It is Penrose's thesis that consciousness is a sort of Godel trick. Back in the 1980s as an undergraduate I would have agreed with this, when I started reading about this. I read Hofstadter's book "Godel, Escher, Bach" and began pondering these things. I have however come to think there were problems with this. It is clear humans are not consistent Turing machines or computers. Computers are infernally consistent, and can compute numerical sequences, but they do not make an inductive leap in saying the set of natural numbers has infinite cardinality. Humans can rather easily see the set is infinite and however make mistakes.
LC On Wednesday, June 2, 2021 at 11:47:26 AM UTC-5 [email protected] wrote: > 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/3121aa56-24ca-459e-a196-a31a960d356bn%40googlegroups.com.
