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I was actually discussing this today, especially the first fallacious conclusion. With a Ph.D. candidate at Stanford no less . . . I don’t think Gödel was demo

I was actually discussing this today, especially the first fallacious conclusion. With a Ph.D. candidate at Stanford no less . . . I don’t think Gödel was demonstrating the "limitations" of logic. I think he was demonstrating the limitations of lower logics so that we could wield higher logic. Just as Cantor broke through into the transfinite. “From the paradise, that Cantor created for us, no-one can expel us.” I don’t see Gödel’s theorems as expressing the failure of logic, I think the holes(incompleteness) it illuminates are doorways. Gödel prompted people to explore things like plurivalent logic and fuzzy logic, at least in the “west”. https://aeon.co/essays/the-logic-of-buddhist-philosophy-goes-beyond-simple-truth https://aeon.co/essays/the-logic-of-buddhist-philosophy-goes...

jeromebaek 8y ago
Once I had a similar conversation with Scott Aaronson about this. I said the theorem shows the limits of logic; he said it shows the POWER of logic. My reply was: what does it matter? It just depends on perspective. As in: "logic is so powerful, it can even demonstrate its own limitations!" or: "logic is limited, and we know this for eternity, because logic proved it!"
- empath75 8y ago
  It’s not really a limitation of logic, because logic is not constrained to a particular set of axioms.
  - googlemike 8y ago
    But logic is composed of a particular set of axioms and rules - so is not any thing composed of a set of such things itself constrained by the very nature of its parts?
    - empath75 8y ago
      Godels theorem has nothing to say about first order logic.
lihaciudaniel 8y ago
That article that you cited shows no conclusion whatsoever. Its true that the 4 corners of truth in Buddhism are contradictory to the Aristotelian logic. A HN comment even pointed out that fuzzy logic won't fix paradoxes: https://news.ycombinator.com/item?id=7719214 https://news.ycombinator.com/item?id=7719214 >I don’t see Gödel’s theorems as expressing the failure of logic, It shows the limitation of formal systems, which we live and is the universe > I think the holes(incompleteness) it illuminates are doorways. No it doesn't, it shows limitation of understanding.

jeromebaek 8y ago

Once I had a similar conversation with Scott Aaronson about this. I said the theorem shows the limits of logic; he said it shows the POWER of logic. My reply was: what does it matter? It just depends on perspective. As in: "logic is so powerful, it can even demonstrate its own limitations!" or: "logic is limited, and we know this for eternity, because logic proved it!"

empath75 8y ago
It’s not really a limitation of logic, because logic is not constrained to a particular set of axioms.
- googlemike 8y ago
  But logic is composed of a particular set of axioms and rules - so is not any thing composed of a set of such things itself constrained by the very nature of its parts?
  - empath75 8y ago
    Godels theorem has nothing to say about first order logic.

lihaciudaniel 8y ago

That article that you cited shows no conclusion whatsoever. Its true that the 4 corners of truth in Buddhism are contradictory to the Aristotelian logic. A HN comment even pointed out that fuzzy logic won't fix paradoxes: https://news.ycombinator.com/item?id=7719214 https://news.ycombinator.com/item?id=7719214 >I don’t see Gödel’s theorems as expressing the failure of logic, It shows the limitation of formal systems, which we live and is the universe > I think the holes(incompleteness) it illuminates are doorways. No it doesn't, it shows limitation of understanding.