Religion
In reply to the discussion: What is happening in the religious world? [View all]tama
(9,137 posts)Any logical system complex enough to contain number theory (which includes e.g. irrational and transcendental and imaginary numbers ) contains propositions or "a priori truths" that cannot be proven within a finite set of axioms.
The Gödel's proof of unprovability and other related issues of logical undecidables are of course not irrational statements, but rational understanding of them needs to look at them in a wider context than binary opposition between rational and irrational. And in this day and age world view that refuses to accept e.g. Gödel's proof of unprovability cannot be considered rational, but more like wishfull thinking and denial.
And analogically to theism, antitheism and atheism the "leap of faith"/"satori" etc. would seem to point to arational instead of rational or irrational. And the number theorical set of transcendental numbers is the mathematical area of arationals, in some sense.