In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality.
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 makes this branch of philosophy broad and unique.
Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical position that interprets a complex system as the sum of its parts.
In computer science and information science, an ontology encompasses a representation, formal naming, and definition of the categories, properties, and relations between the concepts, data, and entities that substantiate one, many, or all domains of discourse. More simply, an ontology is a way of showing the properties of a subject area and how they are related, by defining a set of concepts and categories that represent the subject.
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.
Religious philosophy is philosophical thinking that is influenced and directed as a consequence to teachings from a particular religion. It can be done objectively, but may also be done as a persuasion tool by believers in that faith. Religious philosophy is concerned with the nature of religion, theories of salvation, conceptions of god, gods, and/or the divine.
Ian MacDougall Hacking is a Canadian philosopher specializing in the philosophy of science. Throughout his career, he has won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, and been a member of many prestigious groups, including the Order of Canada, the Royal Society of Canada and the British Academy.
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly attested from the late 7th century BC to the 4th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, from Anatolia (Turkey) to Italy and North Africa, but were united by Greek culture and the Greek language. The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.
The philosophy of biology is a subfield of philosophy of science, which deals with epistemological, metaphysical, and ethical issues in the biological and biomedical sciences. Although philosophers of science and philosophers generally have long been interested in biology, philosophy of biology only emerged as an independent field of philosophy in the 1960s and 1970s, associated with the research of David Hull. Philosophers of science then began paying increasing attention to biology, from the rise of Neodarwinism in the 1930s and 1940s to the discovery of the structure of DNA in 1953 to more recent advances in genetic engineering. Other key ideas include the reduction of all life processes to biochemical reactions, and the incorporation of psychology into a broader neuroscience.
Michael David Resnik is a leading contemporary American philosopher of mathematics.
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the number 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any natural number is defined by its respective place in that theory. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
Critical realism is a philosophical approach to understanding science, and in particular social science, initially developed by Roy Bhaskar (1944–2014). It specifically opposes forms of empiricism and positivism by viewing science as concerned with identifying causal mechanisms. In the last decades of the twentieth century it also stood against various forms of postmodernism and poststructuralism by insisting on the reality of objective existence. In contrast to positivism's methodological foundation, and poststructuralism's epistemological foundation, critical realism insists that (social) science should be built from an explicit ontology. Critical realism is one of a range of types of philosophical realism, as well as forms of realism advocated within social science such as analytic realism and subtle realism.
The philosophy of medicine is a branch of philosophy that explores issues in theory, research, and practice within the field of health sciences. More specifically in topics of epistemology, metaphysics, and medical ethics, which overlaps with bioethics. Philosophy and medicine, both beginning with the ancient Greeks, have had a long history of overlapping ideas. It was not until the nineteenth century that the professionalization of the philosophy of medicine came to be. In the late twentieth century, debates among philosophers and physicians ensued of whether the philosophy of medicine should be considered a field of its own from either philosophy or medicine. A consensus has since been reached that it is in fact a distinct discipline with its set of separate problems and questions. In recent years there have been a variety of university courses, journals, books, textbooks and conferences dedicated to the philosophy of medicine.
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, which is also known 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. It was named after the philosophers Willard Quine and Hilary Putnam, 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.
David Liggins is a philosopher at the University of Manchester with research interests in metaphysics and philosophy of mathematics.
