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New Riddle Of Induction
The new riddle of induction was presented by Nelson Goodman in ''Fact, Fiction, and Forecast'' as a successor to Hume's original problem. It presents the logical predicates grue and bleen which are unusual due to their time-dependence. Many have tried to solve the new riddle on those terms, but Hilary Putnam and others have argued such time-dependency depends on the language adopted, and in some languages it is equally true for natural-sounding predicates such as "green". For Goodman they illustrate the problem of projectible predicates and ultimately, which empirical generalizations are law-like and which are not. Goodman's construction and use of ''grue'' and ''bleen'' illustrates how philosophers use simple examples in conceptual analysis. Grue and bleen Goodman defined "grue" relative to an arbitrary but fixed time ''t'':Historically, Goodman used ''"V-E day"'' and ''"a certain time t"'' in ''A Query on Confirmation'' (p. 383) and ''Fact, fiction, and forecast'' (3rd e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nelson Goodman
Henry Nelson Goodman (7 August 1906 – 25 November 1998) was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics. Life and career Goodman was born in Somerville, Massachusetts, the son of Sarah Elizabeth (née Woodbury) and Henry Lewis Goodman. He was of Jewish origins. He graduated from Harvard University, AB, ''magna cum laude'' (1928). During the 1930s, he ran an art gallery in Boston, Massachusetts, while studying for a Harvard PhD in philosophy, which he completed in 1941. His experience as an art dealer helps explain his later turn towards aesthetics, where he became better known than in logic and analytic philosophy. During World War II, he served as a psychologist in the US Army. He taught at the University of Pennsylvania, 1946–1964, where his students included Noam Chomsky, Sydney Morgenbesser, Stephen Stich, and Hilary Putnam. He was a research fellow at the Harvard Center for Cogni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
US Government Example For Goodman's New Riddle Of Induction Svg
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territories, nine Minor Outlying Islands, and 326 Indian reservations. The United States is also in free association with three Pacific Island sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Republic of Palau. It is the world's third-largest country by both land and total area. It shares land borders with Canada to its north and with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the most populous country in the Americas and the third most populous in the world. The national capital of the United States is Washington, D.C. and its most populous city and principal financial center is New York City. Paleo-Americans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Background and motivation Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.g. "2 is less than 3", "10 is greater than 5", or "Does Tom have fewer cookies than Sally?". This intuitive concept can be extended to orders on other sets of numbers, such as the integers and the reals. The idea of being greater than or less than another number is one of the basic intuitions of number systems (compare with numeral systems) in general (although one usually is also interested in the actual difference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Well-founded
In mathematics, a binary relation ''R'' is called well-founded (or wellfounded) on a class ''X'' if every non-empty subset ''S'' ⊆ ''X'' has a minimal element with respect to ''R'', that is, an element ''m'' not related by ''s R m'' (for instance, "''s'' is not smaller than ''m''") for any ''s'' ∈ ''S''. In other words, a relation is well founded if :(\forall S \subseteq X)\; \neq \emptyset \implies (\exists m \in S) (\forall s \in S) \lnot(s \mathrel m) Some authors include an extra condition that ''R'' is set-like, i.e., that the elements less than any given element form a set. Equivalently, assuming the axiom of dependent choice, a relation is well-founded when it contains no infinite descending chains, which can be proved when there is no infinite sequence ''x''0, ''x''1, ''x''2, ... of elements of ''X'' such that ''x''''n''+1 ''R'' ''x''n for every natural number ''n''. In order theory, a partial order is called well-fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Order
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word ''partial'' in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable. Informal definition A partial order defines a notion of comparison. Two elements ''x'' and ''y'' may stand in any of four mutually exclusive relationships to each other: either ''x'' ''y'', or ''x'' and ''y'' are ''incompar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irreflexive
In mathematics, a binary relation ''R'' on a set ''X'' is reflexive if it relates every element of ''X'' to itself. An example of a reflexive relation is the relation " is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations. Definitions Let R be a binary relation on a set X, which by definition is just a subset of X \times X. For any x, y \in X, the notation x R y means that (x, y) \in R while "not x R y" means that (x, y) \not\in R. The relation R is called if x R x for every x \in X or equivalently, if \operatorname_X \subseteq R where \operatorname_X := \ denotes the identity relation on X. The of R is the union R \cup \operatorname_X, which can equivalently be defined as the smallest (with respect to \subseteq) reflexive relation on X ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tractatus Logico-Philosophicus
The ''Tractatus Logico-Philosophicus'' (widely abbreviated and cited as TLP) is a book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein which deals with the relationship between language and reality and aims to define the limits of science. Wittgenstein wrote the notes for the ''Tractatus'' while he was a soldier during World War I and completed it during a military leave in the summer of 1918. It was originally published in German in 1921 as ''Logisch-Philosophische Abhandlung'' (Logical-Philosophical Treatise). In 1922 it was published together with an English translation and a Latin title, which was suggested by G. E. Moore as homage to Baruch Spinoza's ''Tractatus Theologico-Politicus'' (1670). The ''Tractatus'' is written in an austere and succinct literary style, containing almost no arguments as such, but consists of altogether 525 declarative statements, which are hierarchically numbered. The ''Tractatus'' is recognized by philosophers as a signi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrians, Austrian-British people, British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considered by some to be the greatest philosopher of the 20th century. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. In spite of his position, during his entire life only one book of #Legacy, his philosophy was published, 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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universe Of Discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. Overview The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables. Many logicians distinguish, sometimes only tacitly, between the ''domain of a science'' and the ''universe of discourse of a formalization of the science''.José Miguel Sagüillo, Domains of sciences, universe of discourse, and omega arguments, History and philosophy of logic, vol. 20 (1999), pp. 267–280. Examples For example, in an interpretation of first-order logic, the domain of discourse is the set of individuals over which the quantifiers range. A proposition such as is ambiguous, if no domain of discourse has been identified. In one interpretation, the domain of di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Succession
In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. The formula is still used, particularly to estimate underlying probabilities when there are few observations or for events that have not been observed to occur at all in (finite) sample data. Statement of the rule of succession If we repeat an experiment that we know can result in a success or failure, ''n'' times independently, and get ''s'' successes, and ''n − s'' failures, then what is the probability that the next repetition will succeed? More abstractly: If ''X''1, ..., ''X''''n''+1 are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them, :P(X_=1 \mid X_1+\cdots+X_n=s)=. Interpretation Since we have the prior knowledge that we are looking at an experiment for which both success and failure are possible, our estimate is as if we had obse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudolf Carnap
Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. He is considered "one of the giants among twentieth-century philosophers." Biography Carnap's father had risen from being a poor ribbon-weaver to be the owner of a ribbon-making factory. His mother came from an academic family; her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld. As a ten-year-old, Carnap accompanied Wilhelm Dörpfeld on an expedition to Greece. Carnap was raised in a profoundly religious Protestant family, but later became an atheist. He began his formal education at the Barmen Gymnasium and the Gymnasium in Jena. From 1910 to 1914, he attended the University of Jena, intending to write a thesis in physics. He also intently studied Immanuel Kant's '' Critique of Pure Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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