I’m curious if anyone with knowledge of formal logic & mathematics can comment on whether Gödel’s theorems have any relevance to discussions of faith. Specifically to the strident atheists who would pose that science renders belief in God irrational.
Not that Gödel’s theorems have anything to say about God directly. But if I understand correctly they do place some limitation on the formal “proveability” of mathematics. The problem is that I don’t understand very well, and figure I am on thin ice if I say that mathematics, which underlies science, involves a certain leap of faith (by way of defining some axioms) in assuming that mathematics always “works”. But I’m curious if this line of reasoning leads anywhere, or is totally off the mark.
In a related vein there is the Heisenberg uncertainty principle, which puts a specific limit on a certain type of scientific knowledge. Not that it says anything about God. But science proves a formal limitation on the precision with which we can know, or even define, certain physical quantities.
I guess my question is, are these concepts at all useful in demonstrating to rationalists that there are things that are formally outside the bounds of what can be known by pure logic & scientific reason. And that there are certain things that will never be known with scientific certainty.
One problem I see is that you could go off the deep end in the other direction, into a postmodern morass of fuzzy thinking and existentialism. So I wouldn’t push it too far. The other problem is that proving science has limitations is different from proving a valid role for faith. So maybe it’s misguided altogether. Comments welcome.