 1973, followed by a B.Phil. in philosophy in 1974 at Oxford and a M.A. in 1978 at Cambridge. After positions as lecturer and visiting associate professor at different institutions, Tiles became associate professor of philosophy at University of Hawaii at Manoa in 1989, and full professor in 1992. [4]
Tiles' area of work is primarily philosophy and history of logic, mathematics and science, with a special emphasis on French contributions to this area, e.g. by Gaston Bachelard, Georges Canguilhem, Bruno Latour, Michel Foucault, Pierre Bourdieu, Michel Serres, Jean-Claude Martzloff, Karine Chemla, Catherine Jami, and François Jullien. [4]
One of her publications is the 1989 book The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. As the subtitle suggests, it is an example of a book that treats the philosophy of mathematics as inseparable from historical concerns. [5] Despite some criticisms, for its lack of technical detail and correctness, and for pressing the author's philosophical agenda on its readers, [6] it has been recommended as an introductory textbook for undergraduates interested in the philosophy of mathematics. [7] [8] [9]
Georg Ferdinand Ludwig Philipp Cantor was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
Ian MacDougall Hacking was a Canadian philosopher specializing in the philosophy of science. Throughout his career, he won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, and was a member of many prestigious groups, including the Order of Canada, the Royal Society of Canada and the British Academy.
Gaston Bachelard was a French philosopher. He made contributions in the fields of poetics and the philosophy of science. To the latter, he introduced the concepts of epistemological obstacle and epistemological break. He influenced many subsequent French philosophers, among them Michel Foucault, Louis Althusser, Dominique Lecourt and Jacques Derrida, as well as the sociologists Pierre Bourdieu and Bruno Latour.
Early modern philosophy The early modern era of philosophy was a progressive movement of Western thought, exploring through theories and discourse such topics as mind and matter, is a period in the history of philosophy that overlaps with the beginning of the period known as modern philosophy. It succeeded the medieval era of philosophy. Early modern philosophy is usually thought to have occurred between the 16th and 18th centuries, though some philosophers and historians may put this period slightly earlier. During this time, influential philosophers included Descartes, Locke, Hume, and Kant, all of whom contributed to the current understanding of philosophy.
The sociology of scientific knowledge (SSK) is the study of science as a social activity, especially dealing with "the social conditions and effects of science, and with the social structures and processes of scientific activity." The sociology of scientific ignorance (SSI) is complementary to the sociology of scientific knowledge. For comparison, the sociology of knowledge studies the impact of human knowledge and the prevailing ideas on societies and relations between knowledge and the social context within which it arises.
In mathematical logic and philosophy, Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox arises from part of the Löwenheim–Skolem theorem; Thoralf Skolem was the first to discuss the seemingly contradictory aspects of the theorem, and to discover the relativity of set-theoretic notions now known as non-absoluteness. Although it is not an actual antinomy like Russell's paradox, the result is typically called a paradox and was described as a "paradoxical state of affairs" by Skolem.
Sandra G. Harding is an American philosopher of feminist and postcolonial theory, epistemology, research methodology, and philosophy of science. She directed the UCLA Center for the Study of Women from 1996 to 2000, and co-edited Signs: Journal of Women in Culture and Society from 2000 to 2005. She is currently a Distinguished Professor Emeritus of Education and Gender Studies at UCLA and a Distinguished Affiliate Professor of Philosophy at Michigan State University. In 2013 she was awarded the John Desmond Bernal Prize by the Society for the Social Studies of Science (4S).
Michael David Resnik is a leading contemporary American philosopher of mathematics.
Originally, fallibilism is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified, or that neither knowledge nor belief is certain. The term was coined in the late nineteenth century by the American philosopher Charles Sanders Peirce, as a response to foundationalism. Theorists, following Austrian-British philosopher Karl Popper, may also refer to fallibilism as the notion that knowledge might turn out to be false. Furthermore, fallibilism is said to imply corrigibilism, the principle that propositions are open to revision. Fallibilism is often juxtaposed with infallibilism.
Richard Newell Boyd was an American philosopher, who spent most of his career teaching philosophy at Cornell University where he was Susan Linn Sage Professor of Philosophy and Humane Letters. He specialized in epistemology, the philosophy of science, language, and mind.
Helen Elizabeth Longino is an American philosopher of science who has argued for the significance of values and social interactions to scientific inquiry. She has written about the role of women in science and is a central figure in feminist epistemology and social epistemology. She is the Clarence Irving Lewis Professor of Philosophy, Emerita, at Stanford University. In 2016, she was elected to the American Academy of Arts and Sciences.
Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions "What is knowledge?", "How is knowledge acquired?", "What do people know?", "How do we know what we know?", and "Why do we know what we know?". Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims.
Feminist epistemology is an examination of epistemology from a feminist standpoint.
John Corcoran was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on concepts such as the nature of inference, relations between conditions, argument-deduction-proof distinctions, the relationship between logic and epistemology, and the place of proof theory and model theory in logic. Nine of Corcoran's papers have been translated into Spanish, Portuguese, Persian, and Arabic; his 1989 "signature" essay was translated into three languages. Fourteen of his papers have been reprinted; one was reprinted twice.
Tamara Horowitz was an American philosopher who worked on epistemology, feminist philosophy and the philosophy of science. She spent much of her career at the University of Pittsburgh, and was appointed chair of the philosophy department there in September 1999, but died a few months later.
Timothy Joel McGrew is a professor of philosophy at Western Michigan University, and the chair of the department of philosophy there. His research interests include epistemology, the history and philosophy of science, and the philosophy of religion. He is a specialist in the philosophical applications of probability theory.
Feminist philosophy of science is a branch of feminist philosophy that seeks to understand how the acquirement of knowledge through scientific means has been influenced by notions of gender identity and gender roles in society. Feminist philosophers of science question how scientific research and scientific knowledge itself may be influenced and possibly compromised by the social and professional framework within which that research and knowledge is established and exists. The intersection of gender and science allows feminist philosophers to reexamine fundamental questions and truths in the field of science to reveal how gender biases may influence scientific outcomes. The feminist philosophy of science has been described as being located "at the intersections of the philosophy of science and feminist science scholarship" and has attracted considerable attention since the 1980s.
Alan Richard White was an analytic philosopher who worked mainly in epistemology, the philosophy of mind, and, latterly, legal philosophy. Peter Hacker notes that he was "the most skillful developer of Rylean ... ideas in philosophical psychology" and that "if anyone surpassed Austin in subtlety and refinement in the discrimination of grammatical differences, it was White." Richard Swinburne remarks that "during the heyday of 'ordinary language philosophy' no tongue practised it better."
Richard Anthony Fumerton is a Canadian American philosopher and professor of philosophy at the University of Iowa with research interests in epistemology, metaphysics, philosophy of mind and value theory. He has been cited as an influential expert on the position of "metaepistemological scepticism". He received his B.A. in philosophy from the University of Toronto in 1971 and his M.A. and PhD from Brown University in 1973 and 1974, respectively. He has been the F. Wendell Miller Professor of Philosophy at the University of Iowa since 2003.