31.1 Is modeling possible here?
Traditionally, science has depended on mathematics in its attempts to describe phenomena
in detail, and, more recently, on the ability to make formal models of the systems
it is examining. This process began in astronomy, where numerical predictions are
important, and progressed with Galileo and Newton to describe the motion of bodies
on earth. It has taken a while, but now there are extensive computational models
for all kinds of physical processes, from atomic nuclei to chemical combustion to
stellar and galactic evolution. In recent decades, detailed statistical and formal
models have been constructed for genetics, cell and neural activities, and now cognitive
and connectionist models have been simulated on computers to describe psychological
processes. The question is whether such models are still useful in theistic science.
Or does the range of ‘qualities’ in all the various degrees and sub-degrees render
mathematical models impotent?
I will certainly claim that no mathematical or formal model could completely
represent the whole theistic universe, even if we do not include the Divine itself.
But let me suggest some ways in which mathematical models may still be useful, even
if they only partially portray some aspects of each degree and sub-degree. After
all, modelers claim that they are ‘only modeling’ and not producing complete descriptions,
and that hence we should never confuse their models for reality.
The reason that models may still be descriptive in many places in our theistic
multi-level generative structure is because it is forms and structures
which are intellectually knowable, and hence are formally knowable. Loves and dispositions
can be known in terms of forms only in so far as they are characterized by their
effects. Formal models will hence be accurate in some part, just as long
as they describe forms and structures faithfully. To be accurate they must make
comprehensive attempts to describe all the possible effects of the dispositions,
desires or loves.
Formal models must ultimately fail, however, because the possible effects at
any level are ultimately from the life which derives from God. They hence may have
an ‘aspect of infinity’ which cannot be captured by listing finite sets of effects
or even by functional rules for generating formal mappings from causes to effects.
In reality, because all loves come from an infinite God, there will always be the
possibility of new and creative responses. Mathematical modelers should not forget
that their models are only partial and finite. Subject to this proviso, this chapter
considers what kinds of partial and finite models may be usefully constructed.