ONT Fwd: Ontology As Math Or Metaphysics?
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found the old note that started me down this road again,
apparently one that mk sent to the cg list, but since
they are too busy working on other stuff over there,
i think i will pick up on it and muse on it here.
jon awbrey
> Subj: Ontology as math or metaphysics?
> Date: Fri, 3 Nov 2000 09:10:59 -0800 (PST)
> From: Mary Keeler <mkeeler@u.washington.edu>
>
> Here's a little something from the _Collected Papers of CSP_, (Vols.3&7)
> that might also be of interest to some CGers. Daniel Kayser's argument at
> ICCS 98, that AI and philosophy have two different senses of "ontology,"
> doesn't hold up -- even in his own paper (under careful examination).
> John has been trying to sort out the implications of that for CG development
> (it seems to me), and this might help (somehow). However, be aware that
> Peirce would not condemn anyone to do philosophy (ontology as metaphysics)
> in its modern mode, today! Kayser recommends a pragmatic solution for
> AI, Peirce recommends pragmatism for philosophy. But first, has anyone
> considered whether you are trying to do mathematics (see what this means,
> below) or metaphysics--and how that question might clarify what you need
> to be doing (which seems primary to me)? But I certainly don't know
> whether the following will be any help at all, except to stress that any
> sort of ontology work cannot be reduced to mathematics or deductive logic,
> and needs _good_ philosophical investigation and methodology. --Mary
>
> -----------------------------------------------------------------------
> From Vol. 3
> The true difference between the necessary logic of philosophy and
> mathematics is merely one of degree. It is that, in mathematics, the
> reasoning is frightfully intricate, while the elementary conceptions are
> of the last degree of familiarity; in contrast to philosophy, where the
> reasonings are as simple as they can be, while the elementary conceptions
> are abstruse and hard to get clearly apprehended. But there is another
> much deeper line of demarcation between the two sciences. It is that
> mathematics studies nothing but pure hypotheses, and is the only science
> which never inquires what the actual facts are; while philosophy, although
> it uses no microscopes or other apparatus of special observation, is
> really an experimental science, resting on that experience which is common
> to us all; so that its principal reasonings are not mathematically
> necessary at all, but are only necessary in the sense that all the world
> knows beyond all doubt those truths of experience upon which philosophy is
> founded. This is why the mathematician holds the reasoning of the
> metaphysician in supreme contempt, while he himself, when he ventures into
> philosophy, is apt to reason fantastically and not solidly, because he
> does not recognize that he is upon ground where elaborate deduction is of
> no more avail than it is in chemistry or biology (CP 3.560 [Educational
> Review, pp. 209-16, 1898]).
>
> From Vol. 7 [no date on MS]
> 524. If the whole business of mathematics consists in deducing the
> properties of hypothetical constructions, mathematics is the one science
> to which a science of logic is not pertinent. For nothing can be more
> evident than its own unaided reasonings. On the contrary logic is an
> experiential, or positive, science. Not that it needs to make any special
> observations, but it does rest upon a part of our experience that is
> common to all men. Pure deductive logic, insofar as it is restricted to
> mathematical hypotheses, is, indeed, mere mathematics. But when logic
> tells us that we can reason about the real world in the same way with
> security, it tells us a positive fact about the universe. As for
> induction, it is generally admitted that it rests upon some such fact.
> But all facts of this sort are irrelevant to the deduction of the
> properties of purely hypothetical constructions.
> 525. But there is a part of the business of the mathematician
> where a science of logic is required. Namely, the mathematician is called
> in to consider a state of facts which are presented in a confused
> mass. Out of this state of things he has at the outset to build his
> hypothesis. Thus, the question of topical geometry is suggested by
> ordinary observations. In order definitely to state its hypothesis, the
> mathematician, before he comes to his proper business, must define what
> continuity, for the purpose of topics, consists in; and this requires
> logical analysis of the utmost subtlety. Mathematicians still survive
> who are so little versed in reasoning as to deny that we can reason
> mathematically about infinity, although the hypothesis of an endless
> series of whole numbers involves infinity and the hypothesis of
> transcendental irrational quantities involves an infinity of another
> kind. If we cannot reason mathematically about infinity, a fortiori we
> cannot reason mathematically about continuity, and any exact mathematics
> of topical geometry becomes impossible. To clear up these difficulties,
> some consideration of logical matters is indispensable.
> 526. Logic is a branch of philosophy. That is to say it is an
> experiential, or positive science, but a science which rests on no special
> observations, made by special observational means, but on phenomena which
> lie open to the observation of every man, every day and hour. There are
> two main branches of philosophy, Logic, or the philosophy of thought, and
> Metaphysics, or the philosophy of being. Still more general than these is
> High Philosophy [he is referring to phenomenology] which brings to light
> certain truths applicable alike to logic and to metaphysics. It is with
> this high philosophy that we have at first to deal.
>
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