This is a work in progress - all rights reserved.
Copyright © 2006-2008 Tony Giovia
CHAPTER 12 - Truth, Dominant Rules and Recessive Rules v2.0
12.1 - A context is said to be completely truthful when its composing dimensions are exactly defined and completely consistent with the rule or rules used to build the context. (Definition)
12.2 - A context is said to be completely truthful when it is reproducible using exactly defined dimensions operated on in the same way by exactly the same rules. (Definition)
12.3 - If all the dimensions composing a context are not completely consistent with the rule or rules governing the context, but some are consistent while others are not, then that context is partially true and partially false. (Definition)
12.4 - If each dimension composing a context is not uniquely and exactly defined, then the context is partially true and partially false. (Definition)
12.5 - POV contexts are filters used to associate and disassociate dimensions. (Construction)
12.6 – Every complex context has a Dominant Rule (DR) context that associates and disassociates contexts to the complex context. (Definition)
a) Dominant Rules are Point Of View Filters (Construction)
12.7 - The Dominant Rule of a truthful context must include all the dimensions in the perceivable pool of dimensions consistent with the logical or mathematical law of the rule. (Definition)
12.8 – Recessive Rules are contexts in a complex context other than the Dominant Rule. (Definition)
a) Recessive Rules may be Dominant Rules in other contexts. (Construction)
12.9 - A Paradox is a context with two contradictory Dominant Rules. (Definition)
12.10 - A Dilemma is a context with two or more contradictory Recessive Rules. (Definition)
12.11 - A First Level dimension is a dimension physically shared by a rule, Dominant and/or Recessive, and a dimension in the perceivable pool of dimensions. (Definition)
12.13 – An incomplete idea structure is a partially true and partially false context. (Definition)
Truthful statements are generally considered to have one or more of the following dimensions - factual, efficient, practical, understandable and reproducible. Here we are focusing on “reproducible” because it is the most objective of the listed dimensions.
An exact and unique definition is one example of a truthful context. In these cases the composing dimensions are completely consistent with the rule or rules used to define the context. The definition “A red wheelbarrow.” used to describe a wheelbarrow that is red in color is a unique, truthful definition. The wheelbarrow can be physical, painted, photographed, sculpted, etc – the definition still uniquely applies. Specifying the shade of red and the construction or brand or size or quality or type of wheelbarrow will change the definition (“A Sears wheelbarrow with a plastic rose-red bucket and wooden handles”.), but not necessarily the truth of this new, changed definition - if everyone agrees on the definitions of the new dimensions. This is an example of a truthful definition (“A red wheelbarrow.”) nested inside another truthful definition (“A Sears wheelbarrow with a plastic rose-red body and wooden handles”.).
Truth is easy to define in mathematical terms – exactly defined quantities operated on in the same way by exactly defined formulas always produce the same results. In like manner, a logically derived truth using exactly and uniquely defined terms, operated on by exactly defined formulas, will also always produce the same result. This reproducibility is a dimension of Truth and defines an Objective POV (OPOV).
Personal POV (PPOV) contexts also use filters to associate and disassociate dimensions. Definitions of “Truth” based on PPOV contexts and a pool of dimensions are often unreliable because often they do not include all the dimensions in the perceivable pool of dimensions. The classic Indian story of the six blind men and the elephant is a well-known example of this (John Godfrey Saxe’s version is re-printed below). PPOVs have limited usefulness in determining truthful contexts because PPOVs are non-standardized.
A POV context constructed exclusively from a pool of dimensions, and inclusive of all the dimensions in that pool, is a truthful context. Had the five blind men all examined the same part of the elephant, such as the trunk, their definitions of the elephant would have been similar and truthful relative to the pool of dimensions perceivable to them. The pool of dimensions perceivable to the reader of the story is greater than the pool perceivable to each of the blind men, and therefore the reader and the blind men construct different contexts.
Contexts can and often are created using multiple rules. However there must always be one rule that serves as the backbone to the context – a rule that includes all the included dimensions. That rule is the Dominant Rule.
There is only one Dominant Rule for all truthful contexts - the mandatory inclusion of all dimensions in the perceivable pool of dimensions into that context. A partially truthful context filters out perceivable dimensions that do not conform to the rules that created the context – these contexts also have a Dominant Rule, but it necessarily is a different Rule than that of truthful contexts. Considering both language and numerical possibilities, there are an infinite number of Dominant Rules for partially truthful contexts.
Complex contexts may be considered as having two or more internally consistent parts, with each part governed by a rule. While the Dominant Rule oversees all the parts, each part is itself governed by a Recessive Rule that includes some subset of dimensions in the perceivable pool of dimensions. A Recessive Rule may be a Dominant Rule in another context.
“Truth” is therefore dependent on the perceivable pool of dimensions and on the rules used to filter those perceivable dimensions. Reproducible mathematical and logical truths are explicit and transferable to other contexts as complete modules, internally consistent and clearly defined. Contexts become partially true and partially false only when all the dimensions in an perceivable pool are not included in the definition of the context.
In the case of the blind men, each of them makes a truthful statement based on the First Level dimension they shared with the elephant – their physical contact with the elephant. However, based in the more encompassing PPOV of the reader, each blind man makes a partially true and partially false statement. From the reader’s PPOV, each blind man’s PPOV is incomplete because it does not include all the dimensions in the perceivable pool of dimensions.
“Six Blind Men and the Elephant”:
It was six men of Indostan,
To learning much inclined,
Who went to see the Elephant
(Though all of them were blind),
That each by observation
Might satisfy his mind.
The First approach'd the Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
"God bless me! but the Elephant
Is very like a wall!"
The Second, feeling of the tusk,
Cried, -"Ho! what have we here
So very round and smooth and sharp?
To me 'tis mighty clear,
This wonder of an Elephant
Is very like a spear!"
The Third approach'd the animal,
And happening to take
The squirming trunk within his hands,
Thus boldly up and spake:
"I see," -quoth he- "the Elephant
Is very like a snake!"
The Fourth reached out an eager hand,
And felt about the knee:
"What most this wondrous beast is like
Is mighty plain," -quoth he,-
"'Tis clear enough the Elephant
Is very like a tree!"
The Fifth, who chanced to touch the ear,
Said- "E'en the blindest man
Can tell what this resembles most;
Deny the fact who can,
This marvel of an Elephant
Is very like a fan!"
The Sixth no sooner had begun
About the beast to grope,
Then, seizing on the swinging tail
That fell within his scope,
"I see," -quoth he,- "the Elephant
Is very like a rope!"
And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!
So, oft in theologic wars
The disputants, I ween,
Rail on in utter ignorance
Of what each other mean;
And prate about an Elephant
Not one of them has seen!
Translated by John Godfrey Saxe (1816-1887)