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Contemporary developments in logic and the foundations of mathematics, especially Bertrand Russell and Alfred North Whitehead's monumental Principia Mathematica, impressed the more mathematically minded logical positivists such as Hans Hahn and Rudolf Carnap.
" Language-planning " and syntactical techniques derived from these developments were used to defend logicism in the philosophy of mathematics and various reductionist theses.
Russell's theory of types was employed to great effect in Carnap's early anti-metaphysical polemics.

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