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.## Advertising

Sure, but it is not just you to whom a given sentence may have thesameexact 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 communicateconsistently with each other. We cannot think is just solipsisticterms.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 Riemannhypothesis or Goldbach's conjecture have different truth values. Idon't think arithmetical truths which happen to have proofs haveindexical truth values, this is due to CTT. Although most physicaltruths are indexical (or depend on the axioms chosen).We could limit ourselves to decidable arithmetical truths only, butyou'd bump into the problem of consistency of arithmetic or thehalting problem. It makes no sense to me that a machine which isdefined to either halt or not halt would not do either. We might notknow if a machine halts or not, but that doesn't mean that if when ranin any possible world it would behave differently. Arithmetical truthshould be the same in all possible worlds. An observer can find out atruth value, but it cannot "alter" it, unless it is an indexical(context-dependent truth, such as "what time it is now" or "where doyou 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 ofwhat cannot be observed - "this machine never halts" is only true ifno observation of the machine halting can ever be made, in virtue ofhow the machine is defined, yet someone could use variousmeta-reasoning to reach the conclusion that the machine will neverhalt (consistency of arithmetic is very much similar to the haltingproblem - it's only consistent if a machine which enumerates proofsnever finds a proof of "0=1"; of course, this is not provable withinarithmetic itself, thus it's a provably unprovable statement for anyconsistent machine, thus can only be a matter of "theology" as Brunocalls 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.`

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