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Frank Ramsey (mathematician)
Frank Plumpton Ramsey (; 22 February 1903 – 19 January 1930) was a British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the age of 26. He was a close friend of Ludwig Wittgenstein and, as an undergraduate, translated Wittgenstein's ''Tractatus Logico-Philosophicus'' into English. He was also influential in persuading Wittgenstein to return to philosophy and Cambridge. Like Wittgenstein, he was a member of the Cambridge Apostles, the secret intellectual society, from 1921. Life Ramsey was born on 22 February 1903 in Cambridge where his father Arthur Stanley Ramsey (1867–1954), also a mathematician, was President of Magdalene College. His mother was Mary Agnes Stanley (1875–1927). He was the eldest of two brothers and two sisters, and his brother Michael Ramsey, the only one of the four siblings who was to remain Christian, later became Archbishop of Canterbury. He entered Winchester College in 1915 and l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy refers to the Philosophy, philosophical thought, traditions and works of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre-Socratic philosophy, pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" , "to love" and σοφία ''Sophia (wisdom), sophía'', "wisdom". History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology (the nature and origin of the universe), while rejecting unargued fables in place for argued theory, i.e., dogma superseded reason, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redundancy Theory Of Truth
According to the redundancy theory of truth (also known as the disquotational theory of truth), asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence Snow is white' is true" is equivalent to asserting the sentence "Snow is white". The philosophical redundancy theory of truth is a deflationary theory of truth. Overview Redundancy theorists infer from this premise that truth is a redundant concept—in other words, that "truth" is merely a word that it is conventional to use in certain contexts but not one that points to anything in reality. The theory is commonly attributed to Frank P. Ramsey, who argued that the use of words like ''fact'' and ''truth'' was nothing but a roundabout way of asserting a proposition, and that treating these words as separate problems in isolation from judgment was merely a "linguistic muddle", though there remains some debate as to the correct interpretation of his position (Le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic philosophy.Stanford Encyclopedia of Philosophy"Bertrand Russell", 1 May 2003. He was one of the early 20th century's prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against British idealism, idealism". Together with his former teacher Alfred North Whitehead, A. N. Whitehead, Russell wrote ''Principia Mathematica'', a milestone in the development of classical logic and a major attempt to reduce the whole of mathematics to logic (see logicism). Russell's article "On Denoting" has been considered a "paradigm of philosophy". Russell was a Pacifism, pacifist who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul Weiss, Peirce was "the most original and versatile of America's philosophers and America's greatest logician". Bertrand Russell wrote "he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever". Educated as a chemist and employed as a scientist for thirty years, Peirce meanwhile made major contributions to logic, such as theories of Algebraic logic, relations and Quantifier (logic), quantification. Clarence Irving Lewis, C. I. Lewis wrote, "The contributions of C. S. Peirce to symbolic logic are more numerous and varied than those of any other writer—at least in the nineteenth century." For Peirce, logic also encompassed much of what is now called epistemology and the philoso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. Despite his position, only one book of his philosophy was published during his entire life: the 75-page ''Logisch-Philosophische Abhandlung'' (''Logical-Philosophical Treatise'', 1921), which appeared, together with an English translation, in 1922 under the Latin title ''Tractatus Logico-Philosophicus''. His only other published works were an article, "Some Remarks on Logical Form" (1929); a book review; and a children's dictionary. #Works, His voluminous manuscripts were edited and published posthumously. The first and best-known of this posthumous series is the 1953 book ''Philosophical Investigations''. A 1999 survey among American university and college teachers ranked the ''Investigations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernays–Schönfinkel Class
The Bernays–Schönfinkel class (also known as Bernays–Schönfinkel–Ramsey class) of formulas, named after Paul Bernays, Moses Schönfinkel and Frank P. Ramsey, is a fragment of first-order logic formulas where satisfiability is decidable. It is the set of sentences that, when written in prenex normal form, have an \exists^*\forall^* quantifier prefix and do not contain any function symbols. Ramsey proved that, if \phi is a formula in the Bernays–Schönfinkel class with one free variable, then either \ is finite, or \ is finite. This class of logic formulas is also sometimes referred as effectively propositional (EPR) since it can be effectively translated into propositional logic formulas by a process of grounding or instantiation. The satisfiability problem for this class is NEXPTIME In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keynes–Ramsey Rule
In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is expressed as a differential equation relating the rate of change of consumption with interest rates, time preference, and (intertemporal) elasticity of substitution. If derived from a basic Ramsey–Cass–Koopmans model, the Keynes–Ramsey rule may look like :\dot(t) = \sigma \cdot (r - \rho) \cdot c(t) where c(t) is consumption and \dot(t) its change over time (in Newton notation), \rho \in (0,1) is the discount rate, r \in (0,1) is the real interest rate, and \sigma > 0 is the (intertemporal) elasticity of substitution. The Keynes–Ramsey rule is named after Frank P. Ramsey, who derived it in 1928, and his mentor John Maynard Keynes, who provided an economic interpretation. Mathematically, the Keynes–Ramsey rule is a necessary first-order condition for an optimal control problem, also known as an Euler–Lagrange equation In the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey–Cass–Koopmans Model
The Ramsey–Cass–Koopmans model (also known as the Ramsey growth model or the neoclassical growth model) is a foundational model in neoclassical economics that describes the dynamics of economic growth over time. It builds upon the pioneering work of Frank P. Ramsey (1928), with later extensions by David Cass and Tjalling Koopmans in the 1960s. The model extends the Solow–Swan model by Exogenous and endogenous variables, endogenizing the Saving, savings rate through explicit microfoundations of Consumption (economics), consumption behavior: rather than assuming a constant saving rate, the model derives it from the intertemporal optimization of a representative agent who chooses Consumption (economics), consumption to maximize utility over an infinite horizon. This approach leads to a richer dynamic structure in the transition to the long-run Steady state (macroeconomics), steady state, and yields a Pareto efficiency, Pareto efficient outcome.This efficiency result depends not o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey's Theorem
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (say, blue and red), let and be any two positive integers. Ramsey's theorem states that there exists a least positive integer for which every blue-red edge colouring of the complete graph on vertices contains a blue clique on vertices or a red clique on vertices. (Here signifies an integer that depends on both and .) Ramsey's theorem is a foundational result in combinatorics. The first version of this result was proved by Frank Ramsey. This initiated the combinatorial theory now called Ramsey theory, that seeks regularity amid disorder: general conditions for the existence of substructures with regular properties. In this application it is a question of the existence of ''monochromatic subsets'', that is, subsets of connected edges o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belief Revision
Belief revision (also called belief change) is the process of changing beliefs to take into account a new piece of information. The formal logic, logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of intelligent agent, rational agents. What makes belief revision non-trivial is that several different ways for performing this operation may be possible. For example, if the current knowledge includes the three facts "A is true", "B is true" and "if A and B are true then C is true", the introduction of the new information "C is false" can be done preserving consistency only by removing at least one of the three facts. In this case, there are at least three different ways for performing revision. In general, there may be several different ways for changing knowledge. Revision and update Two kinds of changes are usually distinguished: ; update : the new information is about the situation at present, while t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey–Dvoretzky–Milman Phenomenon
In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck. In essence, it says that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids. A new proof found by Vitali Milman in the 1970s was one of the starting points for the development of asymptotic geometric analysis (also called ''asymptotic functional analysis'' or the ''local theory of Banach spaces''). Original formulations For every natural number ''k'' ∈ N and every ''ε'' > 0 there exists a natural number ''N''(''k'', ''ε'') ∈ N such that if (''X'', ‖·‖) is any normed space of dimension ''N''(''k'', ''ε''), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey Problem
The Ramsey problem, or Ramsey pricing, or Ramsey–Boiteux pricing, is a second-best policy problem concerning what prices a public monopoly should charge for the various products it sells in order to maximize social welfare (the sum of producer and consumer surplus) while earning enough revenue to cover its fixed costs. Under Ramsey pricing, the price markup over marginal cost is inversely related to the price elasticity of demand and the Price elasticity of supply: the more elastic the product's demand or supply, the smaller the markup. Frank P. Ramsey discovered this principle in 1927 in the context of Optimal taxation: the more elastic the demand or supply, the smaller the optimal tax. The rule was later applied by Marcel Boiteux (1956) to natural monopolies (industries with decreasing average cost). A natural monopoly earns negative profits if it sets prices equal to marginal cost, so it must set prices for some or all of the products it sells above marginal cost if it is to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
