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

    From Jim Burns@21:1/5 to Ross Finlayson on Tue Feb 4 14:38:05 2025
    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.

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  • From Jim Burns@21:1/5 to Ross Finlayson on Wed Feb 5 13:25:34 2025
    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"?

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  • From Jim Burns@21:1/5 to Ross Finlayson on Thu Feb 6 10:37:35 2025
    On 2/6/2025 1:29 AM, Ross Finlayson wrote:
    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:

    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?

    Hm.
    Have you heard of "first principles" and "final cause"?

    They sound like they're things without a cause.

    If not everything has a cause,
    why (if I understand you) are only these things without a cause?


    I mentioned Judea Pearl's work.
    If I recall correctly,
    when he sets up his formalism for causal relations,
    he explicitly says not quantum mechanics.
    I can see why,
    experiment shows that quantum mechanics breaks local realism.
    We may have some future version of causation
    in which that's not a problem,
    but he has enough on his plate for right now.

    It seems fair to me to say that
    quantum mechanics is uncaused.
    Statistics for radioactive decay, for example, are very firm,
    but which individual atom decays next?
    The impression I have is that
    there is no way _even in principle_ to know that.

    My vague notion of the First Cause
    is that it is a deistic version of God.
    But radioactive decay displays none of the properties
    one would want for a deistic God
    -- including that it is NOT remote from humanity.
    But, apparently, it is uncaused.

    I think we need a better idea of what 'cause' means.

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