On 2/12/2012 15:48, Stephen P. King wrote:

On 2/11/2012 5:15 PM, acw wrote:On 2/11/2012 05:49, Stephen P. King wrote:On 2/9/2012 3:40 PM, acw wrote:I think the idea of Platonia is closer to the fact that if a sentence has a truth-value, it will have that truth value, regardless if you know it or not.Sure, but it is not just you to whom a given sentence may have the same exact truth value. This is like Einstein arguing with Bohr with the quip: "The moon is still there when I do not see it." My reply to Einstein would be: Sir, you are not the only observer of the moon! We have to look at the situation from the point of view of many observers or, in this case, truth detectors, that can interact and communicate consistently with each other. We cannot think is just solipsistic terms.Sure, but what if nobody is looking at the moon? Or instead of moon, pick something even less likely to be observed. To put it differently, Riemann hypothesis or Goldbach's conjecture truth-value should not depend on the observers thinking of it - they may eventually discover it, and such a discovery would depend on many computational consequences, of which the observers may not be aware of yet, but doesn't mean that those consequences don't exist - when the computation is locally performed, it will always give the same result which could be said to exist timelessly.[SPK] My point is that any one or thing that could be affected by the truth value of "the moon has X, Y, Z properties" will, in effect, be an observer of the moon since it is has a definite set of properties as "knowledge". The key here is causal efficacy, if a different state of affairs would result if some part of the world is changed then the conditions of that part of the world are "observed". The same thing holds for the truth value Riemann hypothesis or Goldbach's conjecture, since there would be different worlds for each of their truth values. My point is that while the truth value or reality of the moon does not depend on the observation by any _one_ observer, it does depend for its definiteness on the possibility that it could be observed by some observer. It is the possibility that makes the difference. A object that cannot be observer by any means, including these arcane versions that I just laid out, cannot be said to have a definite set of properties or truth value, to say the opposite is equivalent to making a truth claim about a mathematical object for whom no set of equations or representation can be made.You're conjecturing here that there were worlds where Riemann hypothesis or Goldbach's conjecture have different truth values. I don't think arithmetical truths which happen to have proofs have indexical truth values, this is due to CTT. Although most physical truths are indexical (or depend on the axioms chosen). We could limit ourselves to decidable arithmetical truths only, but you'd bump into the problem of consistency of arithmetic or the halting problem. It makes no sense to me that a machine which is defined to either halt or not halt would not do either. We might not know if a machine halts or not, but that doesn't mean that if when ran in any possible world it would behave differently. Arithmetical truth should be the same in all possible worlds. An observer can find out a truth value, but it cannot "alter" it, unless it is an indexical (context-dependent truth, such as "what time it is now" or "where do you live"). Of course, we cannot talk about the truth value of undefined stuff, that would be non-sense. However, we can talk about the truth value of what cannot be observed - "this machine never halts" is only true if no observation of the machine halting can ever be made, in virtue of how the machine is defined, yet someone could use various meta-reasoning to reach the conclusion that the machine will never halt (consistency of arithmetic is very much similar to the halting problem - it's only consistent if a machine which enumerates proofs never finds a proof of "0=1"; of course, this is not provable within arithmetic itself, thus it's a provably unprovable statement for any consistent machine, thus can only be a matter of "theology" as Bruno calls it).Hi ACW, I am considering that the truth value is a function of the theory with which a proposition is evaluated. In other words, meaningfulness, including truth value, is contextual while existence is absolute.Of course it's a function of the theory. Although, I do think some theories like arithmetic, computability and first-order logic are so general and infectious that they can be found in literally any non-trivial theory. That is, one cannot really escape their consequences. At that point, one might as well consider them absolute. That said, an axiom that says "you're now in structure X and state Y" would be very much contextual.Hi ACW, I was considering something like a field of propositions what say "I am now in structure X_i, state Y_j and an internal model Z_k" and a truth value that is only momentarily "at" any one of them for any given 1p observer moment of experience.

That sounds agreeable.

There is a problem with this though b/c it assumes that the field is pre-existing; it is the same as the "block universe" idea that Andrew Soltau and others are wrestling with.

`Why is a pre-existing field so troublesome? Seems like a similar problem`

`as the one you have with Platonia. For any system featuring time or`

`change, you can find a meta-system in which you can describe that system`

`timelessly (and you have to, if one is to talk about time and change at`

`all).`

What I think we need is something more like Bohm's implicate order idea where the propositions have definite truth values only relative to a finite number of others in a sequence but not a preorder. I am trying to find the words to describe something that is the higher dimensional analogue of a sequence. Pratt et al describe this idea as "higher dimensional automata", it looks more like a physics field of excitations.

A generalization of abstract relations? I'll save reading Pratt's papers until I know more category theory.

Onward! Stephen

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