Mathematical practiceMathematical practice comprises the working practices of professional mathematicians: selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof are convincing, and seeking peer review and publication, as opposed to the end result of proven and published theorems. Philip Kitcher has proposed a more formal definition of a mathematical practice, as a quintuple. His intention was primarily to document mathematical practice through its historical changes.
Lee SmolinLee Smolin (ˈsmoʊlɪn; born June 6, 1955) is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo and a member of the graduate faculty of the philosophy department at the University of Toronto. Smolin's 2006 book The Trouble with Physics criticized string theory as a viable scientific theory. He has made contributions to quantum gravity theory, in particular the approach known as loop quantum gravity.
Constructivism (philosophy of science)Constructivism is a view in the philosophy of science that maintains that scientific knowledge is constructed by the scientific community, which seeks to measure and construct models of the natural world. According to the constructivist, natural science, therefore, consists of mental constructs that aim to explain sensory experience and measurements. According to constructivists, the world is independent of human minds, but knowledge of the world is always a human and social construction.
MathematicismMathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy'. or else it is the epistemological view that reality is fundamentally mathematical. The term has been applied to a number of philosophers, including Pythagoras and René Descartes although the term is not used by themselves. The role of mathematics in Western philosophy has grown and expanded from Pythagoras onwards.
Introduction to Mathematical PhilosophyIntroduction to Mathematical Philosophy is a book (1919 first edition) by philosopher Bertrand Russell, in which the author seeks to create an accessible introduction to various topics within the foundations of mathematics. According to the preface, the book is intended for those with only limited knowledge of mathematics and no prior experience with the mathematical logic it deals with. Accordingly, it is often used in introductory philosophy of mathematics courses at institutions of higher education.
Theoretical philosophyThe modern division of philosophy into theoretical philosophy and practical philosophy has its origin in Aristotle's categories of natural philosophy and moral philosophy. The one has theory for its object, and the other practice. forcetoc In Denmark, Finland, Germany, Netherlands, Sweden, and United States courses in theoretical and practical philosophy are taught separately, and are separate degrees.
Numerical cognitionNumerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics, is primarily concerned with empirical questions.
Aristotelian realist philosophy of mathematicsIn the philosophy of mathematics, Aristotelian realism holds that mathematics studies properties such as symmetry, continuity and order that can be immanently realized in the physical world (or in any other world there might be). It contrasts with Platonism in holding that the objects of mathematics, such as numbers, do not exist in an "abstract" world but can be physically realized. It contrasts with nominalism, fictionalism, and logicism in holding that mathematics is not about mere names or methods of inference or calculation but about certain real aspects of the world.
Anti-psychologismIn logic, anti-psychologism (also logical objectivism or logical realism) is a theory about the nature of logical truth, that it does not depend upon the contents of human ideas but exists independent of human ideas. The anti-psychologistic treatment of logic originated in the works of Immanuel Kant and Bernard Bolzano. The concept of logical objectivism or anti-psychologism was further developed by Johannes Rehmke (founder of Greifswald objectivism) and Gottlob Frege (founder of logicism the most famous anti-psychologist in the philosophy of mathematics), and has been the centre of an important debate in early phenomenology and analytical philosophy.
