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Indeterministic
Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or do not cause deterministically. It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. Heisenberg's uncertainty principle and the "Born rule", proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay "''Chance and Necessity''". The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems. Necessary but insufficient causation Indeterminists do not have to deny that causes exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Will
Free will is the capacity of agents to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actions that are freely chosen. It is also connected with the concepts of advice, persuasion, deliberation, and prohibition. Traditionally, only actions that are freely willed are seen as deserving credit or blame. Whether free will exists, what it is and the implications of whether it exists or not are some of the longest running debates of philosophy and religion. Some conceive of free will as the right to act outside of external influences or wishes. Some conceive free will to be the capacity to make choices undetermined by past events. Determinism suggests that only one course of events is possible, which is inconsistent with a libertarian model of free will. Ancient Greek philosophy identified this issue, which remains a major focus o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Libertarianism (metaphysics)
Libertarianism is one of the main philosophical positions related to the problems of free will and determinism which are part of the larger domain of metaphysics. In particular, libertarianism is an incompatibilist position which argues that free will is logically incompatible with a deterministic universe. Libertarianism states that since agents have free will, determinism must be false. One of the first clear formulations of libertarianism is found in John Duns Scotus. In theological context, metaphysical libertarianism was notably defended by Jesuit authors like Luis de Molina and Francisco Suárez against rather compatibilist Thomist Bañecianism. Other important metaphysical libertarians in the early modern period were René Descartes, George Berkeley, Immanuel Kant and Thomas Reid. Roderick Chisholm was a prominent defender of libertarianism in the 20th century and contemporary libertarians include Robert Kane, Peter van Inwagen and Robert Nozick. Overview The fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpretations Of Quantum Mechanics
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters. Despite nearly a century of debate and experiment, no consensus has been reached among physicists and philosophers of physics concerning which interpretation best "represents" reality. History The definition of quantum theorists' terms, such as ''wave function'' and ''matrix mechanics'', progressed through many stages. For instance, Erwin Schrödinger originally viewed the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propensity Probability
The propensity theory of probability is a probability interpretation in which the probability is thought of as a physical propensity, disposition, or tendency of a given type of situation to yield an Outcome (probability), outcome of a certain kind, or to yield a long-run relative frequency of such an outcome.'Interpretations of Probability', Stanford Encyclopedia of Philosophy] Retrieved 23 December 2006. Propensities are not relative frequencies, but purported ''causes'' of the observed stable relative frequencies. Propensities are invoked to ''explain why'' repeating a certain kind of experiment will generate a given outcome type at a persistent rate. A central aspect of this explanation is the law of large numbers. This law, which is a consequence of the axioms of probability, says that if (for example) a coin is tossed repeatedly many times, in such a way that its probability of landing heads is the same on each toss, and the outcomes are probabilistically independent, then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event
Event may refer to: Gatherings of people * Ceremony, an event of ritual significance, performed on a special occasion * Convention (meeting), a gathering of individuals engaged in some common interest * Event management, the organization of events * Festival, an event that celebrates some unique aspect of a community * Happening, a type of artistic performance * Media event, an event created for publicity * Party, a social, recreational or corporate events held * Sporting event, at which athletic competition takes place * Virtual event, a gathering of individuals within a virtual environment Science, technology, and mathematics * Event (computing), a software message indicating that something has happened, such as a keystroke or mouse click * Event (philosophy), an object in time, or an instantiation of a property in an object * Event (probability theory), a set of outcomes to which a probability is assigned * Event (relativity), a point in space at an instant in time, i.e. a lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Systems
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe. Complex systems are systems whose behavior is intrinsically difficult to model due to the dependencies, competitions, relationships, or other types of interactions between their parts or between a given system and its environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomism
Atomism (from Greek , ''atomon'', i.e. "uncuttable, indivisible") is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms. References to the concept of atomism and its atoms appeared in both ancient Greek and ancient Indian philosophical traditions. Leucippus is the earliest figure whose commitment to atomism is well attested and he is usually credited with inventing atomism. He and other ancient Greek atomists theorized that nature consists of two fundamental principles: ''atom'' and ''void''. Clusters of different shapes, arrangements, and positions give rise to the various macroscopic substances in the world.Berryman, Sylvia, "Ancient Atomism", ''The Stanford Encyclopedia of Philosophy'' (Fall 2008 Edition), Edward N. Zalta (ed.)online/ref> The particles of chemical matter for which chemists and other natural philosophers of the early 19th century found experimental evidence were thought to be indivisibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy (information Theory)
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable X, which takes values in the alphabet \mathcal and is distributed according to p: \mathcal\to , 1/math>: \Eta(X) := -\sum_ p(x) \log p(x) = \mathbb \log p(X), where \Sigma denotes the sum over the variable's possible values. The choice of base for \log, the logarithm, varies for different applications. Base 2 gives the unit of bits (or " shannons"), while base ''e'' gives "natural units" nat, and base 10 gives units of "dits", "bans", or " hartleys". An equivalent definition of entropy is the expected value of the self-information of a variable. The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication",PDF archived froherePDF archived frohere and is also referred to as Shannon entropy. Shannon's theory defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume ''Mécanique céleste'' (''Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to suggest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Distribution Function
In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is also called the percentile function, percent-point function or inverse cumulative distribution function. Definition Strictly monotonic distribution function With reference to a continuous and strictly monotonic cumulative distribution function F_X\colon \mathbb \to ,1/math> of a random variable ''X'', the quantile function Q\colon , 1\to \mathbb returns a threshold value ''x'' below which random draws from the given c.d.f. would fall ''100*p'' percent of the time. In terms of the distribution function ''F'', the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, ''a'' and ''b'', which are the minimum and maximum values. The interval can either be closed (e.g. , b or open (e.g. (a, b)). Therefore, the distribution is often abbreviated ''U'' (''a'', ''b''), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable ''X'' under no constraint other than that it is contained in the distribution's support. Definitions Probability density function The probability density function of the continuous uniform distribution is: : f(x)=\begin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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