turpin@ut-sally.UUCP (Russell Turpin) (08/27/87)
Being one of the earlier posters who appealed to it as a
philosophic criterion for comparing scientific theories, I now
feel obliged to put forth my defense of Ockham's Razor. (The
spelling "Occam" is also correct.)
The first order of business is describing precisely what (in
this article) is an application of Ockham's razor. From reading
the many postings on the subject, it seems there is no concensus
on this. In presenting the definition below, no claim is pressed
that this is closest to what William originally intended. It is
simply the version that I wish to defend.
o The term "theory" refers to a set of statements. The set,
though probably infinite in cardinality, must be finitely
describable to qualify as a usable scientific theory. But in
discussing the relative merits of theories, it is the entire
set that is important. This point is expanded below.
o I assume some noncontroversial method for identifying which
statements are testable by observation. These might include
such statements as "grass is green" or "if A is performed, B
will be observed". (This is a very controversial assumption,
but one that is not the subject of this article.)
o A theory X can now be divided into an "observable component"
C and its non-observable component X - C. Note that X - C
includes mixed statements. (If the integration path is
closed, conservation of flux is observed.) Only statements
that are completely testable are in C. In general, both C
and its complement are infinite.
A theory Y is stronger than (equal to) a theory X if every
statement in X is also in Y (and vice versa). A theory Y with
observational component D has greater (equal) explanatory power
than a theory X with observational component C if every statement
in C is also in D (and vice versa).
The version of Ockham's Razor that this article defends can
now be stated. If X and Y are two theories and Y is properly
stronger than X but has the same explanatory power, then X is
preferred. (If C and D are the observational components of X and
Y respectively, then C = D but X [ Y.)
The justification for this is not difficult. Scientific
theories are not deductively derived. The only reason for putting
any stock in them at all is their explanatory power. A
scientific theory is assumed true because of the observable
statements it predicts (contains). In particular, the only reason
for believing any statement y in Y that is not in D is because it
helps explain D. But in the case above this is not true for the
statements in Y that are not in X. They can all be dropped with
no weakening of the explanatory power of the theory.
By talking about entire theories rather than their finite
descriptions via sets of axioms, the difficulties that arise
because of different equivalent axiomatizations are avoided.
Sometimes two axiomatizations can be directly compared. One set
of axioms may properly contain the other. But this is rare, and
can almost always be ducked by the defenders of a theory by
changing the axiom set. In science, it is an entire theory that
is assumed true. Discussing a theory only in terms of its axioms
is to focus on a description of the theory, usually one of many,
rather than the theory itself.
At this point, a potential criticism of the above view must
be presented and dismissed. It might be argued that in light of
the strong argument above for weak theories, the best theory is
simply the concerned set of testable statements, C. But C
(probably) does not have a finite axiomatization. This puts it
out of the running as a usable theory. While in comparing two
theories one should not worry about particular finite
descriptions, it is undoubtedly true that the motivation behind
posing theories in the first place is to find finite
(understandable) descriptions of the infinite range of observable
phenomena.
A second rejoinder that might be made is that taking such a
strong stance for weak theories completely disallows assuming the
existence of entities that cannot be directly observed. One
cannot assume that electrons exist, only that observations will
be in accord with QED. The first reply to this complaint is that
this is not so bad. The second reply is that definitions come
for free. One can define an electron as the locus of a set of
behavior. Adding a definition to a theory, for simplifying
discussion, should not be viewed as changing its content.
Similarly, mathematical content is not important in comparing
physical theories.
Russellkube@cogsci.berkeley.edu.UUCP (08/31/87)
In article <8851@ut-sally.UUCP> turpin@ut-sally.UUCP (Russell Turpin) writes: > Being one of the earlier posters who appealed to it as a >philosophic criterion for comparing scientific theories, I now >feel obliged to put forth my defense of Ockham's Razor. Thanks for taking the time to make such a thoughtful response. I have only a couple of further remarks. > o The term "theory" refers to a set of statements. Sounds good to me. > o I assume some noncontroversial method for identifying which > statements are testable by observation. > (This is a very controversial assumption, > but one that is not the subject of this article.) I agree that the observational/nonobservational distinction turns out to be pretty bogus when you lean on it too hard but for present purposes it seems fine. > The justification for this is not difficult. Scientific >theories are not deductively derived. The only reason for putting >any stock in them at all is their explanatory power. A >scientific theory is assumed true because of the observable >statements it predicts (contains). In particular, the only reason >for believing any statement y in Y that is not in D is because it >helps explain D. But in the case above this is not true for the >statements in Y that are not in X. They can all be dropped with >no weakening of the explanatory power of the theory. This is an elegant way of putting your point, but I worry that it might be *too* elegant. In particular: You are saying that a theoretical statement y in a theory Y cannot help to explain the truth of an observation sentence if the observation sentence is a consequence of Y - y. But in the "intuitive" sense of `help explain', this doesn't seem right; y can in practice be used to explain observations even though y is `in principle' eliminable. The problem is that `explanation' seems to be a partly psychological concept. It's natural to cash it out in terms of the consequence relation as you have (I'm inclined to do it myself), but it's not clear how much is given up with this abstraction. (It might be no problem here; I think maybe you need only confirmation, not the full concept of explanation, to run your argument; and confirmation is probably more closely tied to consequence.) What the philosophy of science needs, and does not have, is a good theory of explanation. --Paul kube@berkeley.edu, ...!ucbvax!kube