On 21 Dec 2013, at 19:06, Edgar Owen wrote:
Craig, Godel's Theorem applies only to human mathematical systems.
provably assuming that humans are arithmetically sound machine (which is a rather strong assumption).
It doesn't apply to the logico-mathematical system of reality, of which the computational systems of biological organisms including humans are a part.
Why? The answer is straightforward. Because Reality's logico- mathematical system is entirely computational in the sense that every state at every present moment is directly computed from the prior state.
Only in the third person perspective, but with computationalism, all accessible realities are not computation, nor result of computation, but they are the result of infinitely many computations mixed with the first person indeterminacies.
Godel's Theorem does not apply to this.
Right. Gödel' theorem applies to finite or enumerable machines or theories. Not on their models, even in arithmetic.
What Godel's Theorem says is that given some mathematical system it is possible to formulate a correct statement
It is correct if we already know that the theory is correct, which is doubtful for rich theories like "us", in case of comp.
which is not computable from the axioms. But Reality doesn't work that way. It simply computes the next state of itself which is always possible.
Reality does not compute. That's the digital physics thesis, which makes no sense. Indeed, as often explained here: if digital physics is correct then comp is correct, BUT if comp is correct then digital physics is incorrect. thus digital physics entails the negation of digital physics, and this makes digital physics incorrect (for a TOE) in all case (with comp or with non comp).
The implication is that the logico-mathematical system of reality IS AND IN FACT MUST NECESSARILY BE logically consistent and logically complete in every detail. If it wasn't Reality would tear itself apart at the inconsistencies and pause at the incompletenesses and could not exist. But Reality does exist.
OK, but we don't *know* that. We hope that. We know only that we are conscious here-and-now. We don't *know* if there are planets and galaxies. We bet on that. Those are theoretical assumptions.
Reality is analogous to a running software program.
Read the UDA. Apparent realities have to be much bigger than anything we could emulate on a computer. That is already the case for arithmetic itself. You might confuse proof and computation.
Godel's Theorem does not apply. A human could speculate as to whether any particular state of Reality could ever arise computationally and it might be impossible to determine that, but again that has nothing to do with the actual operation of Reality,since it is only a particular internal mental model of that reality.
The universal dovetailer get all states of mind, but no states of physical reality at all, which needs the non computable First Person Indeterminacy on all (relative) computations. Then the bigger "theological (true) reality" is even bigger.
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