Gödel and Turing: we cannot use classical mathematics to build an interpreter that runs classical mathematics Church and Turing: we can use constructive mathematics to run constructive mathematics Minsky and Turing: we can use constructive mathematics to run classical mathematics
-
-
constructive mathematics is not time-less like classical math. a function that has not been computed yet does not have a defined value. pi is a function, not a number. the axiom of choice does not hold. true infinities and continua cannot be constructed
-
construction means that there has to be a machine that can perform the actual computations. in the strong, intuitionist form, we must actually run the proof, i.e. we need to compress it into a form that actually runs on our machine (which leads to a small foundational crack)
- 22 more replies
New conversation -
-
-
Is this like Brouwer intuitionist math? They reject law of excluded middle and proof by reductio ad absurdum so they only accept proof by construction and reject standard continuum math.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Constructive logic isn't a "branch of mathematics" as much as it is a system studied by the branch of mathematics, formal logic. i.e. there significantly more mathematicians that study constructive logic and use it than believe it is the only correct logic
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.