Logical Positivism - Bertrand Russell
In a series of articles I will be forming a bite size guide to the philosophical composition known as Logical Positivism.
Logical positivism was a school of thought that appeared in Vienna in the 1920’s. It was centred around the discussions of a group of philosophers known as the Vienna Circle. They discussed logic, mathematics, language and had a great distaste of metaphysics. They claimed that true knowledge was gained through sense experience and reason alone. Influenced by advances in modern science, logical positivists sought to apply the scientific paradigm to philosophy and show metaphysics to be meaningless.
Bertrand Russell (1872-1970)
Godson of liberal philosopher John Stuart Mill, Bertrand Russell was perhaps best known outside of philosophers as a passionate anti-nuclear, and anti-war, social activist. He was the founding president of the Campaign for Nuclear Disarmament, and was arrested at the age of 89 whilst protesting on its behalf.
From Trelleck in Wales, Russell is probably most famous amongst philosophers for his work on mathematical logic. However, his writings covered every area of philosophy (apart from aesthetics), and his pieces on the philosophy of language are considered by some his most influential.
Russell showed a great talent within logic and mathematics as shown through the book 'Principia Mathematica' which was reviewed highly by the likes of Hans Hahn and Rudolph Carnap, both of the Vienna Circle, and the book went on to become one of the most influential books on logic (the view that (some or all of) mathematics can be reduced to (formal) logic) ever written. The book claimed that all mathematical truths can be translated into logical truths, and that all mathematical proofs may be translated into logical proofs. His theory of types was also used extensively in Logical positivist Carnap’s anti metaphysical polemics.
Russell pioneered arguably one of the most recognisable logical paradoxes; a set-theoretical paradox which has inspired further work in logic, set theory and the philosophy of mathematics. Russell’s Paradox, as it became known, arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. The significance of this paradox was that any sentence could be derived from a contradiction. This led to the further complication that if sets could be found to be inconsistent, thus could undermine the certainty of all mathematical proofs as set theory is key to all areas of mathematics.
Russell shared his findings with Frege, who as a result of the implications of this paradox had to abandon his many previous views on logic.
Russell himself tried to solve his paradox with his Theory of Types. In this theory Russell believed that the paradox could be avoided by categorising sentences into a hierarchy. Lowest levels being sentences or propositions about individuals, the next level for sets of individuals and the next level for sets of sets and onwards continuously. The reasoning for this was that then scope of a particular predicate or condition could applied to sentences, propositions or sets only if they were of the same level.