Hi John,

I was not thinking of truth in any absolute sense. I'm not even sure what that concept means... I was just considering the definiteness of the so-called truth value that one associates with Boolean logic, as in it has a range {0,1). There are logics where this can vary over the Reals! My question is about "where" does arithmetical truth get coded given that it cannot be defined in arithmetic itself? If we consider Arithmetic to be the one and only ontological primitive, it seems to me that we lose the ability to define the very meaningfulness of arithmetic! This is a very different thing than coding one arithmetic statement in another, as we have with Goedel numbering. What I am pointing out is that if we are beign consisstent we have to drop the presumption of an entity to whom a problem is defined, i.e. valuated. This is the problem that I have with all forms of Platonism, they assume something that they disallow: an entity to whom meaning is definite. What distinguishes the Forms from each other at the level of the Forms?



On 10/20/2011 10:18 PM, John Mikes wrote:
Dear Stephen,
as long as we are not omniscient (good condition for impossibillity) there is no TRUTH. As Bruno formulates his reply: there is something like "mathematical truth" - but did you ask for such specififc definition? Now - about mathematical truth? new funamental inventions in math (even maybe in arithmetics Bruno?) may alter the ideas that were considered as mathematical truth before those inventions. Example: the zero etc. It always depends on the context one looks at the problem FROM and draws conclusion INTO.
John M

On Sun, Oct 16, 2011 at 12:48 AM, Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:


        I ran across the following:


    *"Tarski's undefinability theorem*, stated and proved by Alfred
    Tarski <http://en.wikipedia.org/wiki/Alfred_Tarski> in 1936, is an
    important limitative result in mathematical logic
    <http://en.wikipedia.org/wiki/Mathematical_logic>, the foundations
    of mathematics
    <http://en.wikipedia.org/wiki/Foundations_of_mathematics>, and in
    formal semantics <http://en.wikipedia.org/wiki/Semantics>.
    Informally, the theorem states that /arithmetical truth cannot be
    defined in arithmetic/."

        Where then is it defined?



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