CHAPTER 4
WHAT NEEDS EXPLANATION
The Newtonian view, held by most
scientists practising today, is that there are general laws that govern (or
describe) the behavior of things and that a specific fact is considered to be
explained if it can be subsumed under a general law. There is no need to explain the general law, other than
perhaps to subsume it under a more general law. It is the nature of the universe that there should be such
general laws. For Newton, the general laws were those of the Creator of the
universe. Since I do not believe in natural theology - that by examining nature
we are able to tell, one way or the other, whether there is a Creator - the
existence of general laws requires an explanation.
The thesis that I am trying to develop is
that the existence of general laws is an illusion - a trick that can be
explained. So when I say that general laws need explanation, I mean that what needs explanation is how we are led to
believe that there are general laws.
I am going to look now at the notion of
explanation in science so that you can see the different points of view that
are possible. Explanation is linked with understanding. The reason things are explained to people
is so that they will understand.
In his Lectures on Physics
Feynman says:
What do we mean by "understanding"
something? We can imagine that
this complicated array of moving things which constitutes "the world"
is something like a great chess game being played by the gods, and we are observers
of the game. We do not know what
the rules of the game are; all we are allowed to do is to watch the playing.
Of course, if we watch long enough, we may eventually catch on to a few
of the rules. The rules of the game
are what we mean by fundamental physics...If we know the rules we consider that we "understand" the
world. [1]
This is a clear statement that understanding of the
universe comes when we know the "rules of the game" by which he means
the general laws that rule (or describe) the behavior of "things which
constitute the world". Max Jammer in his book Concepts of Force presents this view:
Science, as understood today, has a more restricted
objective; its two major assignments are the description of certain phenomena in
the world of experience and the establishment of general principles for their
prediction and what might be called their "explanation". "Explanation"
here means essentially their subsumption under these principles. [2]
Here Jammer indicates the fact finding part of
science as well as the part that is concerned with explanation. Albert Einstein says much the same
thing but adds a few different notes:
The aim of science is, on the one hand, a
comprehension, as complete as possible, of the connection between the sense
experiences in their totality, and, on the other hand, the accomplishment of
this by the use of a minimum of primary concepts and relations (seeking, as far
as possible, logical unity in the world picture, i.e. paucity in logical
elements)... We do not know whether or not this ambition will ever result in a
definite system. If one is asked for
his opinion he is inclined to answer no.
While wrestling with the problem, however, one will never give up the
hope that this greatest of all aims can really be attained to a very high
degree. [3]
Einstein stresses the need to have
"a minimum of primary concepts and relations". This means that there should be as few
general laws as possible. His hope
was for a unified theory in which all general laws were subsumed in a single
system. He calls the hope of
finding the system "the greatest of all aims" but somehow doubts that
it can be found. He himself did
not succeed, but the shape of his later work always tended in this direction
because he was driven by this as a philosophical ideal. He maintained that scientists must
think about the philosophy of science especially whenever things become problematic:
It has often been said, and certainly not without
justification, that the man of science is a poor philosopher. Why then should it not be the right
thing for the physicist to let the philosopher do the philosophizing? Such might indeed be the right thing at
a time when the physicist believes he has at his disposal a rigid system of fundamental
concepts and fundamental laws which are so well established that waves of doubt
can not reach them; but, it can not be right at a time when the very
foundations of physics itself have become problematic as they are now. At a time like the present [the early
part of the twentieth century], when experience forces us to seek a newer more
solid foundation, the physicist cannot simply surrender to the philosopher the
critical contemplation of the theoretical foundations; for, he himself knows best,
and feels more surely where the shoe pinches. In looking for a new foundation, he must try to make clear
in his own mind just how far the concepts which he uses are justified, and are
necessities. [4]
Louis de Broglie agreed with Einstein in saying that
scientific philosophy should not be left to professional (academic)
philosophers:
What the scientists still sought in their self-made
philosophizing was fructifying world-images and world-ideas - precisely the
ingredient expelled in the universities' analysis [academic philosophers tended
to be positivists]. [5]
It was not a matter of treating the philosophy as an
end in itself but as a way of making the scientist's mind more fertile in new
ideas about the world. Does the
philosophy make any difference at all? Hanson examines this in his book Patterns
of Discovery:
Mach construed dynamical laws as summary descriptions
of sense observations, while for Hertz laws were highly abstract and
conventional axioms whose role was not to describe the subject-matter but to determine
[govern] it. The difference is not
about what the facts are, but it may very well be about how the facts hang
together. Even this difference
would not seem to matter much here, since Mach and Hertz would get the same
answers to their problems. The
real difference, however, only
arises at this point: for though they get the same answer to the
problem, the difference in their conceptual organization guarantees that in their future research
they will not continue to have the same problems... The important differences
in conceptual organization, which
it has been our aim to illuminate, show only in 'frontier' thinking \(me where
the direction of new inquiry has regularly to be redetermined. [6]
Different philosophies lead to different future
directions. How they organize
existing information really does not make much difference. De Broglie says
this:
Reality consists of many strata of existence which
come into view when different methods of investigation are employed. Each generation has its favoured
insight and method which in time, as it reaches a region of low diminishing
returns, becomes exhausted. [7]
This is a very pragmatic attitude and one that is
very scientific. While a particular philosophy is useful, use it; when it shows
"diminishing returns", abandon it.
There is some disagreement among
scientists about the shape of general laws. The if-then-always shape is one
related to cause and effect. Another possibility, discarded by most, is that
things behave in certain ways not because they are caused to do so but rather
because they have a goal to fulfil. This was a view held by the mathematician
Euler as explained by Mach:
Euler's view is that the purposes of the phenomena of nature afford as good a basis of
explanation as their causes. If
this position is taken, it will be presumed a priori that all natural phenomena present a maximum or minimum. But in the solution of mechanical
problems by the ordinary methods, it is possible, if the requisite attention be
bestowed on the matter, to find the expression which in all cases is made a
maximum or a minimum. [8]
In this kind of thinking there is a purpose or telos
- things behave so as to achieve certain ends, for example, move so they take the
shortest path between two points.
Mach is quick to point out that if you work hard enough you can always
find some mathematical "expression" in the motion of an object which
is a maximum or minimum (such as the shortest path).
As Mario Bunge says in his book Causality
and Modern Science:
To say that in behaving the way that they do physical
objects move "with the purpose" of minimizing or conserving the
intensity of a given quantity is not too different from asserting that things
happen as they do "in order that" the laws of nature may be
satisfied. Extremum [maximum or minimum] principles are no more indicative of
end-seeking behavior than any other physical laws... [9]
Finding a mathematical expression that is a maximum
or minimum as an object moves is an act of the scientist; it is man-made, not
part of the "order of things". Mach himself doubted that an order of
things existed. He believed that it was a scientist's job to systematize the
facts about the universe into as small a form as possible, strictly for
practical reasons. This is
sometimes called empiricism.
Reichenbach writes:
In contrast to the transcendental conception of
knowledge the philosophy of the new [logical] empiricism may be called a functional conception of knowledge. In this interpretation, knowledge does not refer to
another world, but so as to perform a function serving purpose, the purpose of
predicting the future. [10]
Here the reference to "the transcendental
conception of knowledge" is to the Newtonian type of philosophy where
general laws somehow transcend the things whose behavior they describe. The word empirical, which just means
based on fact, has been degraded by many scientists. When a relationship (or
formula) is said to be "just an empirical one" it usually means that
some arbitrary mathematical equation has been fitted to experimental facts by
adjusting some parameters in the equation. Much computer work in science is done to obtain the best fit
of certain formulas to experimental data.
It is more scientific to have a theory or model behind the mathematical
equation because facts can always
be fitted by some kind of formula no matter what they are.
Sometimes a set of facts may need two
different formulas, one for part
of the set, another for the rest, to get a good fit. This makes scientists uneasy. Bridgman says:
What is the basis for the feeling that a theory should
not employ two different sorts of mathematical functions joined by a text
instructing us to switch from one to the other? ... I think that there is often a feeling in the background that
a mathematical formulation "really exists" and that the chances of
our having found it are considerably less good as long as the toolmarks of our
handiwork are as evident as they are with two different analytical expressions.
[11]
What is usually hoped for in any empirical fitting of
facts by a formula is that an extremely simple formula will fit very well. Somehow the empirical then becomes more
than empirical. Here is
Heisenberg:
It is difficult to give any good argument for this
hope for simplicity - except the fact that it has hitherto always been possible
to write the fundamental equations in physics in simple mathematical forms. This
fact fits in with the Pythagorean religion, and many physicists share their
belief in this respect, but no convincing argument has yet been given to show
that it must be so [12].
This goal of mathematical simplicity was firmly
planted by Newton. Randall says:
Isaac Newton effected so successful a synthesis of
the mathematical principles of nature that he stamped the mathematical ideal on
science, and the identification of the natural with the rational, upon the
entire field of thought. [13]
And that brings me, as I close off this chapter, to a second thing that needs explanation if the Newtonian position of the strong evidence of design in nature is to be countered: Why are there mathematically simple general laws?
Copyright © 1983 J.N.P. Hume All rights in this book reserved