On 21 Oct 2011, at 22:09, John Mikes wrote:

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).

That's the idea.



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?).

Here you might be too much literal already. The numbers are more of the type of mind ability to distinguish quantities of similar things. It is more in the mind, than in the way we might use a local reality to describe them.


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.

If logic is a human way of thinking, is not logics ways of thinking (note the plural). There are infinities of logic. Classical logic is the way of the greek human thinking, and of the he ideally arithmetically correct machine, which can be studied to learn about us, like the bacteria Escherichia coli can studied for learning something about us.




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.

But here is the problem: what do you mean by "world"? Is there a world? Why not a dream. If you agree that there is something unknown, you believe that there is something to be known or believed OK?




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.

What is the difference with the first person's beliefs? And with the first person knowledge. Are you OK with the idea that a machine can also have her mini-solipsism? (this would not imply that "we" are machine, just that a machine could think). I just try to have a more precise idea of your thinking.

Best,

Bruno




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 in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth cannot be defined in arithmetic."

    Where then is it defined?

Onward!

Stephen
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