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Bayesian Epistemology
Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory. One advantage of its formal method in contrast to traditional epistemology is that its concepts and theorems can be defined with a high degree of precision. It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject to the laws of probability theory, which act as the norms of rationality. These norms can be divided into static constraints, governing the rationality of beliefs at any moment, and dynamic constraints, governing how rational agents should change their beliefs upon receiving new evidence. The most characteristic Bayesian expression of these principles is found in the form of Dutch books, which illustrate irrationality in agents through a series of bets that lead to a loss for the agent no matter which of the probabilistic events occurs. Bayesians have applied these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistemology
Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowledge in the form of skills, and knowledge by acquaintance as a familiarity through experience. Epistemologists study the concepts of belief, truth, and justification to understand the nature of knowledge. To discover how knowledge arises, they investigate sources of justification, such as perception, introspection, memory, reason, and testimony. The school of skepticism questions the human ability to attain knowledge while fallibilism says that knowledge is never certain. Empiricists hold that all knowledge comes from sense experience, whereas rationalists believe that some knowledge does not depend on it. Coherentists argue that a belief is justified if it coheres with other beliefs. Foundationalists, by contrast, maintain th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Alcibiades
The ''First Alcibiades'', also referred to as ''Alcibiades Major'' and abbreviated as ''Alcibiades I'' (), is a dialogue ascribed to Plato, depicting Socrates in conversation with Alcibiades. Content In the preface Alcibiades is described as an ambitious young man who is eager to enter public life. He is extremely proud of his good looks, noble birth, many friends, possessions and his connection to Pericles, the leader of the Athenian state. Alcibiades has many admirers and had many lovers but they have all run away, afraid of his coldness. Socrates was the first of his lovers but he has not spoken to him for many years. Now the older man tries to help the youth with his questions before Alcibiades presents himself in front of the Athenian assembly. For the rest of the dialogue Socrates explains the many reasons why Alcibiades needs him. By the end of ''Alcibiades I'', the youth is much persuaded by Socrates' reasoning, and accepts him as his mentor. The first topic they enter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Gustav Hempel
Carl Gustav "Peter" Hempel (; ; January 8, 1905 – November 9, 1997) was a German writer, philosopher, logician, and epistemologist. He was a major figure in Logical positivism, logical empiricism, a 20th-century movement in the philosophy of science. Hempel articulated the deductive-nomological model of science, scientific explanation, which was considered the "standard model" of scientific explanation during the 1950s and 1960s. He is also known for the raven paradox ("Hempel's paradox") and Hempel's dilemma. Education Hempel studied mathematics, physics and philosophy at the Georg August University of Göttingen, University of Göttingen and subsequently at the Humboldt University of Berlin, University of Berlin and the Heidelberg University. In Göttingen, he encountered David Hilbert and was impressed by Hilbert's program, his program attempting to base all mathematics on solid logical foundations derived from a limited number of axioms. After moving to Berlin, Hempel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Jeffrey
Richard Carl Jeffrey (August 5, 1926 – November 9, 2002) was an American philosopher, logician, and probability theorist. He is best known for developing and championing the philosophy of radical probabilism and the associated heuristic of probability kinematics, also known as Jeffrey conditioning. Life and career Born in Boston, Massachusetts, Jeffrey served in the U.S. Navy during World War II. As a graduate student he studied under Rudolf Carnap and Carl Hempel. He received his M.A. from the University of Chicago in 1952 and his Ph.D. from Princeton in 1957. After holding academic positions at MIT, City College of New York, Stanford University, and the University of Pennsylvania, he joined the faculty of Princeton in 1974 and became a professor emeritus there in 1999. He was also a visiting professor at the University of California, Irvine. Jeffrey, who died of lung cancer at the age of 76, was known for his sense of humor, which often came through in his breezy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the ''base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of Realization (probability), observations given a model configuration (i.e., th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Posterior Probability
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating. In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Probability
A prior probability distribution of an uncertain quantity, simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. In Bayesian statistics, Bayes' rule prescribes how to update the prior with new information to obtain the posterior probability distribution, which is the conditional distribution of the uncertain quantity given new data. Historically, the choice of priors was often constrained to a conjugate family of a given likelihood function, so that it would result in a tractable posterior of the same family. The widespread availability of Markov chain Monte Carlo methods, however, has made this less of a concern. There are many ways to const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an Event (probability theory), event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Lewis (philosopher)
David Kellogg Lewis (September 28, 1941– October 14, 2001) was an American philosopher. Lewis taught briefly at UCLA and then at Princeton University from 1970 until his death. He is closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years. Lewis made significant contributions in philosophy of mind, philosophy of probability, epistemology, philosophical logic, aesthetics, philosophy of mathematics, philosophy of time and philosophy of science. In most of these fields he is considered among the most important figures of recent decades. Lewis is most famous for his work in metaphysics, philosophy of language and semantics, in which his books ''On the Plurality of Worlds'' (1986) and ''Counterfactuals'' (1973) are considered classics. His works on the logic and semantics of counterfactual conditionals are broadly used by philosophers and linguists along with a competing account from Robert Stalnaker; together the Stal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tautology (logic)
In mathematical logic, a tautology (from ) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a ball is and regardless of its colour. Tautology is usually, though not always, used to refer to valid formulas of propositional logic. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contradictions
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." In modern formal logic and type theory, the term is mainly used instead for a ''single'' proposition, often denoted by the falsum symbol \bot; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History By creation of a paradox, Plato's '' Euthydemus'' dialogue demonstrates the need for the notion of ''contradiction''. In the ensuing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
