Addendum I - Mathematical Basis
Value Logic is based on philosopher Robert Harman's ground-breaking work on goodness. Hartman discovered that a thing is good when it has all the properties it is supposed to have as a member of its class. This discovery led to the application of the branch of mathematics known as set theory to the process of thinking about relative goodness, i.e. value. In Value Logic the size and structure of meaning sets are used as the criteria for the classification of concepts into categories. A meaning set is defined as the entire collection of names of properties implicit in the meaning of a concept. By this criteria, good is objectively defined as the degree to which a concept fulfills its meaning set.
When the meaning set is used as the method of categorizing a concept, the collection of natural properties or parts of the thing named by the concept are enumerated. Take, for example, the concept "tree". The first element in the meaning set is the name of the general type of thing into which it falls: in this case tree falls into the type of things named "plant." The other members of the tree's meaning set are all the parts, properties and components that make up a tree. For example: a large plant with roots, trunk, bark, limbs, leaves, sap, seeds, etc. etc . etc.)
Value Logic employs set theory to define different types of meaning sets and to classify all concepts into three categories. Since sets come in different sizes, concepts in a meaning set with a large number of properties (qualities) have greater value (are "more good") than concepts in a meaning set with a lesser number of properties.
- Type I concepts have a fixed finite meaning set. All properties of the set are known. Value Logic categorizes Type I concepts as "S" for Systemic valuation. These concepts relate to and induce black and white thinking. "It is or it isn't a square."
- Type II concepts have elastic finite meaning sets. While the properties in the set are all countable, some, but not all of the properties are known. Value Logic categorizes Type II concepts as "E" for Extrinsic valuation. These concepts relate to and induce comparative thinking. "Chair A is better than chair B."
- Type III concepts are each in a unique meaning set with an infinite number of properties. Value Logic categorizes Type III concepts as "I" for Intrinsic valuation. These concepts relate to and induce sorting and screening for uniqueness. "Each child is indescribably unique."
According to these criteria the names of everything in the universe can be subsumed under one or other of these three types of concepts. The three types of concepts have different richness of meaning based on the size (depth) of their meaning sets. Quantitatively, extrinsic concepts have more properties in their sets and therefore have a greater dimension (gradation) of value than Systemic concepts. Intrinsic concepts, in turn, having an infinite number of properties, have a greater dimension of value than Extrinsic concepts. One can think of Systemic value, Extrinsic value, and Intrinsic value as measures of goodness in the same way that one mile, two miles, and three miles are measure of distance.
The greater the number of properties a meaning set of a concept has, the more value it has. When we value concepts with larger meaning sets over those with smaller meaning sets (I over E, or E over S) we make ethical decisions. When we value concepts with smaller meaning sets over those with larger meaning sets (S over E or I, and E over I) our ethical decision making goes awry. Understanding Value Logic, we can intentionally think about a concept’s dimension of value when we are faced with making ethical decisions.