The set of all sets must be.. Oh what’s the fancy word…. A holomorphism? I don’t remember. I’m at my phone now. The set of all sets must contain both the complete and the incomplete set making it both complete and incomplete. Having a paradox as rule 1 is required for the system to function.
Axiomic systems always result in failure because their basis is that of axiom and proof. There in a constant dance with each other but they are not self generating. They also ignore the source of the axiom: us. There’s 3 parts: axiom proof and us. The belief that it exists in its own platonic realm separate from reality is the main cause of the issue. It doesn’t invalidate it by any means. Just points to limitations of the system, like any system has.
(Edit: wrote this before your last response) I once worked on a ternary logic system –. I prototyped it in Excel, my main scratchpad – and look for solutions for the uncertainties that were practical and pragmatic in nature, to compensate for the areas that the system fails. There’s a similar issue in computer engineering – I believe it’s called a race condition. I’ve seen it happen – especially with video cards. A calculation reaches a race condition – VERY common on video cards with built in matrix transforms – because fundamentally, you’re attempting to squeeze three-dimensional calculations into a two-dimensional space. It’s going to run into problems and it does. When it does, the chips get hot, the Solder melts, and the video card is destroyed. All from a calculation that couldn’t be resolved
Thing is, I’m a commoner. Consider it this way: You understood I was using the terms differently than you did. That means: You understood me.
For me, communication is about being understood and understanding.
If you were grading a paper, you could justly fail me but, I’ve been out of school a very very very long time now tongue emoticon Cheers and I’ll be here if you wish to unpause smile emoticon