On 10/21/2011 4:09 PM, 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"? *
Hi John,
I have yet to find fault in any of your posts! ;-)
It boils down to a definition of the word "meaning", which I take
to include notions of truth value and other properties. Meaningfulness
requires a subject to whom that a meaning occurs, otherwise we are
emptily debating about "if a tree falls ...." To this end such things as
Reals are what is non-contradictorily experienciable by some collection
of mutually communicating entities. This might seem to be just a form of
"consensus realism" but I define "entities" as "anything that can have
its own QM wave-function", so such things as quarks, leptons, paramecia,
mice, tigers and trees, humans, planets, galaxies and super-clusters all
have a vote in the consensus.
I see a similar idea in Hitoshi Kitada's theory of Local Systems
and Andrew Soltau's "Interactive Destiny" idea and they agree with me
(another just a few people that I have communicated with), so I take
this limited validation as a reason not to abandon it for some unknown
alternative.
*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".
*
As I see it, arithmetic is just another way of systematic coding
'differences that make a difference". Ontological question are very very
tricky because it is very difficult to avoid letting one's tacit
assumptions and unconsidered beliefs to obscure problems. From what I
have studied of philosophy so far, I would quibble a little bit with
your wording here. A ceaselessly changing world can be seen easily, we
are looking at an example of one right now. The trick is that the
"ceaseless change" cannot be stochastic, there has to be some form of
invariance on that change, otherwise there is no possibility of a
realistic notion of observer at all. We can consider Boltzman brains
that last for an instant, but unless there are a plurality of such
brains that can actually somehow communicate with each other, they are
no more than instantaneous solipsists.
The way I see it, Being is the sum of the homomorphisms within
Becoming. Becoming is fundamental. Ian Thompson has written a book
<http://www.generativescience.org/books/pnb/pnb.html> that can be viewed
online that discusses some other these ideas (if you want more that H.
Bergson and Heraclitus references and my own babbling). There is also
the writings of Ronald Swan that was taken from us far too soon....
(I'll send you a copy of his paper if you request it.)
*
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.*
Idem per Idem is mere counting at best, so I agree. Counting
requires some categorical separation between range and domain of the map
and a persistent system to implement the mapping. Platonism does not
seem to understand this requirement.
*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?). *
I agree 100%. It is as if the basic fact that communicability is
completely taken for granted. There seems to be no consideration as to
how separate and individual minds can communicate with each other in
ideal monist theories. Material monist theories completely fail to
account for minds, other than some kind of causal inefficacious
illusion. Thus I am led, kicking and screaming, to consider some form of
non-monist ontology to underpin science.
*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. *
I see the totality of existence as unlimited and unnameably
infinite. We are only ever aware of infinitesimal parts of it, so we
agree on this. Logic is just a communicable procedure of relating some
set of "something" to some other set of "something". There are even
multiple forms of sets and logics, so the plurality of possibility is
endless! But there does seem to be a pattern to this madness! It seems
as if for every kind of set there is a logic having its own algebra and
isomorphic to some topological space. So this 4-ality is just another
communicable idea.
**
*You know a lot more in math-related terms than I do, so I gave only
the tips of my icebergs in my thinking. *
I have spent the last 20 years studying philosophy, physics and
mathematics on my own and discussing ideas with many people. I have no
one to blame for my strange ideas except myself. ;-) If they make some
sense to someone other than me, that is wonderful, as sometimes I do not
even understand my own mussing! It is I get possessed. It may just be
madness. ;-P
**
*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. *
I have a similar belief, I try not to name it because to do so
constrains it to be one thing and nothing else! ;-)
Onward!
Stephen
**
*Regards*
**
*John M*
**
**
**
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King
<stephe...@charter.net <mailto: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 <mailto: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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