I really wish I were not doing and worrying about all the matters that have
been keeping me from writing more to xmca ....
... but I did find an interest in a few recent threads ... I'll add my vote
to the anti-internalist renegades, and note that Samoa ain't the only place
where "internal states" are not taken as a natural given of human reality
... this notion is quite culturally and historically specific, and it is
embarassing that it has been fashionable in some circles now for at least a
decade to regard it as foundational for the interface between cognition and
social reality (though it may be an advance that at least some notion that
meaning-making always presupposes an Other has gotten currency among
Cartesian psychologists of cognition). Now just get rid of the parochialism
of internalist-mentalist views of meaning, and you wind up with the not so
astonishing notion that we make meaning about the world in ways that
implicate that for us humans "the world" begins as fundamentally the social
world (or something that does not distinguish the social world and the
"natural" world, but looks more like what people who do distinguish these
two call the social world), so that the foundations of meaning lie not in
representation of the objective Thing ( a late development, rather
modernist and scientificist), but in the creation of community (of which
interpersonal relation-construction is one part; excessive individualism
also exaggerates this part in relation to wider meaning-constructions of
community, as when people make "dialogism" into a two-party system,
neglecting heteroglossia and the wider discourse culture which gives any
words of ours their meanings).
Yeah, yeah, I rant too ... but less often these days!
Another interesting topic that hasn't gone anywhere yet is the question of
the ontological status of mathematical objects (objects? we really mean
forms? or relations, no? what a mathematician calls an "object" has nothing
in common with anything else we call an object, does it? Mathematics is
relations all the way down, no? the "objects" are just placeholders,
"arguments" to define the qualities of the relations. It's a linguistic
convenience. Natural language defines relations on nominal arguments ---
and also between processes, but this is not as semantically well-developed
in Indo-European languages). Now I can see all sorts of philosophical grist
in this. It would lead me, for instance, to Whitehead and the issue of how
to make process a more fundamental basis of relationality than substance,
which leads to interesting recursions, since you can semantically consider
relations to be a type of process (at least in English, where, say, "is" is
a verb, and not, say, a conjunction or preposition). But I don't see what
the 'educational' implications of the ontology of mathematical "objects"
could possibly be. I suspect that the more honest we are with students
about a sophisticated view of this ontology, the less interest they will
have in mathematics and the less seriously they will take the whole thing.
It takes a very sophisticated and mature intellectual perspective to see
the importance of understanding how systems of pure relations can be
self-determining (and moreso once you know, ala Goedel, that this
self-determination is itself indeterminate). Even most scientists have no
use for mathematicians' ways of understanding mathematics. Does someone
have a more optimistic take on this?
more to come on two other threads ...... JAY.
---------------------------
JAY L. LEMKE
PROFESSOR OF EDUCATION
CITY UNIVERSITY OF NEW YORK
JLLBC@CUNYVM.CUNY.EDU
<http://academic.brooklyn.cuny.edu/education/jlemke/index.htm>
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