gedpeck

9 ms·

1. 61.▲
   by gedpeck 2y ago

   You know more than me on logic so I defer to your expertise. https://math.stackexchange.com/questions/4753432/g%C3%B6dels... Andreas Blass in the comments says that the Incompleteness results don’t apply to the se
2. 62.▲
   by gedpeck 2y ago

   I think you are wrong in your first sentence. Take the collection of all true statements and make that your axiomatic system. Andreas Blass in the comments says that Incompleteness does not apply to PA_2. https://math.stackexcha
3. 63.▲
   by gedpeck 2y ago

   It shouldn’t and I didn’t say it should. I gave a fact and asked a question. Why is PA_2 computer science? Computer science ought to be about computation, right? There are non-computable objects that mathematicians study. Is that part o
4. 64.▲
   by gedpeck 2y ago

   Do you have a reference for the second order induction schema being recursively enumerable? My understanding - I’m not a logician - is that the second order Peano Axioms are categorical. The Incompleteness theorems don’t apply to this syst
5. 65.▲
   by gedpeck 2y ago

   What false assumption did I make? I just pointed out a fact and asked a question. How many false assumptions could I have made with just one statement of fact and two questions? If you don’t have a valid answer to the question then don’t
6. 66.▲
   by gedpeck 2y ago

   There are statements provably true about the natural numbers that can’t be proven in first order PA. Are such statements part of computer science? If so, how?
7. 67.▲
   by gedpeck 2y ago

   It’s not a settled issue in the sense that the experts overwhelmingly agree on one side vs. the other. My link was posted to show a contrarian view. Lots of research papers arguing on either side have been written about the Chinese Room.
8. 68.▲
   by gedpeck 2y ago

   I don’t believe you are engaging in a good faith discussion. Your previous comment is worthy of further contemplation but not this one. A computer can not emulate a person’s brain. At least not now and there isn’t sufficient evidence to
9. 69.▲
   by gedpeck 2y ago

   https://en.wikipedia.org/wiki/Chinese_room
10. 70.▲
    by gedpeck 2y ago

    ...something's hard is not a reason to expect it's magic. Something that is impossible to accurately be modeled mathematically is not magic.
11. 71.▲
    by gedpeck 2y ago

    Thanks for the response and perspective. I'll contemplate it more later. While I personally may not have come up with the Incompleteness results humans did. The discussion is about human intelligence in general (particularly applied
12. 72.▲
    by gedpeck 2y ago

    You are claiming to be able to mathematically model consciousness or that it is theoretically possible. So what’s the model or proof that it can theoretically be modeled. Your statements regarding were lacking.
13. 73.▲
    by gedpeck 2y ago

    Yes. It’s a basic result proven in any mathematical logic course at the senior or beginning graduate level. If a Turing Machine can’t prove that it can’t prove the consistency of its axiomatic system from within that system but that it cou
14. 74.▲
    by gedpeck 2y ago

    ..physical laws that are, in principle, fully modeled by mathematical theory that can be simulated on a computer. Consciousness so far appears to be something that can’t be modeled mathematically. Can a Turing Machine conclude that while
15. 75.▲
    by gedpeck 2y ago

    … our brains are physical systems which themselves can be modeled by mathematics.. How do you know this? What is the model? Can an AI come up with the Incompleteness Theorems? It can be proven ZFC that PA is consistent. Can an AI or T
16. 76.▲
    by gedpeck 2y ago

    So go back to the 1950s and the point stands. What does it matter when the actual start date is in terms of the point being right or wrong?