A. Thomas Tymoczko (September 1, 1943 – August 8, 1996) was a philosopher specializing in logic and the philosophy of mathematics. He taught at Smith College in Northampton, Massachusetts from 1971 until his death from stomach cancer in 1996.
Logic is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, thus, hence, ergo, and so on.
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 finding 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.
Smith College is a private women's liberal arts college in Northampton, Massachusetts. Although its undergraduate programs are open to women only, its graduate and certificate programs are also open to men. It is the largest member of the Seven Sisters. Smith is also a member of the Five Colleges Consortium, which allows its students to attend classes at four other Pioneer Valley institutions: Mount Holyoke College, Amherst College, Hampshire College, and the University of Massachusetts Amherst. In its 2018 edition, U.S. News & World Report ranked it tied for 11th best among National Liberal Arts Colleges.
His publications include New Directions in the Philosophy of Mathematics, an edited collection of essays for which he wrote individual introductions, and Sweet Reason: A Field Guide to Modern Logic, co-authored by Jim Henle. In addition, he published a number of philosophical articles, such as "The Four-Color Problem and its Philosophical Significance", which argues that the increasing use of computers is changing the nature of mathematical proof.
He is considered to be a member of the fallibilist school in philosophy of mathematics. Philip Kitcher dubbed this school the "maverick" tradition in the philosophy of mathematics. (Paul Ernest)[ citation needed ]
Broadly speaking, fallibilism is the philosophical claim that no belief can have justification which guarantees the truth of the belief. However, not all fallibilists believe that fallibilism extends to all domains of knowledge.
Philip Stuart Kitcher is a British philosophy professor teaching at Columbia University who specialises in the philosophy of science, the philosophy of biology, the philosophy of mathematics, the philosophy of literature, and, more recently, pragmatism.
Paul Ernest is a contributor to the social constructivist philosophy of mathematics.
He graduated from Harvard University.
Tymoczko was married to comparative literature scholar Maria Tymoczko of the University of Massachusetts Amherst. Their three children include music composer Dmitri Tymoczko and Smith College mathematics professor Julianna Tymoczko.
Maria Fleming Tymoczko is a scholar of comparative literature who has written about translation, medieval Celtic literature, and modern Irish literature including the works of James Joyce. She is a professor of comparative literature at the University of Massachusetts Amherst, and the former president of the Celtic Studies Association of North America. She is known for her calls for a more international and multicultural perspective on translation.
The University of Massachusetts Amherst is a public research and land-grant university in Amherst, Massachusetts. It is the flagship campus of the University of Massachusetts system. UMass Amherst has an annual enrollment of approximately 1,300 faculty members and more than 30,000 students. It was ranked 24th best public university and 64th best national university by U.S. World & News Report in its 2020 rankings.
Dmitri Tymoczko is a composer and music theorist. His music, which draws on rock, jazz, and romanticism, has been performed by ensembles such as the Amernet String Quartet, the Brentano Quartet, Janus, Newspeak, the San Francisco Contemporary Players, the Pacifica Quartet, and the pianist Ursula Oppens. As a theorist, he has published more than two dozen articles dealing with topics related to contemporary tonality, including scales, voice leading, and functional harmonic norms. His article "The Geometry of Musical Chords," was the first music-theory article ever published by the journal Science.
Kurt Friedrich Gödel was an Austro-Hungarian-born Austrian, and later American, logician, mathematician, and analytic philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.
George Boole was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854) which contains Boolean algebra. Boolean logic is credited with laying the foundations for the information age. Boole maintained that:
No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He worked as a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though largely ignored during his lifetime, Giuseppe Peano (1858–1932) and Bertrand Russell (1872–1970) introduced his work to later generations of philosophers.
Alonzo Church was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem. He also worked on philosophy of language.
Peter Thomas Geach was a British philosopher and professor of logic at the University of Leeds. His areas of interest were philosophical logic, ethics, history of philosophy, philosophy of religion and the theory of identity.
Jan Łukasiewicz was a Polish logician and philosopher born in Lemberg, a city in the Galician kingdom of Austria-Hungary. His work centred on philosophical logic, mathematical logic, and history of logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Łukasiewicz of a revolutionary paradigm. The Łukasiewicz approach was reinvigorated in the early 1970s in a series of papers by John Corcoran and Timothy Smiley—which inform modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009. Łukasiewicz is regarded as one of the most important historians of logic.
Hao Wang was a logician, philosopher, mathematician, and commentator on Kurt Gödel.
Henry Nelson Goodman was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics.
Carl Gustav "Peter" Hempel was a German writer and philosopher. He was a major figure in logical empiricism, a 20th-century movement in the philosophy of science. He is especially well known for his articulation of the deductive-nomological model of scientific explanation, which was considered the "standard model" of scientific explanation during the 1950s and 1960s. He is also known for the raven paradox.
The Lwów–Warsaw School was a Polish school of thought founded by Kazimierz Twardowski in 1895 in Lemberg, Austro-Hungary.
Henry Babcock Veatch Jr. was an American philosopher.
Daniel Kolak is a Croatian-American philosopher who works primarily in philosophy of mind, personal identity, cognitive science, philosophy of science, philosophy of mathematics, philosophy of logic, philosophy of religion, and aesthetics. He is professor of philosophy at the William Paterson University of New Jersey and an Affiliate of the Rutgers University Center for Cognitive Science (RuCCS). Kolak is the founder of the philosophical therapy known as cognitive dynamics.
Timothy John Smiley FBA is a British philosopher, appointed Emeritus Knightbridge Professor of Philosophy at Clare College, Cambridge University. He works primarily in philosophy of mathematics and logic.
Western philosophy refers to the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with Greek philosophy of the pre-Socratics such as Thales and Pythagoras, and eventually covering a large area of the globe. The word philosophy itself originated from the Ancient Greek philosophía (φιλοσοφία), literally, "the love of wisdom".
Thomas McKay is an American philosopher currently Professor of Philosophy and Director of Graduate Studies at the Department of Philosophy of Syracuse University. He was chairman of the Department there from 1995-2002. He received his B.A. from Swarthmore College in 1969, his M.A. from University of Massachusetts Amherst in 1972, and his Ph.D., also from the University of Massachusetts, 1974, for a dissertation on "Essentialism and Quantified Modal Logic: Quine's Argument and Kripke's Semantics"
Adrian William Moore is a British philosopher and broadcaster. He is Professor of Philosophy at the University of Oxford and Tutorial Fellow of St Hugh's College, Oxford. His main areas of interest are Kant, Wittgenstein, history of philosophy, metaphysics, philosophy of mathematics, philosophy of logic and language, ethics and philosophy of religion.
Julianna Sophia Tymoczko is an American mathematician whose research connects algebraic geometry and algebraic combinatorics, including representation theory, Schubert calculus, equivariant cohomology, and Hessenberg varieties. She is a professor of mathematics at Smith College.
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