Doing Mathematics Differently
This is a good article, and an important topic, but it mischaracterizes the discipline of mathematics:<p>> the principle that mathematical truth is black or white and provides absolute certainty.<p>> Pure mathematicians like to think that they have absolute truth<p>Formal mathematics has no concept of absolute truth; this is left for philosophy. It's just concerned with axioms and theorems (and their proofs). Whether an axiom reflects reality or not is out of scope, which is the whole point of their invention. As a philosopher you're welcome to debate them, and as a pragmatist you're welcome to choose them (and be compelled to accept their consequent theorems).<p>> Because it is easy for mathematicians to ignore Gödel’s proof. What lurks in their heart of hearts is a commitment to absolute truth, and a universal formal axiomatic theory for all of mathematics.<p>In one sense it's disheartening that we cannot prove or disprove every proposition in every axiomatic system. This is an unreasonable expectation as Gödel proved, but it doesn't invalidate the theorems we <i>have</i> proven and disproven. It also doesn't invalidate all of the programs we have written, even though there are non-terminating programs and uncomputable numbers.