[C] [Wittrs] !!!Re: Re: Metaphysical Versus Mystical
- From: CJ <castalia@xxxxxxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Wed, 13 Jan 2010 21:39:36 -0500
I'd like to address Sean's "dilemma' of the distinction between metaphysical
and mystical "nonsense" by again going back to my initial readings of the
Tractatus and the usefulness of my acquaintance with "group theory" at that time
I have repeatedly made reference to the notions of "groups" as opposed to
"sets" in helping understand the Tractatus..and in understanding Wittgenstein
throughout his writings. Although I don't pretend to be a mathematician is
was my fortuitous appreciation of some of the rudimentary concepts of group
theory which allowed me to immediately understand ( or believe I understood) as
unparadoxical many of the statements of the Tractatus
Hopefully, Sean, you will consider this theme as I raise it again.
Additionally, and importantly, the questions of who the "we" is in the above
statements of mine is crucial. Since it is my impression that the Tractarian
Wittgenstein was rather myopic in his focus of interest....knowledge of the
"world" and the rapid and startling advent of science in his formative years.
So if there is a criticism by Wittgenstein of those engaged in the various
kinds of nonsense it would be a critique of those who speak from within the
language game of "philosophizing" about science or about "knowledge".
The universe is a simple place for W during those years...knowledge which we
tend to speak about (and scientific knowledge at that) versus that which cannot
be known and which we are tempted to speak about (perhaps the mystical)
In the later Wittgenstein the "language game notion" allows him to appreciate
the mitigating factors in the making of various statements as derived from the
role or use those statements play within a variety of different "games of
language".
The Different Kinds of Non-sense addressed by Sean:
(a)The kind of nonsense which can be dismissed as "metaphysical nonsense" is
one where we speak of things which have no meaning as if they have meaning...of
things which may not rightly be conjectured even before their validity might be
verified by some procedure because they do not lend themselves to any
meaningful verification.
In the case of the quest for the proper method for the trisection of the
angle, for example, we were all applying the rules of speaking to a domain
where they seemed appropriate but we were inadvertently misapplying the rules
under which we were functioning in such a manner as to leave us with the
conjuring of a situation where no reasonable action would or could follow.
(b) That which is mystical is where we speak of things which might be said to
exist but cannot be talked about....of course, if they cannot be talked about,
then they cannot be argued or verified either....certainly not within the
'rules of operation" in which our way of speaking is founded.
In {a} we talk about matters which mislead us into believing we can "do"
something to verify our statements about them or not , The mistake is one of
not understanding the rules of speaking.l
In (b) we try to speak about matters but which are simply not amenable to our
speaking or any action that rightful follows from that "speaking". The
"mistake" seems more conspicuous than the mistake in (a) because it more
readily apparent that the statements are not going to validated or not by any
consequent actions on anyone's part.
To escape Nonsense (a) , we must more closely and adequately know and then
correctly operate within the 'rules" or operations that we have as our
"grammar".
To escape Nonsense (b) we must more closely and adequately know our rules and
thus realize that, given the subset of rules which we depend on, they only can
carry us so far and that to discuss further matters we would require an
amendment of the "rules' or "operations" that constitute our current "grammar"
Anticipating what I will say below, If we take complex/imaginary numbers versus
real numbers, or irrational numbers versus rationals, in case case, they were
originally considered to be mystical and something which could not properly be
spoken about. And indeed, given the lack of mathematical sophistication at the
time it was not possible to speak about them in any productive fashion...at
best bewilderment would result. Ultimately the rules for speaking about those
matters were broadened and those 'numbers" were included in the domain about
which we might sensibly speak.
While in (a) the mistake is one of less than apt or adequate implementation of
the rules for speaking (whether "picturing" or what I take to be a more
implicit mathematically based notion of these "rules"), the mistake in (b) is
that, based upon the rules of ones grammar or way of speaking, one is taking a
less than apt or adequate domain about which one is speaking and then no matter
how artfully the rules for speaking are employed the statements will not be
amenable to consequent productive action...such as verification.
> This book will, therefore, draw a limit to thinking, or
> rather ? not to thinking, but to the expression of
> thoughts; for, in order to draw a limit to thinking we
> should have to be able to think both sides of this limit (we
> should therefore have to be able to think what cannot be
> thought). ... The limit can, therefore, only be drawn in
> language and what lies on the other side of the limit will
> be simply nonsense" (27).
In the statement of Wittgenstein's that Sean has seized upon he is making a
rather obvious and straightforward point. It is one of the direct, immediate
and obvious consequence from understanding of aggregates as "groups" rather
than as "sets" However, this is not obvious or straightforward at all if one
is not appreciative of the importance that mathematics and its expression had
for the Wittgenstein of the Tractatus years and truly throughout his life.
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".
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".
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.
>
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