structure for 'Mathematics'    |     alphabetical list of themes    |     expand these ideas

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics

[mathematics is knowable directly by pure reason]

11 ideas
Mathematics can only start from an a priori intuition which is not empirical but pure [Kant]
All necessary mathematical judgements are based on intuitions of space and time [Kant]
Bolzano began the elimination of intuition, by proving something which seemed obvious [Dummett on Bolzano]
Frege's logicism aimed at removing the reliance of arithmetic on intuition [Yourgrau on Frege]
Geometry appeals to intuition as the source of its axioms [Frege]
Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher]
If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
Mathematical intuition is not the type platonism needs [Kitcher]
Intuition is an outright hindrance to five-dimensional geometry [Shapiro]
Intuition doesn't support much mathematics, and we should question its reliability [Shapiro on Maddy]