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NNTP-Posting-Date: Wed, 05 Feb 2025 13:25:42 +0000
Subject: Re: The set of necessary FISONs (axiomless natural deduction)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 5 Feb 2025 05:25:51 -0800
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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.