Just for confirmation, Bruno, you message has been received if not completely comprehended by myself, but just as a saying "received" by your email provider. My only thought might be is "Do we have a choice in what we are observing?" Moreover, "if we somehow do, can we make better by observing." Many would say this is quantum woo, and that is fine by me. The follow up would be, mayhaps if we form a 'better node' say, of millions of observer's we could fix things better? As in Quantum Woo style-all focus upon the same thing? Probably not, so it's back to work for scientists and engineers....
-----Original Message----- From: Bruno Marchal <[email protected]> To: Everything List <[email protected]> Sent: Mon, Jul 19, 2021 9:07 am Subject: Re: Hitler against Godel's Theorem I have answered this, but I don't find my answer. Penrose use Gödel's theorem to argue that we are not machine, by a reasoning similar to one already found, and refuted, by Emil Post, and later developed (wrongly) by Lucas and Penrose. Eventually Penrose got it right, and that kind of argument does not show that Gödel's incompleteness is a problem for Mechanism, but it does show that a machine cannot know which machine she is, nor which computations support it in arithmetic, which is indeed a step in the reduction of the laws of physics to the statistics on all relative computations in arithmetic. That explains why, after deriving the phenomenology of the wave collapse from the Schroedinger equation, like Everett did, it is still necessary to derive the wave equation from the statistics on all computations (as seen from inside, which is the hard part to define, except that it becomes easy once we get the theology of the machine. The propositional machine theology G1* has been given here. It is the modal logic with all theorem of G as axioms, + []A ->A, + p -> []p (for p propositional letter), and importantly without the Necessitation rule. And G is the (normal modal logic) with axiom []([]A -> A) -> []A (the Löb formula). A normal modal theory has [](A->B) -> ([]A -> []B) as axioms, and is closed for the Modus ponens and the necessitation rule. Then the logic of the observable is given by the modal logic of the intensional variant, defined in G1(*) by the logic of []A & <>t & A, and some related.That gives a quantum logic for the observable by universal numbers in arithmetic, naturally related to the many computations structure implied by elementary arithmetic or Turing equivalent. More on this later. I am also testing the mail system, and if the google-group still recognise my old adresses. Bruno On Thursday, June 3, 2021 at 1:28:36 PM UTC+2 Lawrence Crowell wrote: 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/4bf6dfec-463c-4c37-a5a6-610065e03905n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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