Logical Positivism (later also known as Logical Empiricism) is a 20th Century school of philosophy that developed out of Positivism and the early Analytic Philosophy movement, and which campaigned for a systematic reduction of all human knowledge to logical and scientific foundations.
According to Logical Positivists, a statement is meaningful only if it is either purely formal (essentially, mathematics and logic) or capable of empirical verification. This effectively resulted in an almost complete rejection of Metaphysics (and to a large extent Ethics) on the grounds that it is unverifiable. Logical Positivism was also committed to the idea of "Unified Science", or the development of a common language in which all scientific propositions can be expressed, usually by means of various "reductions" or "explications" of the terms of one science to the terms of another more fundamental one. For more details, see the section on the doctrine of Logical Positivism.
The most important early figures in the development of Logical Positivism were the Bohemian-Austrian Positivist philosopher Ernst Mach (1838 - 1916) and the Austrian Ludwig Wittgenstein (especially his "Tractatus" of 1921, a text of great importance for Logical Positivists).
The school grew from the discussions of the so-called "Vienna Circle" of Moritz Schlick (1882 - 1936) in the early 20th Century. A 1929 pamphlet jointly written by Otto Neurath (1882 - 1945), Hans Hahn (1979 - 1934) and Rudolf Carnap (1891 - 1970) brought together some of the major proponents of the movement and summarized the doctrines of the Vienna Circle at that time. The contemporaneous Berlin Circle of Hans Reichenbach (1891 - 1953) also propagated the new doctrines more widely in the 1920s and early 1930s.
A. J. Ayer is considered responsible for the spread of Logical Positivism to Britain, and his 1936 book "Language, Truth and Logic" was very influential. Developments in logic and the foundations of mathematics, especially in the "Principia Mathematica" by the British philosophers Bertrand Russell and Alfred North Whitehead, particularly impressed the more mathematically-minded Logical Positivists.
The movement dispersed in the late 1930's, mainly because of political upheaval and the untimely deaths of Hahn and Schlick. Logical Positivism was essential to the development of early Analytic Philosophy, with which it effectively merged.