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Quine–Putnam Indispensability Argument
The Quine–Putnam 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, and is one of the most important arguments in the philosophy of mathematics. Although elements of the indispensability argument may have originated with thinkers such as Gottlob Frege and Kurt Gödel, Quine's development of the argument was unique for introducing to it a number of his philosophical positions such as naturalism, confirmational holism, and the criterion of ontological commitment. Putnam gave Quine's argument its first detailed formulation in his 1971 book ''Philosophy of Logic''. He later came to disagree with various aspects of Quine's thinking, however, and formulated his own indispensability argument based on the no miracles argument in the philosophy of science. A standard for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willard Quine
Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) 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. Quine was a teacher of logic and set theory. Quine was famous for his position that first order logic is the only kind worthy of the name, and developed his own system of mathematics and set theory, known as New Foundations. In philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the Quine–Putnam indispensability argument, an argument for the reality of mathematical entities.Colyvan, Mark"Indispensability Arguments in the Philosophy of Mathematics" The Stanford Encycloped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penelope Maddy
Penelope Maddy (born 4 July 1950) is an American philosopher. Maddy is Emerita UCI Distinguished Professor of Logic and Philosophy of Science and of Mathematics at the University of California, Irvine. She is well known for her influential work in the philosophy of mathematics, where she has worked on mathematical realism (especially set-theoretic realism) and mathematical naturalism. Education and career Maddy received her Ph.D. from Princeton University in 1979. Her dissertation, ''Set Theoretical Realism'', was supervised by John P. Burgess. She taught at the University of Notre Dame and University of Illinois, Chicago before joining Irvine in 1987. She was elected a Fellow of the American Academy of Arts and Sciences in 1998. The German Mathematical Society awarded her a Gauss Lectureship in 2006. Philosophical work Maddy's early work, culminating in ''Realism in Mathematics'', defended Kurt Gödel's position that mathematics is a true description of a mind-independent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nominalism
In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are at least two main versions of nominalism. One version denies the existence of universalsthings that can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objectsobjects that do not exist in space and time. Most nominalists have held that only physical particulars in space and time are real, and that universals exist only ''post res'', that is, subsequent to particular things. However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), while others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, bananas). Nominalism is primarily a position on the problem of universals. It is opposed to realist philosophies, such as Platonic realism, which assert that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Platonism
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. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. History The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity during the development of other subjects, like physics, is still a matter of prolific debates. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistemology
Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epistemologists study the nature, origin, and scope of knowledge, epistemic justification, the rationality of belief, and various related issues. Debates in epistemology are generally clustered around four core areas: # The philosophical analysis of the nature of knowledge and the conditions required for a belief to constitute knowledge, such as truth and justification # Potential sources of knowledge and justified belief, such as perception, reason, memory, and testimony # The structure of a body of knowledge or justified belief, including whether all justified beliefs must be derived from justified foundational beliefs or whether justification requires only a coherent set of beliefs # Philosophical skepticism, which questions the possibili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causal Theory Of Knowledge
"A Causal Theory of Knowing" is a philosophical essay written by Alvin Goldman in 1967, published in ''The Journal of Philosophy''. It is based on existing theories of knowledge in the realm of epistemology, the study of philosophy through the scope of knowledge. The essay attempts to define knowledge by connecting facts, beliefs and knowledge through underlying and connective series called causal chains. It provides a causal theory of knowledge. A causal chain is repeatedly described as a sequence of events for which one event in a chain causes the next. According to Goldman, these chains can only exist with the presence of an accepted fact, a belief in the fact, and a cause for the subject to believe the fact. The essay also explores the ideas of perception and memory through the use of the causal chains and the concept of knowledge. Background The essay is regarded as an improvement and rebuttal of Edmund Gettier's "Is Justified True Belief Knowledge?", which is one of many att ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Objects
In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, human beings and planets while things like numbers, sets and propositions are abstract objects. There is no general consensus as to what the characteristic marks of concreteness and abstractness are. Popular suggestions include defining the distinction in terms of the difference between (1) existence inside or outside space-time, (2) having causes and effects or not, (3) having contingent or necessary existence, (4) being particular or universal and (5) belonging to either the physical or the mental realm or to neither. Despite this diversity of views, there is broad agreement concerning most objects as to whether they are abstract or concrete. So under most interpretations, all these views would agree that, for example, plants are concrete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ..., linguistics and computer science. History In English, the study of meaning in language has been known by many names that involve the Ancient Greek word (''sema'', "sign, mark, token"). In 1690, a Greek rendering of the term ''semiotics'', the interpretation of signs and symbols, finds an early allusion in John Locke's ''An Essay Concerning Human Understanding'': The third Branch may be called [''simeiotikí'', "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Socrates
Socrates (; ; –399 BC) was a Greek philosopher from Athens who is credited as the founder of Western philosophy and among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem. Socrates was a polarizing figure in Athenian society. In 399 BC, he was accused of impiety and corrupting the youth. After a trial that lasted a day, he was sentenced to death. He spent his last day in prison, refusing offers to help him escape. Plato's dialogues are among the most co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Benacerraf
Paul Joseph Salomon Benacerraf (; born 26 March 1931) is a French-born American philosopher working in the field of the philosophy of mathematics who taught at Princeton University his entire career, from 1960 until his retirement in 2007. He was appointed Stuart Professor of Philosophy in 1974, and retired as the James S. McDonnell Distinguished University Professor of Philosophy. Life and career Benacerraf was born in Paris to Moroccan Jewish parents. In 1939 the family moved to Caracas and then to New York City. When the family returned to Caracas, Benacerraf remained in the United States, boarding at the Peddie School in Hightstown, New Jersey. He attended Princeton University for both his undergraduate and graduate studies. He was elected a fellow of the American Academy of Arts and Sciences in 1998. His brother was the Venezuelan Nobel Prize-winning immunologist Baruj Benacerraf. Philosophical work Benacerraf is perhaps best known for his two papers "What Numbers Cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Baker (philosopher)
Alan R. Baker is a professor of Philosophy in Swarthmore College (Pennsylvania, United States), specializing in the philosophy of mathematics and the philosophy of science. He is also a former U.S. shogi champion. Academic career Baker did his undergraduate studies at the University of Cambridge, earning a bachelor's degree in philosophy with first class honours in 1991. He then moved to the U.S. for graduate school, earning a master's degree in 1995 and a Ph.D. in 1999, both in philosophy from Princeton University. His doctoral supervisors were Paul Benacerraf and Gideon Rosen. After working as an assistant professor at Xavier University, he moved to Swarthmore in 2003.Curriculum vitae (October 2012) , retrieved 2014-04-08. Philosophically, Baker is a [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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