My estimate that there are more than three millon ways to analyze the word ‘God’ (using just four attributes in the analysis) was inflated by some incorrect assumptions. I will now make a second attempt to determine an accurate count of the various combinations and permutations of conditions that form different definitions, taking into consideration some things I learned from the first attempt.

The word ‘God’ is a proper name, and I agree with Swinburne that the meaning of this proper name should be specified by means of a definite description, and the definite description should, in turn, be derived from the definition of a category of beings to which God belongs: ‘divine person’. So, technically, the alternative definitions that I’m considering are not definitions of the word ‘God’, but are definitions of the phrase ‘divine person’ (which is then used to identify the referent of the word ‘God’).

My first assumption is that at least one of the following four attributes is relevant to a correct definition of the phrase ‘divine person’:

Power
Knowledge
Freedom
Goodness

My second assumption is that there are no other attributes besides these four that are relevant to a correct definition of ‘divine person’.

The first assumption seems obviously true. But my second assumption seems obviously false, or at least highly questionable. There are a number of other attributes that might well be relevant to defining ‘divine person’, such as: the creator of the universe, omnipresent, bodiless, and a source of moral obligations.

But the second assumption is justifiable as a simplifying assumption. I’m trying to show that a large number of different definitions for ‘divine person’ can be generated from a small number of attributes. If there are in fact eight or more attributes that are relevant for defining ‘divine person’ then clearly there will be a huge number of definitions that can be based on various combinations and permutations of conditions related to those attributes.

My point is that with just a few attributes, four in this case, one can still generate a very large number of different definitions. So, although my second assumption is probably false, it is justifiable as a way of reducing the scope of possible definitions, of simplifying the circumstances, of making the math and reasoning a bit easier, in order to make a point.

As with my previous calculations, each of the above attributes can occur in four degrees:

Human
Superhuman
PerfectEternally Perfect
If we allow for conditions that specify a range of degrees of the attributes, and if we assume that the acceptable degrees of an attribute must be a continuous range, and not include any gaps (e.g. set aside as implausible definitions that include the requirment that a divine person have either a human or a perfect degree of power –but not a superhuman degree), then there will be ten different degrees or ranges of degree for each attribute:

1. human
2. superhuman
3. perfect
4. eternally perfect
5. human or superhuman
6. superhuman or perfect
7. perfect or eternally perfect
8. human or superhuman or perfect
9. superhuman or perfect or eternally perfect
10. human or superhuman or perfect or eternally perfect

If a definition of ‘divine person’ consisted of a set of four conditions, specifying one of the ten possible ranges of degrees for each of the four attributes, then there would be 10 x 10 x 10 x 10 = 100 x 100 = 10,000 different definitions possible for the phrase ‘divine person’.

One of those 10,000 sets of four conditions would be, for example:
condition 1: has perfect power
condition 2: has perfect knowledge
condition 3: has perfect freedom
condition 4: has perfect goodness

However, the 10,000 different sets of four conditions do not constitue unambigious definitions, because there are two different kinds of conditions: criteria and necessary conditions.

Criteria are weaker than necessary conditions. With a criterial definition, you have a list of conditions, none of which is, by itself, absolutely required. The requirement in a criterial definition is simply that some portion of the conditions be satsified, not that all of the conditions be satisfied. This means that any correct definition that includes a criterion must include at least two criteria, so that no single condition (among the criteria) is required.

Furthermore, criterial definitions can have requirements of different strengths. Consider the above example of a set of four conditions, and assume that those are four criteria (as opposed to being necessary conditions). This set of conditions would be ambigous because there are three different strengths of requirements that could be layed down in this case:

At least three of the four conditions must be satisfied
At least two of the four conditions must be satisfied
At least one of the four conditions must be satisfied.

So the one set of conditions for the four attributes actually is the basis for three different criterial definitions.

If we took the set of four conditions above as necessary conditions, since there is only one standard for necessary conditions (i.e. every necessary condition must be satisfied, without exception), that set of four conditions would be the basis for just one definition.

Given my assumtion that at least one of the four attributes (above) is relevant to defining ‘divine person’, and my assumption that there are no other attributes that are relevant, there are four cases to consider when trying to determine the total number of different possible definitions:

All Four Attributes are Relevant
Only Three Attributes are Relevant
Only Two Attributes are Relevant
Only One Attribute is Relevant

To be continued…