|
Jerry's mention of the need for an underlying philosophy in
science made me think perhaps it might be a good idea to initiate a
discussion of the dualism between so-called "hard science" and "soft
science"-- which correspond to experimental or quantitative science and
theoretical science or qualitative science.
Theoretical science has often been called "philosophy" by
experimentalists, and Robert Rosen was accused (as if it were a dirty
word!) of being a philosopher rather than a scientist, by the same sorts of
people. While my father had no quarrel with philosophers, and studied philosophy
in great detail throughout his life, he did see a clear distinction
between philosophy and theoretical science: Philosophy involves speculation
about unprovable, unknowable, or undefinable things, or about aspects of
those things, without any attempt or ability to develop evidence:
The meaning of life for example, or the existence of
God.
Theoretical science, on the other hand, is the conscious mental act
of taking what evidence exists about any given question and postulating a series
of logical entailment chains, based on what the evidence suggests, in both
directions (what had to be true to get to this, and what the existence of this
makes true from here). It takes the form of "If this, then there must
also be that..." and "In order for this to be, there
must also have been that." So, far from being mere speculation,
theoretical science involves a great deal of knowledge and an ability to connect
incomplete glimpses of evidence into a logically sound entailment pattern which
can then be tested for "congruence" between models based on the theory and
the actual systems that the theory purports to describe.
About this dualism, Robert Rosen wrote (from Life, Itself,
Praeludium):
"Some years ago, the novelist C.P. Snow drew attention to
a dualism that permeates and poisons the intellectual life of our times, a
dualism between science and art, between science and humanism.
The dualism to which snow, among others, drew attention is
indeed real. It has always been real and has existed since human beings first
learned to think and to communicate their thoughts. But the situation is and
always has been, far worse than Snow has depicted. He painted a picture of
science itself as a kind of pure phase, and its relation to other aspects of our
culture as a kind of phase separation; scientists and humanists separating from
each other as oil separates from water, through a preference of like for like,
and an antipathy of like for unlike. But the dualities that Snow depicted also
permeate science itself.
I have, much against my will, been immersed my whole life
in one of these dualities, namely, the antagonism between "theory" and
"experiment." My subject matter herein is another, in fact closely related
duality, that between "hard" science and "soft" science, between quantitative
and qualitative, between "exact" and "inexact."
This duality is not to be removed by any kind of tactical
accommodation by any superficial effort of conciliation or ecumenicism. The
antipathies generated by the duality itself are only symptoms of a far deeper
situation, which has roots partly in specific subject matter, partly in
individual aspirations, and most important, in the embracing of mutually
incompatible weltanschauungen ["worldviews" or "ways of
seeing"], which reflect the deepest aspects of temperament and
personality. It is thus not a matter of logical argumentation or persuasion that
is involved here; it is a matter more akin to religious
conversion.
In what follows, I discuss the duality between qualitative
and quantitative. As we will see, in the sciences this dichotomy rests on
(generally unrecognized) presuppositions about the nature of material reality
and on how we obtain knowledge about it. I will then show that these
presuppositions themselves have formal, mathematical counterparts, which allow
us to reflect this scientific dualism into an exact parallel one that
exists within mathematics itself. This mathematical form of the dualism is
centered around the notion of formalization; it can be expressed as the duality
between syntactics and semantics; between what is true by virtue of form alone,
independent of any external referents, and what is not.
The virtue of doing this is that there is a theorem
(Gödel's Theorem) that actually resolves the issue, at least in part. When we
pull this theorem back into a scientific context, by looking at its
epistemological correlates, we obtain thereby some new and deep insights into
the duality between quantitative and qualitative; between "hard" and "soft". I
think that all concerned will find some surprises in this exercise.
Naturally, in this brief space, I can only give the most
cursory sketch of the ideas involved. But I hope that enough will be said to
provoke some reappraisals on both sides of the duality."
|