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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism

[maths only exists as human psychological states]

3 ideas

8621	Mental states are irrelevant to mathematics, because they are vague and fluctuating [Frege]
	Full Idea: Sensations and mental pictures, formed from the amalgamated traces of earlier sense-impressions, are absolutely no concern of arithmetic; they are characteristically fluctuating and indefinite, in contrast to the concepts and objects of mathematics.
	From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro)
	A reaction: Sounds very like Plato's distinction between the worlds of opinion and knowledge (Ideas 1170 and 2133). This view is fine amidst the implicit dualism of all nineteenth century thought, but how does abstract mathematics link to the soggy brain?

14449	There is always something psychological about inference [Russell]
	Full Idea: There is always unavoidably something psychological about inference.
	From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV)
	A reaction: Glad to find Russell saying that. Only pure Fregeans dream of a logic that rises totally above the minds that think it. See Robert Hanna on the subject.

15211	There is not an exclusive dichotomy between the formal and the logical [Harré/Madden]
	Full Idea: The assumption that there is an exclusive dichotomy between the formal and the psychological is, in our view, an error of enormous consequence.
	From: Harré,R./Madden,E.H. (Causal Powers [1975], 1.I.A)
	A reaction: I agree entirely with this, and am opposed to the Fregean view of the matter. The psychology is the bridge between the physical world and the logic. Frege had to be a platonist, so that the formalism could latch onto something.