*Hi Stephen,*
*it seems you are closing to 'my alley'.  *
*First: if you don't think of  T R U T H  (in any absolute sense, meaning
it's acceptable 'meaning') how can you abide by a version of it?  - What are
the "REALS"? *
*I do not consider 'Arithmetic' the one and only ontological primitive: I
cannot 'see' ontology at all in a world that changes ceaselessly and the
'being' (ontology) turns into 'becoming' (sort of epistemology?) with
changing away at the instant you would realize it "became".

Idem per idem is not a workable position.  You can explain a 'system' only
in terms looking at it from a different (outside?) view. **Platonism is such
a system. I try a "common sense" platform.*
*I asked Bruno several times how he explains as the abstract 'numbers' (not
the markers of quantity, mind you) which makes the fundamentals of the
world. He explained: arithmetically 2 lines (II) and 3 lines (III) making 5
(IIIII) that is indeed  viewable **exactly as quantity-markers (of lines or
whatever). Of course a zero (no lines) would introduce the SPACE between
lines - yet another quantity, so with the 'abstract' of numbers we got
bugged down in measurement techniques (physics?).  *
*Logic? a human way of thinking (cf the Zarathustrans in the Cohen-Stewart
books Collapse of Chaos and The Figment of Reality) with other (undefinable
and unlimited) ways available (maybe) in the 'infinite complexity' of the
world *
*- IF our term of a 'logic' is realizable in it at all. *
**
*You know a lot more in math-related terms than I do, so I gave only the
tips of my icebergs in my thinking. *
**
*Then there is my agnosticism: the belief in the unknown part of the world
that yet influences whatever we think of. We continually learn further parts
of it, but only to the extent of the capabilities of our (restricted) mental
capacity. So whatever we 'know' is partial and inadequate (adjuste,
incomplete) into our 'mini-solipsism' of Colin Hales. *
**
*Regards*
**
*John M*
**
**
*
*
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King <stephe...@charter.net>wrote:

> 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?
>
> Onward!
>
> Stephen
>
>
> 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>wrote:
>
>> Hi,
>>
>>     I ran across the following:
>>
>> http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem
>>
>> *"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?
>>
>> Onward!
>>
>> Stephen
>> --
>>
>
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