Criticisms of predecessors
Psychologistic accounts of mathematics
Frege objects to any account of mathematics based on psychologism, that is the view that math and numbers are relative to the subjective thoughts of the people who think of them. According to Frege, psychological accounts appeal to what is subjective, while mathematics is purely objective: mathematics are completely independent from human thought. Mathematical entities, according to Frege, have objective properties regardless of humans thinking of them: it is not possible to think of mathematical statements as something which evolved naturally through human history and evolution. He sees a fundamental distinction between logic (and its extension, according to Frege, math) and psychology. Logic explains necessary facts the order of ideas, whereas psychology studies certain thought processes in individual minds.
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