*************
The following message is relayed to you by trom@lists.newciv.org
************
Hi Mickle and Jurgen
Thanks for the nice compliments. I still didn't feel right about the
Boolean algebra so reviewed it today and found an error in my math. I fixed
it below.
Sincerely,
Pete
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, white and red 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:
((right here is where you see why Dennis felt the need for the algebraic
symbols. The phrase "to know is the causative action of bringing an
effect into existence and the phrase "to be known" is the passive action
of perceiving what someone else has brought into existence. Now, when we
formulate this into the statements of the to know goals package it
becomes "Must be known" is the causative
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. )
((OOPs! Still had an error. 4x4x2=32 not 16. The correct formula is
(4+4)x2=16 and looks like this:
For self origin self other
1. Xy x
2. Xy x
3. x(1-y) x
4. x(1-y) x
5. y(1-x) x
6. y(1-x) x
7. (1-x)(1-y) x
8. (1-x)(1-y) x
For other origin self other
1. Xy x
2. Xy x
3. x(1-y) x
4. x(1-y) x
5. y(1-x) x
6. y(1-x) x
7. (1-x)(1-y) x
8. (1-x)(1-y) x
Line 1 and 2 Starting at the top from self's point of view xy is the
complementary goal must be known, must know first originated by self
then originated by other.
Line 3 and 4 is the goals must be known, must not know (x(1-y)) in
conflict originated by self on line 3 and by other on line 4.
Line 5 and 6 are the conflicting goals must know, must not be known
(y(1-x)) originated by self online 5 and by other on line 6.
Line 7 and 8 are the complementary goals must not be known, must not
know ((1-x)(1-y)) originated first by self on line 7 then by other on
line 8.
The next block of 8 lines is the same from other's point of view.
Now why did Dennis add the second point of view for others to this? From
self's viewpoint in the first 8 statements self is at Must be known but
never at Must Know. Only in the second block of 8 lines is self at Must
Know and other occupies the Must be Known leg. All 16 lines are necessary
for self to occupy each of the 4 legs and be opposed by each of the
oppositions or compliments and either be the origin or the recipient of the
action.))
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.
_______________________________________________
Trom mailing list
Trom@lists.newciv.org
http://lists.newciv.org/mailman/listinfo/trom
