[Wittrs] fragment re Wittgenstein in math teaching

[kirby urner]

>From another discussion list (fixed a couple typos)

http://groups.google.com/group/mathfuture/msg/e464479a3606ad89

(original context)


Kirby


====

One of the philosophical conundrums I work on is this:

(a) as a Wittgenstein camper (a kind of "occupy philosophy" school),
I'm trained to think of "meaning" in operational terms, i.e.
regardless of definitions, you will be fine tuning your meanings on
the front lines in applications, in the "war zone" of "math at work"
(not suggesting there need be violence -- on the contrary, if the math
is any good, it'll show you a way free, like a martial art).  To think
this way, I've needed to wean myself from any simplistic view of
language based on nominalist and/or Platonist paradigms in the sense
that I no longer see "meaning" as a kind of "pointing" by referents to
their meanings (even if "pointing" is still an important way of
communicating).

(b) as a Pythonista, I'm blessed with a rather elegant nominalist
logic, with namespaces comprised of names referring to objects on the
heap.  The objects do the real work, whereas the names are more like
TV remotes:  they provide the controls, crafted in syntax, that give
scripts agency over their players, make them do stuff (the imperative
paradigm).  So I've got a "perfect nominalism in a bottle" that in
dimmer days I might come to view as a heresy, and reflexively attack
based on Wittgensteinian predilections.

My synthesis of these two is to associate Python with Wittgenstein in
his Tractatus phase, as embraced by the Vienna Circle of his day.
Here's the propositional calculus Russell was hoping for, a simple
nominalist paradigm but nuanced and endowed enough to run on machinery
at lightning fast speeds.  This is what workaday logic became:  the
backbone of the global economy, or its organizing rubric.  Leibniz had
anticipated the drift of the zeitgeist (he was good at that).

On the other hand, to gain perspective, I operationally develop
meaning by spinning new ones into existence, showing off the power of
the PI (Philosophical Investigations) and what it teaches us.
Tractatus relates to tractare or traction, work through friction,
dragging a stick through the dirt, behind a tractor, a plow.  This
tractor then starts behaving much like a turtle in Logo, leaving
patterns in the field.  We discover a more explorational vista wherein
nominalism gives way to the more flexible (less rigid) and mature
philosophy of the later Wittgenstein.

Yeah, "clear as mud" as Maureen would say (one of my teachers).  Just
giving a snapshot of where my head's at sometimes, between grading
papers and cooking with math teachers, engaging in various logistics /
maneuvers (how to feed OccupyPortland and still keep our other
circuits open?  -- Metro needs more bizmos around the perimeter,
education mobiles.... (a two way street, geeks learn even more than
they teach, to stay geeks)).

http://controlroom.blogspot.com/2011/10/at-wherecamppdx.html

"""
During one of the breaks, I showed Igal the faux socialist realist
memes I've been weaving into my Pythonic Andragogy, complete with
Tractor Art. Given he reads Cyrillic, we slowed down and zoomed in on
some of my slides. I gave him the whole presentation in under three
minutes, including the Cult of Athena slide at the end.
"""

Kirby