On 3/25/2013 6:10 AM, Alberto G. Corona wrote:
> I suspect that this impossibility is because math uses concept of a
> model, while truth refers to the match of facts of the model with
> facts of the reality . Or at least to facts of a metamodel outside of
> the model. That is AFAIK the Tarsky idea.
Hi Alberto,
I am trying to extract a definition of "reality". I have proposed a
non-trivial definition: "Reality is that which is incontrivertable for
some collection of intercommunicating observers". There is a point to
this definitions use of each the words. Up until the era of QM, it has
been assumed that all observables are commutative, e.g. that a single
ideal observer could see everything all at once. We see this in the
famous quote from Laplace.
"We may regard the present state of the universe as the effect of its
past and the cause of its future. An intellect which at a certain moment
would know all forces that set nature in motion, and all positions of
all items of which nature is composed, if this intellect were also vast
enough to submit these data to analysis, it would embrace in a single
formula the movements of the greatest bodies of the universe and those
of the tiniest atom; for such an intellect nothing would be uncertain
and the future just like the past would be present before its eyes."
The thing is, it is simply not true. We have an overabundance of
evidence and yet the idea continues to be assumed. So, as an alternative
I am proposing an alternative that is built on the notion of mutual
non-contradiction of observations that can be communicated between
observers.
>
> For example, "All men are mortal is true" . Here suppose that "all
> men are mortal" is a fact of a model that admit inductive silogisms.
This rest on observations by men... a narrow subset of possible
observers. Protons never die... but they are not men...
>
> True in this case can express a match of the fact "All men are mortal"
> with reality. or a match with a metamodel in which the trueness of
> the model "all men are mortal" is assumed as an axiom.
>
> In both cases the whole statement "all men are mortal is true" is
> outside of the model in which the statement "all men are mortal" is
>
> However I can make an ordinaty mathematical model of matches between
> models and metamodels. That is the boolean logic.
Surely it is Boolean in its relations, but is it in its content? It
assumes too much power in its implications.
>
>
> 2013/3/23 Stephen P. King <stephe...@charter.net
> <mailto:stephe...@charter.net>>
>
> "In 1936 Tarski proved a fundamental theorem of logic:
> the *undefinability of truth*. Roughly speaking, this says
> there's no consistent way to extend arithmetic so that it talks
> about 'truth' for statements about arithmetic. Why not? Because
> if we /could/, we could cook up a statement that says "I am not
> true." This would lead to a contradiction, the Liar Paradox: if
> this sentence is true then it's not, and if it's not then it is.
>
> This is why the concept of 'truth' plays a limited role in most
> modern work on logic... surprising as that might seem to novices! ..."
>
>
> https://plus.google.com/u/0/117663015413546257905/posts/jJModdTJ2R3https://plus.google.com/u/0/117663015413546257905/posts/jJModdTJ2R3
>
>
> --
> Onward!
>
> Stephen
>
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> Alberto.
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Onward!
Stephen
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