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Hi Mickel
I kept thinking about you question on "Common Classes" realized I still
had something misunderstood on the Logical Notes section of TROM. On
reviewing that section I found what I had missed and here is the result.
Dennis uses Boolean algebra to make sure he considered all the possible ways
two individuals could interact concerning a goal. It took me a while to
understand what he was doing with the algebraic formulas so I thought it
might help to show what they are about.
Logical Notes
This section can be glossed over if desired. The purpose of the section is
to demonstrate to those interested that the subject of the goals package
rests upon a firm logical foundation.
The subject of logic rests upon two fundamental axioms:
1. The common class of a concept and its absence does not exist. (x(1-x))=0.
This equation is only satisfied when x is either zero or unity. Thus, in the
algebra of classes (Boolean algebra) (symbolic logic) the symbols can only
have the value of zero or unity.)
(((A "Common Class" is a group of items that share characteristics of two
parent classes. View this as two circles overlapping. The area of overlap
is the common class as it is part of both circles.
(x(1-x))=0 View this formula as a bucket full of black marbles and white
marbles. If you pull out one marble it can be either white or black. There
are no other possibilities so this equation says "Can I pull out a marble
that is both black and white? The answer is no so in Boolean algebra you put
the value for false which is zero.)))
2. The universe can be divided into any concept and its absence. (x + (1-x)
=1.)
(((Using the same bucket of black and white marbles this statement says that
if you pull out a marble it will be either black or white. The equation
then reads if I pull out a marble it must be either black or white and the
answer is the Boolean value for true which is the number 1.)
>From these two basic axioms all other logical propositions are derived. One
of these propositions states that the types of possible classes that can
exist with two concepts, x, y, are four. Their sum equals the universe:
unity.
xy + x(1-y) + y(1-x) + (1-x)(1-y) = 1
(1 and 2 above dealt with one value and its absence. Now we have two values
and their absences. Lets picture two buckets. The first has black marbles
and white marbles to represent X and its absence 1-X the second bucket has
red and blue marbles to represent Y and its absence 1-Y. if we pull out one
marble at random from each bucket we can get the combinations of black and
red, black and blue, red and white and white and blue. Those are the only
possible combinations so the equation states these 4 combinations of two
values and their absences are all of the possible combinations we can get in
this situation and the answer is true or the Boolean value 1.)))
Any goals package contains two concepts; these plus their absences
(negatives) constitute the four legs of the package.
The 'To know' package is such a package. If we represent 'To know' by x, and
'To be known' by y, we can see from the above equation regarding two
concepts that the four possible classes are:
xy This is the class To know and To be known. These are
complementary postulates, and are a no-game class.
x(1-y) This is the class To know and To not be known. These are conflicting
postulates, and are a game class.
y(1-x) This is the class To be known and To not-know. These are conflicting
postulates, and are a game class.
(1-x)(1-y) This is the class To not-know and To not be known. These are
complementary postulates, and are a no- game class.
The sum of these four classes is the totality of the universe of the two
concepts. "To know" and "To be known". Within these four classes, then, the
whole subject of knowing and being known is contained. When we consider each
of these four classes from the viewpoint of 'self' and 'others' we arrive at
2x4=8 classes. When we consider each of these 8 classes from the viewpoint
of 'origin' and 'receipt' we arrive at 2x8=16 classes. These 16 classes are
the 16 levels we find when we examine the 'To know' goals package. We can
equally, of course, cut the universe into any two purposes in the form 'To -
' and 'To be -', and arrive at the same conclusion viz: That the whole
universe of the two concepts is within that package.
(At this point I made the mistake of thinking that Dennis was talking about
the Level 5 chart. He is not. The level 5 chart only deals with the two
games conditions between two opponents which is the middle two values above
(x(1-y) and y(1-x)) the other two are "no game" conditions and not on the
level 5 chart.
So what Dennis is showing here is that on any goal an individual can
interact with another in only 4 ways. Two of these will be friendly no games
conditions and two will be conflicts between opposing goals. When you add
in the 4 combinations from the others point of view you get 8 points of view
of this goal and when you consider who started in interaction, self or
other, this would make 16 different combination of how self and other could
interact on this goal.
Stated a little different there are:
4 ways self can pursue a goal with other
4 ways other can pursue a goal with self
And either self or other started the current effort toward a goal
Thus a total of 4x4x2=16 different ways to pursue a goal.
Since these are ALL the ways these two could interact we can be assured that
while we are taking apart a goals package in the mind we are not leaving
something undone. Dennis proves here that he has considered all the
possibilities. )
Thus, we have proven within the rigors of strict logical reasoning that any
goals package contains the full universe of its component concepts, and that
no part of life is external to the package. In the language of the
mathematician the 16 levels of the goals package are necessary and
sufficient for our purposes.
Hope this helps
Keep on TROMing
Pete
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