History
Late 19th-century English philosophy was dominated by British idealism, as taught by philosophers such as F.H. Bradley and Thomas Hill Green. It was against this intellectual background that the founders of analytic philosophy, G. E. Moore and Bertrand Russell, articulated the program of early analytic philosophy.
Since its beginning, a basic principle of analytic philosophy has been conceptual clarity, in the name of which Moore and Russell rejected Hegelianism, which they accused of obscurity and idealism. Inspired by developments in modern logic, the early Russell claimed that the problems of philosophy can be solved by showing the simple constituents of complex notions.
Russell, during his early career, along with collaborator Alfred North Whitehead, was much influenced by Gottlob Frege, who developed predicate logic, which allowed a much greater range of sentences to be parsed into logical form than was possible by the ancient Aristotlean logic. Frege was also an influential philosopher of mathematics in Germany at the beginning of the 20th century. In contrast to Husserl's 1891 book Philosophie der Arithmetik, which attempted to show that the concept of the cardinal number derived from psychical acts of grouping objects and counting them, Frege sought to show that mathematics and logic have their own validity, independent of the judgments or mental states of individual mathematicians and logicians (which were the basis of arithmetic according to the "psychologism" of Husserl's Philosophie). Frege further developed his philosophy of logic and mathematics in The Foundations of Arithmetic and The Basic Laws of Arithmetic where he provided an alternative to psychologistic accounts of the concept of number.
Like Frege, Bertrand Russell and Alfred North Whitehead attempted to show that mathematics is reducible to fundamental logical principles. Their Principia Mathematica (1910–1913) encouraged many philosophers to renew their interest with the development of symbolic logic. Additionally, Bertrand Russell adopted Frege's predicate logic as his primary philosophical method, a method he thought could expose the underlying structure of philosophical problems. For example, the English word “is” has three distinct meanings by predicate logic:
- For the sentence 'the cat is asleep', the is of predication means that "x is P" (denoted as P(x))
- For the sentence 'there is a cat', the is of existence means that "there is an x" (∃x);
- For the sentence 'three is half of six', the is of identity means that "x is the same as y" (x=y).
Russell sought to resolve various philosophical issues by applying such definite distinctions, most famously in his analysis of definite descriptions in "On Denoting."
Read more about this topic: Analytic Philosophy
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