On Wed, Jan 13, 2010 at 6:39 PM, CJ <
castalia@optonline.net> wrote:
<< snip >>
> When Wittgenstein speaks of the "limits of _expression_" he is pointing
> directly to the manner in which the rules of a system of operations
> determine what will or will not fall within the scope or landscape of any
> such iteration of those operations or rules. It is the rules or operations
> which essentially "limit" the domain of what can be expressed. In "Group
> theory" this basic property is known as "closure." It embodies the charting
> of a 'limit" from within and not having to be at external "vantage point" as
> one must be when seeking to express oneself in "sets".
> The integers are a "group" with respect to the operations "addition" What
> this means is that you can repeatedly implement sequential additions and
> you will never arrive at a number that is not an integer. You need not have
> an external or God like vantage point to know that you can never be able to
> exceed the 'limits" determined by the successive implementation of these
> operations. That is one of the definition s of a group: It's closure or
> self contained nature. IF you maintain the successive application of
> addition the successive application of its operations only leads to further
> members of the group. In a group such as the "shuffling of a deck of cards"
> no matter how many times you apply a 'shuffle" you are always only going to
> yield up the equivalent of another single "shuffle" that could have been
> made. This group also demonstrates "closure".
I like seeing some group theory come in, with "closure" and "internally
consistent" or "internally logical" having some resonance.
There's a hermetic theme here, foreshadowing "private language"
and its (by definition) nonsensical nature. At the world limit, it's all
internal and therefore "private" in some sense (as in "belonging
to God"), yet it's still operational (follows rules, has grammar).
Group Theory gets Biblical with that "CAIN and Abel" language
game (a feature in some math texts), where CAIN stands for
Closure, Associative, Inverse and Neutral, the basic needs
of a group (Neutral means an identity element, 0 in the case of
addition, with an inverse being "that which forms the identity
when added to" whatever member of the group (to "subtract S"
means to "add the additive inverse of S")).
Having one's language be the limits of one's world is like having
the finite permutations of some character set, say the characters
of the I Ching, sufficient to picture not the details, but something
canonical nonetheless.
Note: I have some Group Theory on tap for teachers, with the
Flash animation being more kid-friendly, but fair warning
there's a "welcome to the machine" noise (Pink Floyd
allusion) so you might want to turn down those speakers:
4dsolutions.
net/ocn/flash/
group.html
The pun on Abel (as in CAIN and Abel) is of course some
groups are "Abelian" (named for Niels Henrik Abel), meaning
their binary operation is commutative, in addition to being
associative.
> When the further operation of "multiplication" is considered and we allow
> for the successive application of either of the two operations, addition or
> multiplication, we end up with a different group, the "rationals", and,l
> again that group is closed and the 'limits of _expression_" are known.....for
> those involved they do not need to have a "vantage point " or "view' from
> outside of irrational numbers or imaginary or complex numbers or so on in
> order to be aware (once they are aware of the grammar of use which arises
> from the restriction to the operations of addition and multiplication) that
> these are the 'limits of _expression_".
>
I see where you're going with this: waxing and waning.
If you play your cards right, you might graduate from grouphood to
ringhood to fieldhood.
The rationals form a field, meaning you have CAIN and Abel for
two operations (+ and *), two identities (0 and 1), and a distributive
law. By analogy, one could see these "new levels of closure" do
not predict one another, i.e. as you say "they do not need to
have a 'vantage point' or 'view' from outside of the irrational
numbers or imaginary or complex numbers or so on in order
to be aware".
Wittgenstein talked a lot about waking from a dream. These
context changes happen. There's no way to say "I am awake"
at a next level, when you're still awake in the previous dream.
> There is much more to the application of the language and stratagems of
> 'Group theory" to interpreting Wittgenstein.
> As to the notion of "form of life" and the relation of "form of life" to
> "language games", I believe that we are still operating while seeking to
> ignore the puzzle which remains as to just how "form of life" relates to
> "language game" other than as some amorphous "backdrop"..
..There is much
> more to this issue and to the far from automatic manner in which a variety
> of "language games" arise from each of a variety of distinct 'forms of
> life". The issue has to do with the manner in which "rules" or 'operations"
> are adopted by the participants.
..as the "language game " is shaped.
> Moreover, the kind of "therapeutic" becoming familiar with the grammar of
> how we speak that Wittgenstein gives us is a crucial tool in our society
> coming to terms with how a form of life might give rise to one or another
> "language game" , with one or another set of rules and operations behind it.
>
You're continuing with the theme of "bringing to consciousness"
as in raising to a higher level of awareness, the rules one might
be following.
Because part of the grammar around "rules" is you don't need
to be aware of them to follow them.
Wittgenstein'
s techniques are therapeutic in bringing us to
greater appreciation of the rules we're actually following. He
adds an empirical dimension to philosophy, a field work
component, like anthropology.
The approach is refreshing, as one studies everyday
communications ("the media"), assembles reminders from
this raw material.
This gives philosophy a more "worker owned" feel, as
anyone is free to investigate language games.
Wholes unpredicted by their parts, waking up to the next
level of play... but then there's going the other direction
too. Dropping to a lower level, falling under a spell.
Fly's go back into fly bottles every day.
Kirby
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