[FRIAM] Abduction

Thu Dec 27 19:21:49 EST 2018

Lee Rodulph wrote: 

As I have learned from Nick, Peirce is also committed to the defense of "the
dignity of fallible knowledge" (at least, I *think* I've learned that from
Nick; but I might be wrong...).

Well, it’s possible your learned the sentiment from me, but your way of
expressing it, is, like Glen’s “level prejudice”, a patentable thought, and
I would like to be the first to license it.  

Nick 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

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lrudolph at meganet.net
Sent: Thursday, December 27, 2018 9:24 AM
To: 'The Friday Morning Applied Complexity Coffee Group' <friam at redfish.com>
Subject: Re: [FRIAM] Abduction

Glen wrote, in relevant part, "Like mathematicians, maybe we have to
ultimately commit to the ontological status of our parsing methods?"  I wish
to question the implicit assumption that mathematicians _do_ (or even _ought
to_) "ultimately commit to the ontological status" of _anything_ in
particular.

I wrote (some time ago, and not here) something I will still stand by.  It
appears at the beginning of a me-authored chapter in a me-edited book,
"Qualitative Mathematics for the Social Sciences: Mathematical models for
research on cultural dynamics"; the "our" and "we" in the first sentence
refer to me and my coauthor in an introductory chapter, not to me-and-a-
mouse-in-my-pocket.  (Note that I am a mathematician, _not_ a social
scientist, and only very occasionally a mathematical modeler of any sort.) I
have edited out some footnotes, etc., but in return have expanded some of
the in-line references {inside curly braces}.

===begin===

In our Introduction (p. 17) we quoted "three statements, by mathematicians
{Ralph Abraham; three guys named Bohle-Carbonell, Booß, Jensen, who I'd not
heard of before working on the book; and Phil Davis} on mathematical
modeling". Here is a fourth.

(D) Mathematics has its own structures; the world (as we perceive and
cognize it) is, or appears to be, structured; mathematical modeling is a
reciprocal process in which we _construct/discover/bring into awareness_
correspondences between mathematical structures and structures `in the
world´, as we _take actions that get meaning from, and give meaning to,_
those structures and correspondences. 

Later (p. 24 ff.) we briefly viewed modeling from the standpoint of
"evolutionary epistemology" in the style of Konrad Lorenz (1941) {Kant´s
doctrine of the a priori in the light of contemporary biology}. In this
chapter, I view modeling from the standpoint informally staked out by (D),
which I propose to call "evolutionary ontology." My discussion is sketchy
(and not very highly structured), but may help make sense of this volume and
perhaps even mathematical modeling in general.

Behind (D) is my conviction that there is no need to adopt any particular
ontological

attitude(s) towards "structures", in the world at large and/or in
mathematics, in order to proceed with the project of modeling the former by
the latter and drawing inspiration for the latter from the former. It is, I
claim, possible for someone simultaneously to adhere to a rigorously
`realist´ view of mathematics (say, naïve and unconsidered Platonism) and to
take the world to be entirely insubstantial and illusory (say, by adopting a
crass reduction of the Buddhist doctrine of Maya), _and still practice
mathematical modeling in good faith_ if not with guaranteed success. Other
(likely or unlikely) combinations of attitudes are (I claim) just as
possible, and equally compatible with the practice of modeling.  

I have the impression that many practitioners, if polled (which I have not
done), would declare themselves to be both mathematical `formalists´ and
physical `realists´. I also have the impression that a large, overlapping
group of practitioners, observed in action (which I have done, in a small
and unsystematic way), can reasonably be described to _behave_ like
thoroughgoing ontological agnostics.  Mathematical modeling _as human
behavior_ is based, I am claiming, on acts of pattern-matching (or
Gestalt-making)-which is to say,in other language, on
creation/recognition/awareness of `higher order structures´ relating some
`lower order structures´-that one performs (or that occur to one)
independently of one´s ontological stances. That is not all there is to it,
as behavior; but that is its basis.

===end===

To take Glen's question in (perhaps) a different direction, I note that Imre
Lakatos also used the word "ultimate" about mathematicians, as follows: "But
why on earth have `ultimate´ tests, `final authority´? Why foundations, if
they are admittedly subjective?  Why not honestly admit mathematical
fallibility, and try to defend the dignity of fallible knowledge from
cynical scepticism, rather than delude ourselves that we can invisibly mend
the latest tear in the fabric of our "ultimate" intuitions?" As I have
learned from Nick, Peirce is also committed to the defense of "the dignity
of fallible knowledge" (at least, I *think* I've learned that from Nick; but
I might be wrong...).

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