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Carnap, Lewis, and others take a pragmatic stand on the question of choosing betwe * [[Rudolf Carnap]] (important exponent of [[logical positivism]], teacher of Quine)

...mathematics is reducible to logic, and hence nothing but a part of logic (Carnap 1931/1883, 41). Logicists hold that mathematics can be known ''a priori'', [[Rudolf Carnap]] (1931) presents the logicist thesis in two parts:

* Carnap, Rudolf (1958), ''Introduction to Symbolic Logic with Applications'', Dover Publica

Modern Formalists, such as [[Rudolf Carnap]], [[Alfred Tarski]] and [[Haskell Curry]], continue to maintain that mathe ...at mathematics is reducible to logic, hence nothing but a part of logic. (Carnap 1931/1883, 41).

* [[Rudolf Carnap|Carnap, Rudolf]] (1931), "Die logizistische Grundlegung der Mathematik", ''Erkenntnis'' 2,

* [[Rudolf Carnap|Carnap, Rudolf]] (1931), "Die logizistische Grundlegung der Mathematik", ''Erkenntnis'' 2,

...at mathematics is reducible to logic, hence nothing but a part of logic. (Carnap 1931/1883, 41). [[Rudolf Carnap]] (1931) presents the logicist thesis in two parts:

...at mathematics is reducible to logic, hence nothing but a part of logic. (Carnap 1931/1883, 41). [[Rudolf Carnap]] (1931) presents the logicist thesis in two parts:

| In recent years Carnap has tended to explain analyticity by appeal to | the language. All other statements of the language are, Carnap assumes,