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Axiom

Axiom
An axiom or postulate is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.[1] The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident. In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Etymology[edit] The word "axiom" comes from the Greek word ἀξίωμα (axioma), a verbal noun from the verb ἀξιόειν (axioein), meaning "to deem worthy", but also "to require", which in turn comes from ἄξιος (axios), meaning "being in balance", and hence "having (the same) value (as)", "worthy", "proper". Ancient geometers maintained some distinction between axioms and postulates. Historical development[edit] Early Greeks[edit] Postulates Related:  Scienza☢️ Theories

Non sequitur (logic) Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises.[1] In a non sequitur, the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. All invalid arguments are special cases of non sequitur. The term has special applicability in law, having a formal legal definition. Many types of known non sequitur argument forms have been classified into many types of logical fallacies. In everyday speech, a non sequitur is a statement in which the final part is totally unrelated to the first part, for example: Life is life and fun is fun, but it's all so quiet when the goldfish die. It can also refer to a response that is totally unrelated to the original statement or question: Mary: I wonder how Mrs. The fallacy of the undistributed middle takes the following form: All Zs are Bs.Y is a B.Therefore, Y is a Z.

Adaptive system The term adaptation is used in biology in relation to how living beings adapt to their environments, but with two different meanings. First, the continuous adaptation of an organism to its environment, so as to maintain itself in a viable state, through sensory feedback mechanisms. Second, the development (through evolutionary steps) of an adaptation (an anatomic structure, physiological process or behavior characteristic) that increases the probability of an organism reproducing itself (although sometimes not directly).[citation needed] Generally speaking, an adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts. Some artificial systems can be adaptive as well; for instance, robots employ control systems that utilize feedback loops to sense new conditions in their environment and adapt accordingly. The Law of Adaptation[edit] Let .

Truth-bearer Introduction[edit] Some distinctions and terminology as used in this article, based on Wolfram 1989[3] Chapter 2 Section1) follow. It should be understood that the terminology described is not always used in the ways set out, and it is introduced solely for the purposes of discussion in this article. Use is made of the type–token and use–mention distinctions.Reflection on occurrences of numerals might be helpful.[4] In grammar a sentence can be a declaration, an explanation, a question, a command. In logic a declarative sentence is considered to be a sentence that can be used to communicate truth. A character[nb 1] is a typographic character (printed or written) etc. A word token[nb 2] is a pattern of characters. A sentence-token[nb 6] is a pattern of word-tokens. A referring-expression[nb 13] is expression that can be used to pick out or refer to particular entity. Sentences in natural languages[edit] Theory 1a: All and only meaningful-declarative-sentence-types[nb 17]) are truth-bearers

Making Systems Thinking More Than a Slogan From climate change and deforestation to collapsing fisheries, species extinction and poisons in our food and water, our society is unsustainable and it is getting worse fast. Many advocate that overcoming these problems requires the development of systems thinking. We’ve long known that we live on a finite “spaceship Earth” in which “there is no away” and “everything is connected to everything else.” The challenge lies in moving from slogans about systems to meaningful methods to understand complexity, facilitate individual and organizational learning, and catalyze the changes we need to create a sustainable society in which all can thrive. Here, I’ll describe how the world operates as a system — and how businesses can respond effectively to the challenges we face. Systems thinking is used in the World Economic Forum report (2011) All too often, however, we treat problems in isolation, ignoring the networks of feedback that bind us to one another and to nature. 2) Recognize constraints.

Butterfly effect In chaos theory, the butterfly effect is the sensitive dependency on initial conditions in which a small change at one place in a deterministic nonlinear system can result in large differences in a later state. The name of the effect, coined by Edward Lorenz, is derived from the theoretical example of a hurricane's formation being contingent on whether or not a distant butterfly had flapped its wings several weeks earlier. Although the butterfly effect may appear to be an unlikely behavior, it is exhibited by very simple systems. For example, a ball placed at the crest of a hill may roll into any surrounding valley depending on, among other things, slight differences in its initial position. History[edit] Chaos theory and the sensitive dependence on initial conditions was described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.[1] He later proposed that such phenomena could be common, for example, in meteorology. Illustration[edit] , then

Truth-bearer Introduction[edit] Some distinctions and terminology as used in this article, based on Wolfram 1989[3] Chapter 2 Section1) follow. It should be understood that the terminology described is not always used in the ways set out, and it is introduced solely for the purposes of discussion in this article. A character[nb 1] is a typographic character (printed or written) etc. A word token[nb 2] is a pattern of characters. A sentence-token[nb 6] is a pattern of word-tokens. A referring-expression[nb 13] is expression that can be used to pick out or refer to particular entity. Sentences in natural languages[edit] As Aristotle pointed out, since some sentences are questions, commands, or meaningless, not all can be truth-bearers. Theory 1a: All and only meaningful-declarative-sentence-types[nb 17]) are truth-bearers Criticisms of Theory 1a Some meaningful-declarative-sentence-types will be both truth and false, contrary to our definition of truth-bearer, e.g. Revision to Theory 1a Theory 1b: Theory 1c

Vienna Circle 1924–1936 group of philosophers and scientists The Vienna Circle (German: Wiener Kreis) of logical empiricism was a group of elite philosophers and scientists drawn from the natural and social sciences, logic and mathematics who met regularly from 1924 to 1936 at the University of Vienna, chaired by Moritz Schlick. The Vienna Circle had a profound influence on 20th-century philosophy, especially philosophy of science and analytic philosophy. The philosophical position of the Vienna Circle was called logical empiricism (German: logischer Empirismus), logical positivism or neopositivism. It was influenced by Ernst Mach, David Hilbert, French conventionalism (Henri Poincaré and Pierre Duhem), Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein and Albert Einstein. During the era of Austrofascism and after the annexation of Austria by Nazi Germany most members of the Vienna Circle were forced to emigrate. History of the Vienna Circle[edit] The "First Vienna Circle" (1907–1912)[edit] [edit]

MINDSPACE Behavioural Economics Update: Professor Cass Sunstein, co-author of Nudge: Improving Decisions about Health, Wealth, and Happiness, will speak at the Institute for Government on 22 March 2013. Background New insights from science and behaviour change could lead to significantly improved outcomes, and at a lower cost, than the way many conventional policy tools are used. MINDSPACE: Influencing behaviour through public policy was published by the Institute for Government and the Cabinet Office on 2 March 2010. The report explores how behaviour change theory can help meet current policy challenges, such as how to: reduce crime tackle obesity ensure environmental sustainability. Today's policy makers are in the business of influencing behaviour - they need to understand the effects their policies may be having. Blogs MINDSPACE grows up – behavioural economics in government Reaction "brilliant" - Sir Gus O'Donnell, Cabinet Secretary "this is the best report of its kind - it is reflective and practical at the same time.

Proposition Historical usage[edit] By Aristotle[edit] By the logical positivists[edit] Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example, yes–no questions present propositions, being inquiries into the truth value of them. On the other hand, some signs can be declarative assertions of propositions without forming a sentence nor even being linguistic, e.g. traffic signs convey definite meaning which is either true or false. Propositions are also spoken of as the content of beliefs and similar intentional attitudes such as desires, preferences, and hopes. By Russell[edit] Bertrand Russell held that propositions were structured entities with objects and properties as constituents. Relation to the mind[edit] In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. Treatment in logic[edit] Objections to propositions[edit] thus defining proposition in terms of synonymity.

Philippe Guillemant - Vers la physique de demain Data Theory Probability interpretations The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, we interpret the probability values of probability theory. There are two broad categories[1][2] of probability interpretations which can be called "physical" and "evidential" probabilities. Evidential probability, also called Bayesian probability (or subjectivist probability), can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. Philosophy[edit] in

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