(I got called away to do some jobs around the house!)

We should go further. Gödel's Theorem states, informally, that every branch of mathematics is incomplete or inconsistent. That includes these various geometries. And there is a huge gulf between "this is consistent" and "we haven't found an inconsistency". The whole of quantum mechanics and relativity are based on these branches of mathematics which may themselves be fundamentally flawed *and we simply haven't seen how yet*.

I was otherwise occupied when the question of fuzzy logic came up. It is not, to be honest, a branch I know a great deal about but it is certainly the case that the various alternatives are designed so that when something is unambiguously true or unambiguously false they give identical results to classical logic. They are, then, extensions to classical logic rather than alternatives. But the big problem lies in the premises, not the logic. Imagine we have a 'guess the weight of the cake' competition and the best guess is 1.9kg, when the actual weight is 2kg. Now, 1.9kg is 'not true', but it is clearly 'truer' in some sense than 0.1kg. If you have a fuzzy logic that is between 0 and 1, as most are, should we simply say this 0.95? Or 0.9? or 0.99? And is the 0.1kg actually more accurate than 1g, or are they equally manifestly wrong? SO, as I say, the biggest difficulty is no the logic, per se, but in agreeing the 'inputs'.