HANblogLAKA:
Commentary in Shaman Annotation of
Principia Mathematica by Whitehead & Russell 4/4
This work is a commentary on Bertrand
Russell's three chapter introduction to the first edition of Principia
Mathematica, written as a young man, and published in 1911, co authored
with mathematician Alfred North Whitehead.
Links trace to my Hanbloglaka blog posts with Russell's introductory text supporting my observations and commentary here.
“Speaking for myself, the rules regarding the use of
functions, and the broad restrictions of the vicious-circle principle seemed
to be very restrictive, and cumbersome obstacles arise at every turn.”
-Comic Book Sham
|
“This goes very far to shrinking that field providing
important specific arguments to guide us in using propositions, and seeing
more specifically how functions fit into useful calculations.”
-Comic Book Shaman
|
“This is mainly perceived in the abstract, and our comfort level with its ambiguity at
this point, may be indicative of our confidence in Principia Mathematica.”
-Comic Book Shaman
|
“To study this system calls for a leap of faith. For even
as the rational perception of value
may take hold early, there is so much that must be absorbed with no clear application beyond ambiguity
in sight that this is a trip into the shaman mind.”
-Comic Book Shaman
|
“Very likely anyone reading this work is interested from a
philosophical field of study. I suspect few mathematicians in the post
war era ever bothered to pursue the intensional aspects of the system,
instead seeking some arcane advantage by perusing an obscure text that
everyone knew of, but few had actually read.”
-Comic Book Shaman
|
“Two world wars changed the field of mathematics radically;
from a few Cambridge professors corresponding with their counterparts in Berlin
or Rome with papers of pure universal mathematics.”
-Comic Book Shaman
|
“War, industry and big profits changed the Mathematicscape
in every way imaginable, so that by 1950, the mind of the mathematician was
so far removed from that resembling Bertrand Russell’s, as he struggled to
finish developing our system from 1905-1910, as to be seen as completely divergent in both process
and intent.”
-Comic Book Shaman
|
“Just
a few days ago I awoke from a dream and marveled at it. In the dream I was
talking to some people, and realized that I knew what I was talking about.”
-Comic Book Shaman
|
“I saw
the humor but could not connect the meaning to the truth of the humor until
the dream I had today.”
-Comic Book Shaman
|
“My dream today
gave me clarity on this question, and it lies in the relation of variables
and apparent variables.”
-Comic Book Shaman
|
“’The source material that is quoted
from Principia Mathematica is definitively without error and therefore
correct.’
This is a definite statement that
obviously contains no ‘real’ variables. Still, one may infer two apparent
variables in that sentence:
1) future posts may contain error in the
source material;
2) other parts of the previous posts are or
may not be without error.
Although this example seems obscure, in some
form it arises in every use of language including simple declarative
sentences.”
-Comic Book Shaman
|
“The element of
time acts to degrade everything and language structure is not exempt from the
effect.”
-Comic Book Shaman
|
“This clarifies
the meaning of my dream: not that I knew what I was saying, but that
others understood my meaning”
-Comic Book Shaman
|
“Well it ain’t no use to sit and wonder why babe.
If yuh don’t know by now.”
-Bob Dylan
“The matrix is the womb, the rock where precious minerals
are extracted; and here, basis for the construction of the Hierarchy of
Functions and Propositions.”
-Comic Book Shaman
|
“These distinctions are well understood by all shamans and
used exclusively among themselves and our spirit helpers.”
-Comic Book Shaman
|
“Such use of language for us is merely intensional and rarely spoken aloud, only in oblique
indication for points of clarity.”
-Comic Book Shaman
|
“In our system the authors had no thought or intention to
address or define native American Indian thought or perception, this is clear
by the systems structure, and the use that they chose to demonstrate its
practical extensional use: the principle text of the work Principia
Mathematica.”
-Comic Book Shaman
|
“The intention was to create a metaphysical end run past
language to a notational symbolic system that can convey extreme complexity
in a clear, compact manner and without error.”
-Comic Book Shaman
|
“Ironically once the system is assimilated clearly in a
reader's mind, her perception alters to a state where language regains useful
function.”
-Comic Book Shaman
|
“Unfortunately it works only one way, just as one
understands everything involving language, expression, intension and
aspiration in all cultures, she can
only respond obliquely and mysteriously; or by means of artistic expression to be understood. This should become clearer
in ahead.”
-Comic Book Shaman
|
“The authors’ approach to the Axiom of Reducibility is
curious to my thinking. This axiom is subject to the greatest caution in
presentation, and alternative proofs are suggested; and ahead we will find
further explanation and justification.”
-Comic Book Shaman
|
“I believe that Russell was uneasy about this axiom on two
grounds. On the essential aspects of the system, the metaphysics in thinking
and understanding it, this axiom is superfluous, because it is no help in
these aspects at all. The value of the axiom is in justifying the symbology
by which, in use, one will communicate with notation to a remote reader. ”
-Comic Book Shaman
|
“Secondly, the axiom of reducibility serves to reduce both
labor and length of symbolic notation, and Russell understood the clear
validity of it, but at the same time, as a classically trained academic he
was very uneasy about the final ambiguity inherent in this aspect.”
-Comic Book Shaman
|
“ I believe that this axiom is entirely palliative for
Bertrand Russell’s sense of vulnerability with the underlying ambiguity that
permeates the system, and he well understood that he could not be disputed in
the metaphysics, because if one gets it they get it; but if they don’t get
it, still they have no other concrete
basis to dispute it.”
-Comic Book Shaman
|
“But in the notational aspect it is fairly easy to call him
out on the small contradictions that are addressed by the axiom of
reducibility. It was not enough that the axiom solved by intension a number
of problems inherent in the system, it required justification beyond utility,
by extension.”
-Comic Book Shaman
|
“In terms of hanbloglaka, or more broadly North American
Indian thought and perception, this axiom is total diversion, but I am not
persuaded that it is without value that I haven’t yet perceived.”
-Comic Book Shaman
|
“The essence of shaman knowledge is to see with multiple
perspectives without preconceived assumptions, and regarding actions and
propositions through to their logical conclusion.”
-Comic Book Shaman
|
“Still there is always accepted ambiguity,
and in the end being wrong is not worse that being right, the only disgrace
is in false pride, or claiming knowledge one does not possess.”
-Comic Book Shaman
|
“It is clear that our
system prevents contradictions by understanding how they may arise and steering clear. As we have seen above in
the authors’ treatment of four classic mathematical contradictions, their
resolution presented is not the result of any external changes in the
problems themselves; but solely in our
perception of the problems in terms of our system.”
-Comic Book Shaman
|
“Nearly all
insolvable problems can find a resolution with a new approach, a fresh look
or a change in attitude.”
-Comic Book Shaman
|
“Addressing
contradictions is key to translating the use in real world value of the system into practice.”
-Comic Book Shaman
|
“This is also the clearest explanation thus far of the
basic understanding of shaman sight; or seeing through externalities that distract and prevent most human beings
from using their ability to recognize
complex
and difficult problems, let alone thinking
them through and separating their causes
and solutions.”
-Comic Book Shaman
|
“When we want to discern reality, in contradictory intentions no matter how large or small, sorting it
out is a matter of looking at all sides of the issue without prejudice;
propositions placed in evidence that include self-referential arguments that are
the ones that unravel as
vicious-circle fallacies.”
-Comic Book Shaman
|
“Don’t presume these gremlins: truth, falsehood, function,
name, reality, relation, etc. must be intentionally removed, though perhaps
they may be, these typical ambiguities may foul the water but conversely they
allow us to open the tap of creativity that makes this system, and all
mathematics happen in the first place.”
-Comic Book Shaman
|
“Our premise
stated previously is that complexity begins with just two significant parts
of speech.”
-Comic Book Shaman
|
“Our experience in life
and conversation shows us that misunderstandings are very common.
Unfortunately almost the norm. Here we learn to spot the aspects of language
that lead to misunderstanding, and by attempting to avoid making these
ourselves, and carefully practicing
to see them in others language it
is possible to clarify problem usage
kindly.
This way more precise understanding may be possible.”
-Comic Book Shaman
|
“This
part digs in and offers real clarity to the ambiguity in everyday language.
We can begin to see here the origin of conversation and written language’s
undoing.”
-Comic Book Shaman
|
“These
aspects are mostly or completely unknown in Indian languages in North
America.”
-Comic Book Shaman
|
“It is only in the
shaman spirit aspect that metaphysical thought or communication is required;
these served the function of healing, sciences, religion, agriculture and
even a very useful and developed sort of computer technology very similar to
memory based techniques used by the greatest engineers, architects, artists
and clerics in the West for centuries.”
-Comic Book Shaman
|
“Indian cultures
were concerned with life, a life connected to the land and the seasons and
human concerns in which physical possessions were minor, trivial matters to
most people”
-Comic Book Shaman
|
“Society
structure was complex and tribal to
be sure; but everyone had their place, and these roles were nearly always
voluntary and clearly evident.”
-Comic Book Shaman
|
“In these societies
languages were rudimentary by Western standards, but they held, and still
hold great variety and complexity for native speakers. They are brilliantly
functional because they are entirely separate from the metaphysical,
grammatical and rhetorical aspects that are the province of Chiefs and
shamans.”
-Comic Book Shaman
|
“A final
important aspect to help understand how this worked is to recall that these
cultures were non-material and that money was once unknown.”
-Comic Book Shaman
|
“Here are ways
of recognizing and reconciling the seemingly opposite natures of mathematics
and philosophy.”
-Comic Book Shaman
|
“As with all
intractable differences, reconciliation can come without changing a problem,
or even by compromise for that matter. The trick to working things out is to
change our perception of the issues involved.”
-Comic Book Shaman
|
“Looking around
for aspects that agree together can be a road to seeing a formal equivalence
of value. So many obstacles arise in simple misunderstandings from the
imprecise use of language, even especially after multiple attempts at
clarification.”
-Comic Book Shaman
|
“We tend to believe mathematical problems have reliable
answers that are provable and constant, but that more human questions
involving beliefs, emotions, speculations, etc., are a completely different
matter.”
-Comic Book Shaman
|
“In fact, although the propositional equations we are
learning to construct may seem a bit more complex than typical math, they are
actually similar; and plainly behave in the same ways, but reveal any errors
clearly.”
-Comic Book Shaman
|
“Once again
these aspects are only in small part about understanding the system or
thinking like an Indian does. These last posts more directly go towards
communicating complex thought clearly to others, and a systematic means of
notation. ”
-Comic Book Shaman
|
“I feel that by the time most persons reach an
understanding of the system we find that we no longer require the purpose we
set out to satisfy.”
-Comic Book Shaman
|
“If one
understands the system well at every step, she changes in her perception of
dominant culture, common use of language, as the process of metaphysics
affects each one’s brain chemistry, and all of life as it goes on around us.”
-Comic Book Shaman
|
“If one is very
strongly attached to a stake in dominant culture, earning money as a means of living life, such as responsibility
for supporting family or debt; I am not certain that she can learn this
system at all, or could even consider investing
the time it requires.”
-Comic Book Shaman
|
“Here
describing incomplete symbols clarifies where aspects of logical philosophy
diverge and are distinct from mathematical logic. ”
-Comic Book Shaman
|
“Also we learn techniques of thinking about, and also
phrasing functions, relations and classes in new ways, so that they do not
lead to vicious-circle fallacies as
they may if carelessly thought of, or expressed.”
-Comic Book Shaman
|
“Remember that
this system helps us to perceive and understand terrific complexities and
combine them clearly and without error, and most usefully with
brevity.”
-Comic Book Shaman
|
“As time is a true barrier in expressing complexity,
especially in common language, this system can be valuable to anyone with
that goal. ”
-Comic Book Shaman
|
“If interested readers have even a fair grasp of the system
presented here by now, this is a true mental achievement. ”
-Comic Book Shaman
|
“Virtually
everything presented is abstract form that has no real meaning itself; but
great value as a system of organizing and expressing any subject we choose.”
-Comic Book Shaman
|
“This sort of system is
only made necessary by the complexity that has evolved in Western language as
a result of technology, science, philosophy, theology, etc.; North American Indian peoples do not think in the terms of
our system. Instead, our system allows
us to think in similar ways as those Indian peoples.”
-Comic Book Shaman
|
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