It is curious, how one often mistrusts one’s own opinions if they are stated by someone else. - Douglas Hofstadter

It now becomes clear that consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.

In short, Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.

Seeing anything as waves suggests immediate knobs: wavelength, frequency, amplitude, speed, medium, and a host of other basic notions that define the essence of undularity. Seeing anything as particles suggests totally different knobs: mass, shape, radius, rotation, constituents, and a host of other basic notions that define the essence of corpuscularity.