Bertrand Arthur William Russell, 3rd Earl Russell, was a British mathematician, logician, philosopher, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic philosophy.
In the philosophy of mathematics, intuitionism, or neointuitionism, is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Truth or verity is the property of being in accord with fact or reality. In everyday language, it is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.
In mathematics, a binary relation on a set is reflexive if it relates every element of to itself.
A propositional attitude is a mental state held by an agent or organism toward a proposition. In philosophy, propositional attitudes can be considered to be neurally-realized causally efficacious content-bearing internal states. Linguistically, propositional attitudes are denoted by a verb governing an embedded "that" clause, for example, 'Sally believed that she had won'.
Bernard Bosanquet was an English philosopher and political theorist, and an influential figure on matters of political and social policy in the late 19th and early 20th centuries. His work influenced but was later subject to criticism by many thinkers, notably Bertrand Russell, John Dewey, William James and Ludwig Wittgenstein. Bernard was the husband of Helen Bosanquet, the leader of the Charity Organisation Society.
Logical atomism is a philosophical view that originated in the early 20th century with the development of analytic philosophy. It holds that the world consists of ultimate logical "facts" that cannot be broken down any further, each of which can be understood independently of other facts.
Ivor Owen Grattan-Guinness was a historian of mathematics and logic.
The Muirhead Library of Philosophy was an influential series which published some of the best writings of twentieth century philosophy. The original programme was drawn up by John Muirhead and published in Erdmann's History of Philosophy in 1890. This statement was published in slightly altered form in subsequent volumes:
The following outline is provided as an overview of and topical guide to epistemology:
James Opie Urmson was a philosopher and classicist who spent most of his professional career at Corpus Christi College, Oxford. He was a prolific author and expert on a number of topics including British analytic/linguistic philosophy, George Berkeley, ethics, and Greek philosophy.
A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an object is anything that has been formally defined, and with which one may do deductive reasoning and mathematical proofs. Typically, a mathematical object can be a value that can be assigned to a variable, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, sets, functions, expressions, geometric objects, transformations of other mathematical objects, and spaces. Mathematical objects can be very complex; for example, theorems, proofs, and even theories are considered as mathematical objects in proof theory.
The aspects of Bertrand Russell's views on philosophy cover the changing viewpoints of philosopher and mathematician Bertrand Russell (1872–1970), from his early writings in 1896 until his death in February 1970.
Aspects of philosopher, mathematician and social activist Bertrand Russell's views on society changed over nearly 80 years of prolific writing, beginning with his early work in 1896, until his death in February 1970.
Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All proposed definitions are controversial in their own ways.
British philosophy refers to the philosophical tradition of the British people. "The native characteristics of British philosophy are these: common sense, dislike of complication, a strong preference for the concrete over the abstract and a certain awkward honesty of method in which an occasional pearl of poetry is embedded".
George Spencer-Brown was an English polymath best known as the author of Laws of Form. He described himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, consulting psychotherapist, author, and poet".
Leonard James Russell, FBA was a British philosopher. He was Professor of Philosophy at the University of Birmingham from 1925 to 1950.
