I will now try to determine how many different definitions of ‘divine person’ can be generated from the four previously specified attributes, in the case that all four attributes are relevant to a definition of the phrase ‘divine person’.

I. All Four Attributes are Relevant

A. Four Conditions are Criterial and None are Necessary Conditions
If all four attributes are relevant, one sub-category of definitions would be purely criterial definitions, where all four conditions were criteria, rather than necessary conditions.
As we saw in my previous post, a definition of ‘divine person’ (based on four attributes) will include four conditions, each of which specifies one range of degrees (out of ten possible ranges) for each of the four attributes.
There are 10,000 different such sets of four conditions. Right now we are considering definitions that can be formed when all four conditions in such sets of conditions are treated as criteria.
Three different strengths of requirements can be applied to a set of four criterial conditions:
At least three conditions must be satisfied
At least two conditions must be satisfied
At least one condition must be satisfied
Therefore, the number of purely criterial definitions of ‘divine person’ that can be generated when all four attributes are relevant and all four conditions are criteria is: 10,000 sets of four conditions x 3 strengths of requirements = 30,000 definitions.

B. Four Conditions are Necessary Conditions and None are Criterial
Since there is only one standard in the case of a set of necessary conditions (i.e. all conditions must be satisfied), the 10,000 different sets of four conditions yeild 10,000 different definitions of ‘divine person’ that consist of four necessary conditions.

C. Three Conditions are Criterial and One is a Necessary ConditionMixing criterial conditions and necessary conditions creates more interesting combinations and permutations (N = Necessary Condition; C = Criterial Condition):
Each column in the above table represents 10,000 sets of four conditions, so the four columns in this table represent at least 40,000 different definitions of the phrase ‘divine person’ that include three criterial conditions and one necessary condition.
However, in the case of defintions that include three criteria, there are two different possible strengths of requirments:
At least two of the (criterial) conditions must be satisfied
At least one of the (criterial) conditions must be satisfied
Thus, each of the 40,000 sets of conditions represented by the above table is ambigous and each of them can be used to generate two definitions. So, the number of definitions of ‘divine person’ that can be generated involving three criterial conditions and one necessary condition is: 40,000 sets of conditions x 2 strengths of requirements = 80,000 definitions.
D. Two Conditions are Criterial and Two are Necessary ConditionsThis subset of definitions also involves mixing of criterial and necessary conditions, which increases the number of possible permutations:
Once again, each column in this table represents 10,000 different sets of four conditions. So, the six columns of this table represent 60,000 different sets of four conditions that involve two criterial conditions and two necessary conditions.
When you have two criteria in a definition, there is only one strength of requirement that can be used:
At least one of the (criterial) conditions must be satisfied
So, there is no ambiguity here as there was in the case involving three criterial conditions. Thus, there are 60,000 different definitions of ‘divine person’ that involve two criterial conditions and two necessary conditions.
E. One Condition is Criterial and Three are Necessary Conditions
This particular subset is easy to enumerate. There are no definitions in this case, because you need to have at least two criteria in order to use criteria at all in a correct definition.
F. Adding up Definitions from the Five Subsets (A through E)
So, we can now determine the number of definitions of ‘divine person’ that can be derived from the four attributes, the four degrees of those attributes (and the resulting ten ranges of degrees of an attribute), and the two types of conditions (criterial vs. necessary), and the different strengths of requirements for criterial definitions, in the case that all four attributes are relevant for the definition:
30,000 definitions (where all four conditions are criterial).
10,000 definitions (where all four conditions are necessary conditions).
80,000 definitions (where three conditions are criterial and one is a necessary condition).
60,000 definitions (where two conditions are criterial and two are necessary conditions).
0 definitions (where one condition is criterial and three are necessary conditions).
The total number of definitions, when all four attributes are relevant is:
180,000 definitions.
In the next installment, I will determine how many defintions can be formed in the case that only three of the four attributes are relevant for a definition of ‘divine person’.