Our technology is an extension of the work of several brilliant men. G. E. Moore developed insights into the concepts of valuing, Georg Cantor developed the science of transfinite mathematics and Robert Hartman quantified Moore’s work and identified relationships to Cantor’s work.
G. E. Moore established principles concerning how we define an object as good. He realized that an object being defined as good was a quality established by the person evaluating an object, moral principle, etc. For example, if one were accustomed to sitting on the ground, one might consider a stool a good chair. However, if one were accustomed to sitting in a plush, overstuffed lounge chair, one might consider a stool a bad chair. Moore worked to establish principles of how individual valued objects and the components of valuing. He identified three categories that comprised the components of valuing – uniqueness, comparativeness and concepts. Applying these components to his son, Moore realized that his son had an unlimited number of qualities and that made him unique. He also realized that his son could be compared to other boys as being better or worse. In the component of concepts, his son also either fit or did not fit in the class of gender defined as male.
Based on the philosophical work of G. E. Moore, Dr. Robert Hartman identified the following categories (dimensions) of the way in which an individual would evaluate/value an object, idea, or any other event presented to them.
G. E. Moore established principles concerning how we define an object as good. He realized that an object being defined as good was a quality established by the person evaluating an object, moral principle, etc. For example, if one were accustomed to sitting on the ground, one might consider a stool a good chair. However, if one were accustomed to sitting in a plush, overstuffed lounge chair, one might consider a stool a bad chair. Moore worked to establish principles of how individual valued objects and the components of valuing. He identified three categories that comprised the components of valuing – uniqueness, comparativeness and concepts. Applying these components to his son, Moore realized that his son had an unlimited number of qualities and that made him unique. He also realized that his son could be compared to other boys as being better or worse. In the component of concepts, his son also either fit or did not fit in the class of gender defined as male.
Based on the philosophical work of G. E. Moore, Dr. Robert Hartman identified the following categories (dimensions) of the way in which an individual would evaluate/value an object, idea, or any other event presented to them.
- Concepts: a concept has a specific, definable set of qualifying features and the subject of the evaluation either fills/completes this set of features or the subject does not belong in this concept. Moore’s son either was or was not a male
- Abstracts: this category also has a specific, definable set of qualifying features for the subject, but the subject is not required to fill/complete all of the features in order to be identified in this ‘class’ of subjects. It may be evaluated as a ‘good’ subject, a ‘bad’ subject or any number of variations of subjective valuation. This is the dimension of comparative values. When Moore compared his son, as a male, to the other boys with whom he associated, he would evaluate his son as ‘better’, ‘worse’, ‘about the same’, etc.
- Uniqueness: In order to be classed in this category, a subject must have an infinite number of qualifying features. This category consists of subjects that are ‘unique unto themselves’, that is, they are one of a kind, there is no other like them in the universe. Any number of comparative valuations is then used to value the subject. Moore’s child was not just a male, he was his son, he was unique in the world with an infinite number of qualifying features. However, Moore could also evaluate these features as compared to another child and consider them as being better, worse or any number of valuations.
Hartman’s search for a mathematical system that provided relationships between the dimensions he had identified led him to the work of Georg Cantor. Georg Cantor established the theorems and axioms for the mathematics of Set Theory, which he later extended to establish relationships between finite and infinite sets of numbers. According to Cantor:
- the finite set of numbers taken to a finite power was identified as the set of numbers N
- the finite set of numbers taken to an infinite power was identified as Alef
- the infinite set of numbers taken to an infinite power was identified as Alef One
Using mathematical principles from finite mathematics, Cantor proved that the value of ‘the combinations of sets of finite/infinite numbers’ was valued in the same manner as finite mathematics. That is, the numerical sets combinations producing the greatest number of numerical variables was given the highest value and the numerical sets combinations yielding the fewest of number of numerical variables was given the lowest value. Therefore, the set of numbers consisting solely of finite numbers [N ^(to the power of) N] would have a lower value than the set of numbers consisting of infinite numbers [Alef One ^(to the power of) Alef One].
Cantor identified three sets of numbers that had specific qualifying parameters and Hartman identified three dimensions that had corresponding numerical parameters. When Hartman applied Cantor’s mathematics to the dimensions that individuals use in the process of valuing a subject, he established the following equalities.
- Hartman’s dimension of Concepts corresponded with Cantor’s set of N. Hartman’s definition of the dimension of a concept has a definable number of attributes and the item either does or does not fit in that concept. Cantor’s definition of a set of numbers N is a set that is composed of finite numbers taken to a finite power. For the purpose of simplification, from this point on, the dimension of concepts will be referred to as black or white functions.
- Hartman’s dimension of Abstracts corresponded with Cantor’s set of Alef. Hartman’s definition of the dimension of an abstract has a definable number of attributes and the item is valued in comparative terms so it has an infinite number of comparative attributes that can be assigned to it. Cantor’s definition of a set of numbers Alef is a set that is composed of finite numbers taken to an infinite power. The dimension of abstracts will be referred to as comparative functions.
- Hartman’s dimension of Uniqueness corresponded with Cantor’s set of Alef One. Hartman’s definition of the dimension of uniqueness has an infinite number of attributes and the item is valued in comparative terms so it has an infinite number of comparative attributes that can be assigned to it. Cantor’s definition of a set of numbers Alef One is a set that is composed of infinite numbers taken to a infinite power. The dimension of uniqueness will be referred to as unique functions.
Hartman then developed instruments that were made up of verbal statements, each statement representing a mathematical function from the norms established in transfinite mathematics. The data representing the cognitive structure of an individual is collected by allowing an individual to order these statements in a free form format, from their perspective of best statement to worst statement. The individual’s ordering of the statements is then analyzed against the norm established in transfinite mathematics.
Each page of the instrument is a forced-rank closed system, therefore, each statement must be given its own unique ranking, no two statements can have the same rank, there cannot be two statements ranked as #1 or three statements ranked as #5, etc. The perceived value of each statement to the individual and the order in which these statements are ranked (by being compared to each other), generates a series of patterns that is a representation of ‘how’ a person thinks, that is, the individual’s cognitive structure. Each statement of the instrument becomes a part of a series of patterns that are compared to the norms established in transfinite mathematics and are the keys that are used in the evaluation and interpretation of the individual’s cognitive structure. Statement patterns are used in evaluation and no single statement has the ability to produce a significant impact on an individual’s evaluation.
Hartman identified a mathematical system that was capable of measuring and establishing relationships between the dimensions of valuing. He also established basic interpretations of how the scores effected the actions of an individual.
MindsIView has advanced this work in several areas.
- We've developed new instruments containing statements that are more easily understood by the applicant.
- We've taken the basic scoring developed by Hartman and developed interpretive algorithms that convert the mathematical scores into an evaluation of an individual’s personal culture or how they do things.
- We've taken these scores and produced functional reports that can be used to improve the performance of an individual or to predict the performance of a job applicant.
- We've developed different instruments to determine how experience and education will produce a modification of perceptions and behavior in a particular discipline.
Dr. Hartman established the theorems of the science of cognitive structure measurement, MindsIView has taken these theorems and developed practical applications. This new science provides a measuring system that is isomorphic with an individual’s cognitive structure and symbolically formulates the vast field of personal values (cultures), reflecting in systematic detail what philosophers have said about cognitive structures (valuing, perceptions, personal cultures, etc.) and more significantly, what they have not said.
