Page 31 - Modern Spatiotemporal Geostatistics

12 Modern Spatiotemporal Geostatistics — Chapter 1

experimental data, (ii.) fitting mathematical functions to these data, and (Hi.)
piling up more experimental data and tests.
It is widely recognized, however, that there are some serious problems with
such a framework. Indeed, modern developments in scientific reasoning have
stressed deep-seated difficulties associated with pure inductivism (see, e.g.,
Popper, 1962; Carnap, 1966; Harre, 1989; Chalmers, 1994; Dunbar, 1996;
Newton, 1997). Scientific progress is not based merely on pure induction.
It involves a significant amount of theorizing, as well. Data accumulation
surely plays an important role in the growth of science. The data, however,
are theory-dependent. Experiments involve planned, theory-guided interference
with nature. Change in a theoretical viewpoint regarding a phenomenon results
in a change of data. By not referring to theory to adjudicate, the use of pure
induction to infer a law from the data leads to indeterminate results (discussed
on p. 16 in the section entitled "Indetermination thesis"). It also fails to include
explanation in the scientific process, and it lacks global prediction features
(i.e., extrapolation is not possible beyond the range of the data). Therefore,
there is no scientific knowledge independent of theory.
This important shift in views concerning the appropriate scientific rea-
soning framework which occurred during the 20th century was reflected in the
foregoing discussions of Examples 1.1-1.9. Indeed, a central theme of these ex-
amples was that, in the context of modern spatiotemporal geostatistics, a map
is viewed as a representation of a scientific theory regarding the spatiotemporal
distribution of the natural variable it represents (Postulate 1.1). According to
this postulate, it is absolutely important to perform a deeper theoretical analy-
sis of the mapping problem. A map without theoretical interpretation does not
constitute a mature body of scientific information. And it should be expected
that the more knowledge and diversified kinds of data we need to process, the
less straightforward this theoretical representation will be.
Certainly, all scientific disciplines involve some form of induction in their
early descriptive stages. However, as Dunbar (1996) emphasized in his treatise
on the scientific method, any discipline that remains locked in this stage can do
nothing except describe correlations in natural processes: it can never aspire
to full scientific status by providing explanation and understanding. The
latter are very important stages that involve theories and mathematical models
developed from sets of hypotheses and assumptions.

EXAMPLE 1.10: Rigorous and clearly formulated theories are a prerequisite
for precise observation statements and scientific predictions. That there exist
elaborate theories (molecular physics, thermodynamics, etc.) presupposed by
the observation statement, "the molecular structure of the fluid was affected
by heating," should not need much arguing. The meaning of scientific terms
used in experimental investigations depends on the role they play in a specific
theory (e.g., the term "entropy" has a different meaning in thermodynamics
than in information theory; or, the term "covariance" has a different meaning
in geostatistics than in relativity theory).