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A Treatise On Probability
''A Treatise on Probability'', published by John Maynard Keynes in 1921, provides a much more general logic of uncertainty than the more familiar and straightforward 'classical' theories of probability. This has since become known as a "logical-relationist" approach, and become regarded as the seminal and still classic account of the logical interpretation of probability (or probabilistic logic), a view of probability that has been continued by such later works as Carnap's ''Logical Foundations of Probability'' and E.T. Jaynes ''Probability Theory: The Logic of Science''. Keynes's conception of this generalised notion of probability is that it is a strictly logical relation between evidence and hypothesis, a degree of partial implication. It was in part pre-empted by Bertrand Russell's use of an unpublished version. In a 1922 review, Bertrand Russell, the co-author of ''Principia Mathematica'', called it "undoubtedly the most important work on probability that has appeared ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes ( ; 5 June 1883 – 21 April 1946), was an English economist and philosopher whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in mathematics, he built on and greatly refined earlier work on the causes of business cycles. One of the most influential economists of the 20th century, he produced writings that are the basis for the schools of economic thought, school of thought known as Keynesian economics, and its various offshoots. His ideas, reformulated as New Keynesianism, are fundamental to mainstream economics, mainstream macroeconomics. He is known as the "father of macroeconomics". During the Great Depression of the 1930s, Keynes spearheaded Keynesian Revolution, a revolution in economic thinking, challenging the ideas of neoclassical economics that held that free markets would, in the short to medium term, automatically provide full employment, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence
Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to machine perception, perceive their environment and use machine learning, learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon (company), Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Amazon Alexa, Alexa); autonomous vehicles (e.g., Waymo); Generative artificial intelligence, generative and Computational creativity, creative tools (e.g., ChatGPT and AI art); and Superintelligence, superhuman play and analysis in strategy games (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Stuart Mill
John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, politician and civil servant. One of the most influential thinkers in the history of liberalism and social liberalism, he contributed widely to social theory, political theory, and political economy. Dubbed "the most influential English-speaking philosopher of the nineteenth century" by the ''Stanford Encyclopedia of Philosophy'', he conceived of liberty as justifying the freedom of the individual in opposition to unlimited state and social control. He advocated political and social reforms such as proportional representation, the emancipation of women, and the development of labour organisations and farm cooperatives. The ''Columbia Encyclopedia'' describes Mill as occasionally coming "close to socialism, a theory repugnant to his predecessors". He was a proponent of utilitarianism, an ethical theory developed by his predecessor Jeremy Bentham. He contributed to the investigation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Bacon
Francis Bacon, 1st Viscount St Alban (; 22 January 1561 – 9 April 1626) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of natural philosophy, guided by the scientific method, and his works remained influential throughout the Scientific Revolution. Bacon has been called the father of empiricism. He argued for the possibility of scientific knowledge based only upon inductive reasoning and careful observation of events in nature. He believed that science could be achieved by the use of a sceptical and methodical approach whereby scientists aim to avoid misleading themselves. Although his most specific proposals about such a method, the Baconian method, did not have long-lasting influence, the general idea of the importance and possibility of a sceptical methodology makes Bacon one of the later founders of the scientific method. His portion of the method based in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Smuts
Field Marshal Jan Christian Smuts, (baptismal name Jan Christiaan Smuts, 24 May 1870 11 September 1950) was a South African statesman, military leader and philosopher. In addition to holding various military and cabinet posts, he served as Prime Minister of the Union of South Africa from 1919 to 1924 and 1939 to 1948. Smuts was born to Afrikaner parents in the British Cape Colony. He was educated at Victoria College, Stellenbosch before reading law at Christ's College, Cambridge on a scholarship. He was called to the bar at the Middle Temple in 1894 but returned home the following year. In the leadup to the Second Boer War, Smuts practised law in Pretoria, the capital of the South African Republic. He led the republic's delegation to the Bloemfontein Conference and served as an officer in a commando unit following the outbreak of war in 1899. In 1902, he played a key role in negotiating the Treaty of Vereeniging, which ended the war and resulted in the annexation of the So ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holism
Holism is the interdisciplinary idea that systems possess properties as wholes apart from the properties of their component parts. Julian Tudor Hart (2010''The Political Economy of Health Care''pp.106, 258 The aphorism "The whole is greater than the sum of its parts", typically attributed to Aristotle, is often given as a summary of this proposal. The concept of holism can inform the methodology for a broad array of scientific fields and lifestyle practices. When applications of holism are said to reveal properties of a whole system beyond those of its parts, these qualities are referred to as emergent properties of that system. Holism in all contexts is often placed in opposition to reductionism, a dominant notion in the philosophy of science that systems containing parts contain no unique properties beyond those parts. Proponents of holism consider the search for emergent properties within systems to be demonstrative of their perspective. Background The term "holism" was coined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Reasoning
Inductive reasoning refers to a variety of method of reasoning, methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike Deductive reasoning, ''deductive'' reasoning (such as mathematical induction), where the conclusion is ''certain'', given the premises are correct, inductive reasoning produces conclusions that are at best ''probable'', given the evidence provided. Types The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. Inductive generalization A generalization (more accurately, an ''inductive generalization'') proceeds from premises about a Sample (statistics), sample to a conclusion about the statistical population, population. The observation obtained from this sample is projected onto the broader population. : The proportion Q of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...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] |
Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to Ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laws Of Thought
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally they are taken as laws that guide and underlie everyone's thinking, thoughts, expressions, discussions, etc. However, such classical ideas are often questioned or rejected in more recent developments, such as intuitionistic logic, dialetheism and fuzzy logic. According to the 1999 '' Cambridge Dictionary of Philosophy'', laws of thought are laws by which or in accordance with which valid thought proceeds, or that justify valid inference, or to which all valid deduction is reducible. Laws of thought are rules that apply without exception to any subject matter of thought, etc.; sometimes they are said to be the object of logic. The term, rarely used in exactly the same sense by different authors, has long been associated with three equally am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
