On Tue, Jun 1, 2021 at 8:38 AM Lawrence Crowell < [email protected]> wrote:
> Godel's theorems are our friend. It is even a friend in physics. With > physics I think it is a "sieve" that conforms physical principle to have > horizon conditions, whether uncertainty principles or event horizons in GR, > that conform physical reality to fit within the Church-Turing thesis. > Some claim Godel proved that the human mind is more than just a Turing Machine, but I disagree. Godel found a way to use numbers to write a sentence that talks about itself, it says "I am not provable in this formal system", and the operations of a particular Turing Machine are analogous to a formal system; however a human being can look at that sentence and see that it is true even though the machine itself could never produce it, therefore the human mind can do something the Turing machine can't. However, what Godel proved is that an operating system powerful enough to perform arithmetic THAT IS CONSISTENT cannot be complete, and he says no operating system can prove its own consistency. But when human beings are not doing formal logic exercises but just living everyday lives their operating system is most certainly not consistent, they can have two logically contradictory opinions at the same time, a brief glance at politics shows it is very common. And humans can be absolutely positively 100% certain about something, (that is to say they have proven it to their own satisfaction), and still be dead wrong. Godel's biography illustrates this point, he refused to eat and died of starvation because he was absolutely positively 100% certain that his food was being poisoned. So we are inconsistent Turing machines. And even today we could easily make a machine that could answer any question, provided you don't mind if it sometimes gave an answer that was wrong or even idiotic. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv03O5S9JbCwO1c3rckWEeL%3D6i%3DZH8o1pwvG8GmpBB_eSg%40mail.gmail.com.
