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Quasi-empirical
Quasi-empiricism in mathematics is the attempt in the philosophy of mathematics to direct philosophers' attention to mathematical practice, in particular, relations with physics, social sciences, and computational mathematics, rather than solely to issues in the foundations of mathematics. Of concern to this discussion are several topics: the relationship of empiricism (see Penelope Maddy) with mathematics, issues related to realism, the importance of culture, necessity of application, etc. Primary arguments A primary argument with respect to quasi-empiricism is that whilst mathematics and physics are frequently considered to be closely linked fields of study, this may reflect human cognitive bias. It is claimed that, despite rigorous application of appropriate empirical methods or mathematical practice in either field, this would nonetheless be insufficient to disprove alternate approaches. Eugene Wigner (1960) noted that this culture need not be restricted to mathematics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-empiricism
Quasi-empirical methods are methods applied in science and mathematics to achieve epistemology similar to that of empiricism (thus ''quasi- + empirical'') when experience cannot falsify the ideas involved. Empirical research relies on empirical evidence, and its empirical methods involve experimentation and disclosure of apparatus for reproducibility, by which scientific findings are validated by other scientists. Empirical methods are studied extensively in the philosophy of science, but they cannot be used directly in fields whose hypotheses cannot be falsified by real experiment (for example, mathematics, philosophy, theology, and ideology). Because of such empirical limits in science, the scientific method must rely not only on empirical methods but sometimes also on quasi-empirical ones. The prefix ''quasi-'' came to denote methods that are "almost" or "socially approximate" an ideal of truly empirical methods. It is unnecessary to find all counterexamples to a theory; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilary Putnam
Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) 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. Putnam was known for his willingness to apply equal scrutiny to his own philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposed its flaws. As a result, he acquired a reputation for frequently changing his positions. In philosophy of mind, Putnam is known for his argument against the type-identity of mental and physical states ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word And Object
''Word and Object'' is a 1960 work by the philosopher Willard Van Orman Quine, in which the author expands upon the line of thought of his earlier writings in ''From a Logical Point of View'' (1953), and reformulates some of his earlier arguments, such as his attack in "Two Dogmas of Empiricism" on the analytic–synthetic distinction. The thought experiment of radical translation and the accompanying notion of indeterminacy of translation are original to ''Word and Object'', which is Quine's most famous book. Synopsis Quine emphasizes his Naturalism (philosophy), naturalism, the doctrine that philosophy should be pursued as part of natural science. He argues in favor of naturalizing epistemology, supports physicalism over phenomenalism and mind-body dualism, and extensionality over intensionality, develops a behavioristic conception of sentence-meaning, theorizes about language learning, speculates on the ontogenesis of reference, explains various forms of ambiguity and vaguenes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imre Lakatos
Imre Lakatos (, ; hu, Lakatos Imre ; 9 November 1922 – 2 February 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pre-axiomatic stages of development, and also for introducing the concept of the "research programme" in his methodology of scientific research programmes. Life Lakatos was born Imre (Avrum) Lipsitz to a Jewish family in Debrecen, Hungary, in 1922. He received a degree in mathematics, physics, and philosophy from the University of Debrecen in 1944. In March 1944 the Germans invaded Hungary, and Lakatos along with Éva Révész, his then-girlfriend and subsequent wife, formed soon after that event a Marxist resistance group. In May of that year, the group was joined by Éva Izsák, a 19-year-old Jewish antifascist activist. Lakatos, considering that there was a risk that she would be captured and forced to betray them, decided that her ... [...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 Coul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundation Ontology
In information science, an upper ontology (also known as a top-level ontology, upper model, or foundation ontology) is an ontology (in the sense used in information science) which consists of very general terms (such as "object", "property", "relation") that are common across all domains. An important function of an upper ontology is to support broad semantic interoperability among a large number of domain-specific ontologies by providing a common starting point for the formulation of definitions. Terms in the domain ontology are ranked under the terms in the upper ontology, e.g., the upper ontology classes are superclasses or supersets of all the classes in the domain ontologies. A number of upper ontologies have been proposed, each with its own proponents. Library classification systems predate upper ontology systems. Though library classifications organize and categorize knowledge using general concepts that are the same across all knowledge domains, neither system is a replac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum (classical), Lyceum and the wider Aristotelianism, Aristotelian tradition. His writings cover many subjects including Physics (Aristotle), physics, biology, zoology, metaphysics, logic, ethics, aesthetics, Poetics (Aristotle), poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, History of geology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that Western culture, the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato's Ontology
The theory of Forms or theory of Ideas is a philosophical theory, fuzzy concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggests that these Forms are the only objects of study that can provide knowledge. The theory itself is contested from within Plato's dialogues, and it is a general point of controversy in philosophy. Nonetheless, the theory is considered to be a classical solution to the problem of universals. The early Greek concept of form precedes attested philosophical usage and is represented by a number of words mainly having to do with vision, sight, and ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arabia
The Arabian Peninsula, (; ar, شِبْهُ الْجَزِيرَةِ الْعَرَبِيَّة, , "Arabian Peninsula" or , , "Island of the Arabs") or Arabia, is a peninsula of Western Asia, situated northeast of Africa on the Arabian Plate. At , the Arabian Peninsula is the largest peninsula in the world. Geographically, the Arabian Peninsula includes Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, the United Arab Emirates (UAE), and Yemen, as well as the southern portions of Iraq and Jordan. The largest of these is Saudi Arabia. In the classical era, the southern portions of modern-day Syria, Jordan, and the Sinai Peninsula were also considered parts of Arabia (see Arabia Petraea). The Arabian Peninsula formed as a result of the rifting of the Red Sea between 56 and 23 million years ago, and is bordered by the Red Sea to the west and southwest, the Persian Gulf and the Gulf of Oman to the northeast, the Levant and Mesopotamia to the north and the Arabian Sea and the Indian Oce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India
India, officially the Republic of India ( Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia. Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago., "Y-Chromosome and Mt-DNA data support the colonization of South Asia by modern humans originating in Africa. ... Coalescence dates for most non-European populations average to between 73–55 ka.", "Modern human beings—''Homo sapiens''—originated in Africa. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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