David Peat

30 From Certainty to Uncertaintywill also know that 2 + 2 = 4. Indeed, when human beings search forintelligent life in the universe they do so by beaming out mathematicaldata because scientists and astronomers are convinced that mathematicsis the universal language of the cosmos.If the substantiality of matter dissolves into uncertainty andcomplementarity, at least we should still find security in mathematics.This was the view held by mathematicians and philosophers at the startof the twentieth century. All that was required was a rigorous proofthat mathematics is the ultimate certainty, a proof that is final andharbors no degree of ambiguity.In essence, mathematicians wanted to prove two things:1. Mathematics is consistent: Mathematics contains no internalcontradictions. There are no slips of reason or ambiguities. No matterfrom what direction we approach the edifice of mathematics, it willalways display the same rigor and truth.2. Mathematics is complete: No mathematical truths are left hanging.Nothing needs adding to the system. Mathematicians can proveevery theorem with total rigor so that nothing is excluded from theoverall systemBut why all the fuss? Why the need for such definitive proofs? After all,mathematics has been in existence since the time of the ancient Greeks.Great cathedrals were constructed according to mathematical principlesand have stood for centuries. Mathematics sends a rocket to themoon and works out a multinational corporation’s annual accounts. Ifmathematical answers were uncertain, or if accountants suddenly discoveredthat mathematics was leaving something out of a balance sheet,our financial world would come to an abrupt halt. In every case mathematicsworks perfectly, so why bother to dot the final “i” and cross thefinal “t”?An appeal to common sense may work for most of us, but philosopherspoint out that, although mathematics is founded in logic, somemathematical results look bizarre and counterintuitive. We can’t relyon common sense to tell us mathematics always works, they tell us; wewant certainty, and we want proof of consistency and completeness.