Philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.
TruthTruth is the property of being in accord with fact or reality. In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences. Truth is usually held to be the opposite of falsehood. The concept of truth is discussed and debated in various contexts, including philosophy, art, theology, law, and science. Most human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion, including journalism and everyday life.
Probability interpretationsThe 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, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities.
Vienna CircleThe Vienna Circle (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.
RelativismRelativism is a family of philosophical views which deny claims to objectivity within a particular domain and assert that valuations in that domain are relative to the perspective of an observer or the context in which they are assessed. There are many different forms of relativism, with a great deal of variation in scope and differing degrees of controversy among them. Moral relativism encompasses the differences in moral judgments among people and cultures.
Ludwig Wittgenstein'Ludwig Josef Johann Wittgenstein' (ˈvɪtgənʃtaɪn,_-staɪn ; ˈluːtvɪç ˈjoːzɛf 'joːhan ˈvɪtɡn̩ʃtaɪn; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considered by some to be the greatest philosopher of the 20th century. From 1929 to 1947, Wittgenstein taught at the University of Cambridge.
Baruch SpinozaBaruch (de) Spinoza (24 November 1632 – 21 February 1677) was a philosopher of Portuguese-Jewish origin, born in Amsterdam, the Dutch Republic, and mostly known under the Latinized pen name Benedictus de Spinoza. One of the foremost and seminal thinkers of the Enlightenment, modern biblical criticism, and 17th-century Rationalism, including modern conceptions of the self and the universe, he came to be considered "one of the most important philosophers—and certainly the most radical—of the early modern period".
MetaphilosophyMetaphilosophy, sometimes called the philosophy of philosophy, is "the investigation of the nature of philosophy". Its subject matter includes the aims of philosophy, the boundaries of philosophy, and its methods. Thus, while philosophy characteristically inquires into the nature of being, the reality of objects, the possibility of knowledge, the nature of truth, and so on, metaphilosophy is the self-reflective inquiry into the nature, aims, and methods of the activity that makes these kinds of inquiries, by asking what is philosophy itself, what sorts of questions it should ask, how it might pose and answer them, and what it can achieve in doing so.
Scientific theoryA scientific theory is an explanation of an aspect of the natural world and universe that can be (or a fortiori, that has been) repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning.
Scientific realismScientific realism is the view that the universe described by science is real regardless of how it may be interpreted. Within philosophy of science, this view is often an answer to the question "how is the success of science to be explained?" The discussion on the success of science in this context centers primarily on the status of unobservable entities apparently talked about by scientific theories. Generally, those who are scientific realists assert that one can make valid claims about unobservables (viz.
