display all the ideas for this combination of philosophers
22 ideas
16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
8739 | Geometry studies the Euclidean space that dictates how we perceive things [Kant, by Shapiro] |
16919 | Geometry rests on our intuition of space [Kant] |
8740 | Geometry would just be an idle game without its connection to our intuition [Kant] |
16899 | Geometrical truth comes from a general schema abstracted from a particular object [Kant, by Burge] |
16920 | Numbers are formed by addition of units in time [Kant] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
9632 | Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR] |
3343 | Euclid's could be the only viable geometry, if rejection of the parallel line postulate doesn't lead to a contradiction [Benardete,JA on Kant] |
8737 | Kant suggested that arithmetic has no axioms [Kant, by Shapiro] |
5557 | Axioms ought to be synthetic a priori propositions [Kant] |
12421 | Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant] |
16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
17617 | Maths is a priori, but without its relation to empirical objects it is meaningless [Kant] |
16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
12458 | Kant taught that mathematics is independent of logic, and cannot be grounded in it [Kant, by Hilbert] |
2795 | If 7+5=12 is analytic, then an infinity of other ways to reach 12 have to be analytic [Kant, by Dancy,J] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |