There is no such thing as abstractly knowing something

 

"Whether a mathematical proposition is true or not is indeed independent of physics. But the proof of such a proposition is a matter of physics only . There is no such thing as abstractly proving something, just as there is no such thing as abstractly knowing something. Mathematical truth is absolutely necessary and transcendent , but all knowledge is generated by physical processes, and its scope and limitations are conditioned by the laws of nature. One can define a class of abstract entities and call them ‘proofs’ (or computations), just as one can define abstract entities and call them triangles and have them obey Euclidean geometry . But you can not infer anything from that theory of ‘ triangles’ about what angle you will turn through if you walk around a closed path consisting of three straight lines. Nor can those ‘proof ’ do the job of verifying mathematical statements. A mathematical ‘ theory of proof s’ has no bearing on which truths can or can not be proved in reality , or be known in reality ; and similarly a theory of abstract ‘ computation ’ has no bearing on what can or can not be computed in reality ."