[FRIAM] Motives - Was Abduction

Sat Jan 12 01:53:36 EST 2019

Thanks, Lee, for "conceit".  If it means what it says it means to anybody
but you, I may have to reconsider my decade long use of term, metaphor.  

Do I find myself in a rats' nest of category theorists?  I had always
thought that category was a rather outré field, that mathematicians were a
little embarrassed to be interested in.  An now suddenly they are as think
on the ground as rabbits.  Help me understand the teams, here, the 
 um 

categories.

N

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

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

-----Original Message-----
From: Friam [mailto:friam-bounces at redfish.com] On Behalf Of
lrudolph at meganet.net
Sent: Friday, January 11, 2019 7:57 PM
To: friam at redfish.com
Subject: Re: [FRIAM] Motives - Was Abduction

Nick writes, in relevant part:

> I am not sure what monads and monism have to do with each other, other 

> than that they share a linguistic root.  Honest.  I have trouble 

> seeing the connection.

...

> I don't have much of a grip on MonADism.  As I understand monads, they 

> are irreduceable "atoms" of existence.  They have no innards.

The "monads" of category theory did not arise under that name, and they
absolutely have "innards".  Why Saunders MacLane renamed them (as I just
learned by checking Wikipedia) that is probably known to many, but not to
me; as an instance of the "working mathematician" to whom his book
"Categories for the Working Mathematician" was purportedly addressed (J.

Frank Adams has a reference in one of his books to "Categories for the Idle
Mathematician"), I have a long experience of observing category theorists'
whimsy (e.g., Peter Freyd's "kittygory" for a "small category", Peter
Johnstone's "pointless topology", etc., etc.), and I suspect that MacLane
was mostly indulging in that rather than riffing on antique philosophy.
Certainly the word is short and snappy, and that's sufficient to explain why
it caught on.

To the extent that it can be useful and accurate to describe some bit of
mathematics (or a name for that bit of mathematics) by applying to it the
term "metaphor" borrowed from rhetoric, it will almost always be MORE useful
and MORE accurate (if harder for Nick to deal with) to apply to it another
term borrowed from rhetoric, "conceit". Consulting Wikipedia, I find that
"modern literary criticism", damn its collective eyes, has redefined that
good old word for its own malign ends.  What *I* mean by it is (I find by
consulting the rather pre-modern Princeton Encyclopedia of Poetry and
Poetics) a generalization away from literature of the "metaphysical conceit"
(as contrasted with the "Petrarchian conceit"; and named for the
Metaphysical Poets, not for William James's coterie): "An intricate [...]
metaphor [...] in which the [...] qualities or functions of the described
entity are presented by means of a vehicle which shares no physical features
with the entity" (of course the "physical features"

business is not part of *my* meaning).

That is, a conceit is a metaphor that pays serious attention to the
multi-level *structures* and *functions* involved on both sides of the
trope.  A simple metaphor need have no innards; a conceit can be jam-packed
with them, but not arbitrarily jam-packed.  (The part of the preceding
sentence before the semi-colon is itself a pretty simple metaphor.  The part
after the semi-colon at least tends towards conceit. 

If I started to distinguish different kinds and functions of innards that
bodies can have--bones, muscles, vital and less-vital organs, etc.--and
likewise to distinguish different substructures that metaphors can have,
along with functions that they perform in the service of metaphorical
communication, and THEN set up a correspondence between the bodily innards
and the metaphorical substructures that "respected" their respective
functions...that would be a conceit.  Which I don't intend to work on any
further at the moment.)

The category-theorists among us may think I'm describing morphisms etc.

etc.  If they do, then they're committing metaphor (or thinking that I am).
If they go further, and try to make sense about rhetorical activities by
applying category theory, then they're committing conceit.

Enough for now.

Lee

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