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by theWheez 2473 days ago
Yes, I understand that, and am well aware of Godel's position on its application. Hence my statement that I extrapolate it further than intended.

My extrapolation is influenced by the Curry-Howard isomorphism, equating computer programs and mathematical proofs. Extrapolation to "reality" and philosophy, to me, comes from my belief of computing as universal and that consciousness is not so separate from computing.
1 comments
psychometry 2473 days ago
That's kind of ridiculous, though. You completely lose the sense of the theorem once you expand the axioms beyond those explicitly defined. It would be like saying we don't know whether a boulder will stop rolling down a hill or not...because of the Halting Problem. That's just not how mathematics works.
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theWheez 2473 days ago
I'm not expanding the axioms, I'm comparing the paradoxical nature of mathematics to other systems.

I'm not saying that reality is encompassed in the theorem because "mathematics", I'm positing that if mathematics, a man-made formal system, is self-consistent but requires a true, unprovable statement, then perhaps other man-made systems might reveal similar paradoxes, when put under scrutiny.

Mathematics is unique in that it is systematic and, as Godel discovered, able to be self referential and explicitly outline this paradox. Yet one can recreate the sense of the theorem in English with the phrase "this sentence is false".

This doesn't invalidate mathematics, nor English, nor any system. It simply demonstrates that what we may consider the "sound" logic of mathematics is paridoxical, and I believe that this paradox, this strange loop, is not unique to Godel's mathematical theory alone.

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psychometry 2472 days ago
Considering the Godel sentence is a purely syntactical construction, I think even Godel himself would have a very difficult time even imagining what an analog would be in some higher system (much less actually constructing one). This is why he was so critical of attempts by others (e.g. Wittgenstein) to knock down the theorem by discussing its philosophical implications.
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