more from this thinker | more from this text
Full Idea
For Kant the only legitimate infinity is the so-called potential infinity, not the actual infinity.
Gist of Idea
Kant only accepts potential infinity, not actual infinity
Source
report of Immanuel Kant (Critique of Pure Reason [1781]) by James Robert Brown - Philosophy of Mathematics Ch.5
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.65
A Reaction
This is part of what leads on the the Constructivist view of mathematics. There is a procedure for endlessly continuing, but no procedure for arriving. That seems to make good sense.
13212 | Infinity is only potential, never actual [Aristotle] |
22929 | Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin] |
9632 | Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR] |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |