Willard Van Orman Quine was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978.
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
Hilary Whitehall Putnam was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century. He made significant contributions to philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. Outside philosophy, Putnam contributed to mathematics and computer science. Together with Martin Davis he developed the Davis–Putnam algorithm for the Boolean satisfiability problem and he helped demonstrate the unsolvability of Hilbert's tenth problem.
"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a 1960 article by the physicist Eugene Wigner. In the paper, Wigner observes that a physical theory's mathematical structure often points the way to further advances in that theory and even to empirical predictions.
Sydney Chapman was a British mathematician and geophysicist. His work on the kinetic theory of gases, solar-terrestrial physics, and the Earth's ozone layer has inspired a broad range of research over many decades.
Hartry H. Field is an American philosopher. He is Silver Professor of Philosophy at New York University; he is a notable contributor to philosophy of science, philosophy of mathematics, epistemology, and philosophy of mind.
Models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge. The philosopher Wesley C. Salmon described scientific inquiry:
The search for scientific knowledge ends far back into antiquity. At some point in the past, at least by the time of Aristotle, philosophers recognized that a fundamental distinction should be drawn between two kinds of scientific knowledge—roughly, knowledge that and knowledge why. It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why. Knowledge of the former type is descriptive; knowledge of the latter type is explanatory. It is explanatory knowledge that provides scientific understanding of the world.
Brian John Copeland is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand, and author of books on the computing pioneer Alan Turing.
Model-dependent realism is a view of scientific inquiry that focuses on the role of scientific models of phenomena. It claims reality should be interpreted based upon these models, and where several models overlap in describing a particular subject, multiple, equally valid, realities exist. It claims that it is meaningless to talk about the "true reality" of a model as we can never be absolutely certain of anything. The only meaningful thing is the usefulness of the model. The term "model-dependent realism" was coined by Stephen Hawking and Leonard Mlodinow in their 2010 book, The Grand Design.
Stephan Hartmann is a German philosopher and Professor of Philosophy of Science at Ludwig Maximilian University of Munich, known for his contributions to formal epistemology.
Christian List is a German philosopher and political scientist who serves as professor of philosophy and decision theory at the Ludwig Maximilian University of Munich and co-director of the Munich Center for Mathematical Philosophy. He was previously professor of political science and philosophy at the London School of Economics. List's research interests relate to social choice theory, formal epistemology, political philosophy, and the philosophy of social science.
Australian philosophy refers to the philosophical tradition of the people of Australia and of its citizens abroad. Academic philosophy has been mostly pursued in universities. It has been broadly in the tradition of Anglo-American analytic philosophy, but has also had representatives of a diverse range of other schools, such as idealism, Catholic neo-scholasticism, Marxism, and continental, feminist and Asian philosophy.
An Introduction to the Philosophy of Mathematics is a 2012 textbook on the philosophy of mathematics by Mark Colyvan. It has a focus on issues in contemporary philosophy, such as the mathematical realism–anti-realism debate and the philosophical significance of mathematical practice, and largely skips over historical debates. It covers a range of topics in contemporary philosophy of mathematics including various forms of mathematical realism, the Quine–Putnam indispensability argument, mathematical fictionalism, mathematical explanation, the "unreasonable effectiveness of mathematics", paraconsistent mathematics, and the role of mathematical notation in the progress of mathematics. The book was praised as accessible and well-written and the reaction to its contemporary focus was largely positive, although some academic reviewers felt that it should have covered the historical debates over logicism, formalism and intuitionism in more detail. Other aspects of the book that received praise were its coverage of mathematical explanation, its appeal to mathematicians and other non-philosophers, and its discussion questions and further readings, whilst its epilogue and short length received a more mixed reception.
The Indispensability of Mathematics is a 2001 book by Mark Colyvan in which he examines the Quine–Putnam indispensability argument in the philosophy of mathematics. This thesis is based on the premise that mathematical entities are placed on the same ontological foundation as other theoretical entities indispensable to our best scientific theories.
The Quine–Putnam indispensability argument, also known simply as the indispensability argument, is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. Named after the philosophers Willard Quine and Hilary Putnam, it is one of the most important arguments in the philosophy of mathematics and is widely considered to be one of the best arguments for platonism.
Philosophy of ecology is a concept under the philosophy of science, which is a subfield of philosophy. Its main concerns centre on the practice and application of ecology, its moral issues, and the intersectionality between the position of humans and other entities. This topic also overlaps with metaphysics, ontology, and epistemology, for example, as it attempts to answer metaphysical, epistemic and moral issues surrounding environmental ethics and public policy.
Russell Marcus is a philosopher specializing in philosophy of mathematics and the pedagogy of philosophy. He is Chair of Philosophy at Hamilton College and vice president of the American Association of Philosophy Teachers.
Friederike Moltmann is a linguist and philosopher. She has done pioneering work at the intersection of philosophy and linguistics, especially on the interface between metaphysics and natural language semantics, but also on the interface between philosophy of mind and mathematics. She is an important proponent of natural language ontology. She is currently Research Director at the French National Centre for Scientific Research (CNRS) in Paris.
In 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. 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.
David Liggins is a philosopher at the University of Manchester with research interests in metaphysics and philosophy of mathematics.
