Re: The set of necessary FISONs (axiomless natural deduction)

On 02/04/2025 08:26 PM, Ross Finlayson wrote:

On 02/04/2025 11:38 AM, Jim Burns wrote:

On 2/4/2025 4:59 AM, Ross Finlayson wrote:

On 02/04/2025 01:44 AM, Ross Finlayson wrote:

On 02/03/2025 06:15 PM, Jim Burns wrote:

>

If there is a mere contingent contrivance which
describes what I'd like described,
I will use it and be grateful for it.

>

The, "fundamental question of metaphysics",
or, "why is there something rather than nothing",
has [...]
that _strong mathematical platonism_ makes for
that it's possible to arrive at
an axiomless geometry [...]

>
Mathematics is poorly.suited to addressing
why there is something.
>
Mathematics addresses all descriptions (roots),
what is, what might be, and what cannot be,
and the consequences growing from descriptions (vines).
Its techniques show us that, from some roots,
vines grow which have bad fruit (contradictions),
We prune vines and roots with bad fruit.
>
We look for descriptions of what (really) exists
among the unpruned vines.
Being fruit of an unpruned vine is not the same
as describing what exists, although,
it is closer (in some cosmic sense) to existing than
being fruit of a pruned vine.
>
Mathematics can't tell us what is,
although it can tell us what isn't.
>
----
In some circumstances,
the vines have been pruned so severely that
very little is left to choose from.
I suppose someone might argue that there, at least,
mathematics tells us what IS, not only what ISN'T.
>
⎛ I'm thinking of string theory,
⎜ the attempted unification of physical forces.
⎜ If I understand correctly,
⎜ in order for string theory to be consistent,
⎜ there must be eleven dimensions.
⎜ Which appears to be wildly wrong.
⎜ However,
⎜ one proposal is that the extra dimensions are
⎜ curled up tighter than our instruments can detect.
⎜ How would we know they're undetectably existing?
⎜ In this not.yet.realized scenario,
⎜ all the vines without eleven dimensions get pruned,
⎝ mathematically or experimentally.
>
>

>
>
What it's all about is
"The Principle of Sufficient Reason".
>
There's that
the principle of sufficient reason is satisfying, and,
the principle of sufficient reason is satisfied.
>
So, axiomatics, or modern weak logicist positivism
or the nominalism or fictionalism all about same,
have unfounded axioms that supposedly thusly make
for both that anything that can be derived can be
derived, yet also of course that anything that can
be derived must be derived, here that's model theory,
and a structuralist view, and it's equi-interpretable
with proof theory, insofar as inter-subjectivity is
established, and equi-interpretability, in language.
>
Then, idealism has that the Principle of Sufficient Reason
is more than weak logicist positivism's "qualitas occultas",
as Schopenhauer puts it. Instead the Principle of
Sufficient Reason is for something like Leibnitz' universals,
and very much so for Hegel's dually-self-infraconsistent
the "Being and Nothing", and Time.
>
Then, from what Derrida calls for Husserl the pre-geometric
world, before the Lebenswelt our inter-subjective realm,
has that the stronger mathematical platonism,
may arrive at a stronger logicist positivism,
of course taking the best of both of those.
>
>
>
"String Theory" needn't more than one dimension -
it's called holographic or hologrammatic,
it's plainly merely a continuum mechanics,
and these "extra dimensions" you've heard of
are merely book-keeping scratch-pads for the
continuum mechanics, and not necessarily "real".
>
I.e., they have a mathematical interpretation and
a physical interpretation, in the models of the theories,
yet really there's also one with a "The Universe" with
a "The Continuum Mechanics" or a "The Continuum" of
a "The Space-Time" with a "the time".
>
>
>
Then, mathematics, and logic, can very well arrive
at why there's something, for example geometry, since
axiomless natural geometry can arrive at a spiral space-filling
curve a natural continuum, and _derive_ Euclid's.
>
>

It's like, when you read Carl Boyer,
an eminent historian of mathematics,
about Pythagoras, and, "all is number",
there's that mathematics and its philosophy,
is more than "merely imaginary", and so
that the universe of mathematical objects,
exists objectively, and how it does, is profound.
Not invented: profound.