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NNTP-Posting-Date: Thu, 06 Feb 2025 06:29:44 +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 22:29:57 -0800
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On 02/05/2025 10:19 PM, Ross Finlayson wrote:
> On 02/05/2025 10:25 AM, Jim Burns wrote:
>> On 2/5/2025 8:25 AM, Ross Finlayson wrote:
>>> On 02/04/2025 08:26 PM, Ross Finlayson wrote:
>>>> On 02/04/2025 11:38 AM, Jim Burns wrote:
>>
>>>>> [...]
>>>>
>>>> What it's all about is
>>>> "The Principle of Sufficient Reason".
>>
>> ⎛ The principle of sufficient reason states that
>> ⎝ everything must have a reason or a cause.
>> https://en.wikipedia.org/wiki/Principle_of_sufficient_reason
>>
>> What causes everything to have a cause?
>> Does that have a cause? Is the cause itself?
>>
>> I think that 'cause' is insufficiently described
>> For this discussion.
>>
>> Judea Pearl and his colleagues have done admirable work
>> in this area.
>>
>>>> There's that
>>>> the principle of sufficient reason is satisfying, and,
>>>> the principle of sufficient reason is satisfied.
>>
>> Does making an unsupported claim ("There's that...")
>> count as offering a reason?
>> May I offer unsupported claims as reasons, too?
>>
>>>> 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.
>>
>> "That anything that can be derived can be derived"
>> is clearly true. Axiomatic, even. So what?
>>
>> "That anything that can be derived must be derived"
>> is clearly false,
>> if you mean what I mean by 'derive':
>> among other things,
>> a non.empty list of actions by finite beings (me and my ilk)
>>
>> Those which can be derived
>> are infinitely.many.
>> The resources available to derive with
>> are finite.
>> If the rule is
>> "That anything that can be derived must be derived",
>> then the rulemaker will be disappointed.
>>
>> "Unfounded axioms" sounds to me like
>> a key to making sense of what you mean by
>> "axiomless geometry" and its ilk.
>> Is it
>> not "no axioms", but "no unfounded axioms"?
>>
>>
>
> Hm. Have you heard of "first principles" and "final cause"?
>
> In logicist positivism, it's either/or "an axiom system"
> and "science", is the usual idea.
>
> Anyways it's usually attributed to "idealism"
> vis-a-vis "the analytical", and there's quite
> a long story about it it's sort of nice to
> have ideals.
>
> Then, something like Hegel's "Being and Nothing",
> if you read the Wissenschaft der Logik, is pretty
> great, then there's Kant's Sublime, pretty usual,
> these being the things that the analytical tradition
> does not and cannot say much about, yet, Hegel and
> Kant do, because they're idealists.
>
> Then, "anti-Platos" like Wittgenstein, Nietszsche,
> and Heidegger, say, sort of have that Gadamer arrives
> for hermeneutics at "amicus Plato", and, the Tractatus
> Logico-Philosophicus, which is really sort of a reading
> of Leibniz' monadology or about the radical origination
> of things, is quite, strongly platonic, and idealistic.
>
> If you're going to have a theory at all,
> it might as well be the good one.
>
>
> Then, here Duns Scotus' super|natural is considered
> pretty great, and Chrysippus of course provides the
> modal against Plotinus and his fallacies of material
> implication, making sure that Aristotle won't be fooled.
>
>
>


https://www.youtube.com/watch?v=LKnZUg9jPf0&list=PLb7rLSBiE7F4_E-POURNmVLwp-dyzjYr-&index=11

"Logos 2000:  philosophical theory"