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Raven Paradox
The raven paradox, also known as Hempel's paradox, Hempel's ravens, or rarely the paradox of indoor ornithology, is a paradox arising from the question of what constitutes evidence for the truth of a statement. Observing objects that are neither black nor ravens may formally increase the likelihood that all ravens are black even though, intuitively, these observations are unrelated. This problem was proposed by the logician Carl Gustav Hempel in the 1940s to illustrate a contradiction between inductive logic and intuition. Paradox Hempel describes the paradox in terms of the hypothesis: : (1) ''All ravens are black''. In the form of an implication, this can be expressed as: ''If something is a raven, then it is black.'' Via contraposition, this statement is equivalent to: : (2) ''If something is not black, then it is not a raven.'' In all circumstances where (2) is true, (1) is also true—and likewise, in all circumstances where (2) is false (i.e., if a world is imagined in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raven
A raven is any of several larger-bodied bird species of the genus ''Corvus''. These species do not form a single taxonomic group within the genus. There is no consistent distinction between "crows" and "ravens", common names which are assigned to different species chiefly on the basis of their size. The largest raven species are the common raven and the thick-billed raven. Etymology The term "raven" originally referred to the common raven (''Corvus corax''), the type species of the genus ''Corvus'', which has a larger distribution than any other species of ''Corvus'', ranging over much of the Northern Hemisphere. The modern English word ''raven'' has cognates in all other Germanic languages, including Old Norse (and subsequently modern Icelandic) and Old High German , all of which descend from Proto-Germanic . Collective nouns for a group of ravens (or at least the common raven) include "rave", "treachery", "unkindness" and "conspiracy". In practice, most people use the more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erkenntnis
''Erkenntnis'' is a journal of philosophy that publishes papers in analytic philosophy. Its name is derived from the German word "Erkenntnis", meaning "knowledge, recognition". The journal was also linked to organisation of conferences, such as the Second Conference on the Epistemology of the Exact Sciences, of which it published the papers and accounts of the discussions. First series (1930–1940) When Hans Reichenbach and Rudolf Carnap took charge of ''Annalen der Philosophie und philosophischen Kritik'' in 1930 they renamed it ''Erkenntnis'', under which name it was published 1930–1938. The journal was published by the '' Gesellschaft für Empirische Philosophie'', or the Berlin Circle and the Verein Ernst Mach, Vienna. In the first issue Reichenbach noted that the editors hoped to gain a better understanding of the nature of all human knowledge through consideration of the procedures and results of a variety of scientific disciplines, whilst also hoping that philosophy need ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-valued Logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradoxes Of Material Implication
The paradoxes of material implication are a group of tautology (logic), true formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated as "if ... then ...". A material conditional formula P \rightarrow Q is true unless P is true and Q is false. If natural language conditionals were understood in the same way, that would mean that the sentence "If the Nazis won World War Two, everybody would be happy" is vacuously true. Given that such problematic consequences follow from a seemingly correct assumption about logic, they are called ''paradoxes''. They demonstrate a mismatch between classical logic and robust intuitions about meaning (philosophy), meaning and reasoning. Paradox of entailment As the best known of the paradoxes, and most formally simple, the paradox of entailment makes the best introduction. In natural language, an instance of the paradox of entailment ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language. Notation In l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I And Type II Errors
In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a "false negative" finding or conclusion; example: "a guilty person is not convicted"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process. By selecting a low threshold (cut-off) value and modifying the alpha (α) level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in medical science, biometrics and computer science. Intuitively, type I errors can be thought of as errors of ''commission'', i.e. the researcher unluck ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Popper
Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the classical inductivist views on the scientific method in favour of empirical falsification. According to Popper, a theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can (and should) be scrutinised with decisive experiments. Popper was opposed to the classical justificationist account of knowledge, which he replaced with critical rationalism, namely "the first non-justificational philosophy of criticism in the history of philosophy". In political discourse, he is known for his vigorous defence of liberal democracy and the principles of social criticism that he believed made a flourishing open society possible. His political philosophy embraced ideas from major democratic political ideologies, inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relative Frequencies
In statistics, the frequency (or absolute frequency) of an Event (probability theory), event i is the number n_i of times the observation has occurred/recorded in an experiment or study. These frequencies are often depicted graphically or in tabular form. Types The cumulative frequency is the total of the absolute frequencies of all events at or below a certain point in an ordered list of events. The (or empirical probability) of an event is the absolute frequency Normalizing constant, normalized by the total number of events: : f_i = \frac = \frac. The values of f_i for all events i can be plotted to produce a frequency distribution. In the case when n_i = 0 for certain i, pseudocounts can be added. Depicting frequency distributions A frequency distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grue And Bleen
The new riddle of induction was presented by Nelson Goodman in ''Fact, Fiction, and Forecast'' as a successor to problem of induction, Hume's original problem. It presents the logical Predicate (mathematical logic), 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 Scientific law, law-like and which are not. Goodman's construction and use of ''grue'' and ''bleen'' illustrates how philosophers use simple examples in analytic philosophy, 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"' ... [...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] |
Natural Kind
"Natural kind" is an intellectual grouping, or categorizing of things, in a manner that is reflective of the actual world and not just human interests. Some treat it as a classification identifying some structure of truth and reality that exists whether or not humans recognize it. Others treat it as intrinsically useful to the human mind, but not necessarily reflective of something more objective. Candidates examples of natural kinds are found in all the sciences, but the field of chemistry provides the paradigm example of elements. John Dewey held a minority view that belief in unconditional natural kinds is a mistake, a relic of obsolete scientific practices. W. V. O. Quine and Hilary Kornblith held the majoirity view that natural kinds are the unchanging structure of truth and reality. Hilary Putnam rejects descriptivist approaches to natural kinds with semantic reasoning. Hasok Chang and Rasmus Winther hold the emerging view that natural kinds are useful and evolving scientific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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