An Expanded Way of Explaining the Principle of Parsimony

[Daniel Mullarkey]

An expanded way of explaining the principle of parsimony is this: "Out of several explanations that fit the facts at hand, the simplest explanation that raises the fewest unanswerable questions is the correct one."

[Burkhard]

On Monday, 16 December 2013 02:30:29 UTC, Daniel Mullarkey wrote:
> An expanded way of explaining the principle of parsimony is this: "Out of several explanations that fit the facts at hand, the simplest explanation that raises the fewest unanswerable questions is the correct one."

Are you sure you mean "expanded"? It seems to be rather the
opposite, a condensed version, and in fact so condensed
that it ends up somewhere between misleading and false.

One thing that is needed in addition e.g. is quite a
massive "ceteris paribus". The principle of parsimony
is just one of several rules f thumb scientists can and
do use to decide between theories of euqal empirical content.

Others include a "principle of productivity" - go with
the theory that produces the greatest number of interesting
research questions that look solvable with the means of
the theory" (that is Larry Laudan's main criterion
that he first formulated in "Progress and its Problems:
Towards a Theory of Scientific Growth" and has refined
ever since.

another one is: go for that theory that requires the
least revisions in other well supported theories that
we have accepted in the past - the principle of
conservative knowledge revision as formulated
e.g. by Paul Thagard in "Conceptual Revolutions"

There are a couple of others, some from rational
choice theory, others focus more on the way
science is a collaborative endeavour that also
requires efficient communication between
participants. Others yet are derived from
the theory of measurements and the limitations
we get from there.

The next problem is your use of the word
"correct". If you mean with it simply: the
one we have good, rational reasons to prefer
over the others", few will disagree. That's
because pragmatic reasons count in this case too
- how easy is it to test the theory, how
easy is it to communicate its content to
someone from outside your cultural
group etc, all of which can benefit from
simplicity.

If you mean however with "correct" something
like "true" (for a given preferred theory of
truth), things are much more difficult and
problematic.

Now, for Occam, when he formulated the idea,
it was indeed about truth. For him, simplicity
meant perfection, and that in turn means that a
perfect deity woudl also create the simplest,
most elegant world possible (a salutary note to
contemporary creationists btw, Occam quote rightly
identified simplicity as hallmark for good,
intelligent design - anticipating KISS is you
like, whereas the modern numbnuts tend to get
all hot and bothered about "complexity").

Problem is of course that when you use the
principle of parsimony in a secular setting,
you lose the historical justification that it
once had.

Again, no problem if you see it as just a
pragmatic choice: simple is easier and more
productive. Or indeed as an aesthetic
criterion: we chose the simpler theory,
ceteris paribus, because it is more
beautiful. People who argue like this
typically put these quotes side by side;

Art is the elimination of the unnecessary.
Pablo Picasso

Everything should be made as simple as possible,
but not simpler.
Albert Einstein

and their main examples tend to come from
theoretical physics, especially the
variants of string theory, where hard data to
decide between different theories is often hard to
come by. A particularly
good example in my opinion for this way to
justify the parsimony principle is
Cohen and Stewart's The Collapse of Chaos.
They also say a lot about the limitations of
the principle as just one "rule of thumb"
amongst many

But if you see it as an ontological principle,
something that guarantees truth, you need to
think about a new rationale. This has
turned out to be remarkably difficult to do.
A good, but by now somewhat dated analysis of
these efforts is in Mario Bunge's The Myth of
Simplicity: Problems in Scientific Philosophy
from 1963. as a physicalist himself, he is
quite happy about the principle, but
recognises that any attempt to elevate it
beyond a purely pragmatic rule so far have
failed. A more recent discussion that looks
at attempts to give it a probabilistic foundation
more limited in scope but with truly excellent
application to inferences in the theory of
evolution is by Eliot Sober, “Let’s Razor
Ockham’s Razor.” Explanation and its Limits, in
his "From a biological point of view".

Which brings me to the last point, the most
promising looking attempts to find a new
foundation for parsimony come from
statistics, and in particular Bayesianism.
Herer, you try often to make an analogy between
"best fit" and parsimony.

Examples include e.g. include Jefferys and
Berger, "Ockham's Razor and Bayesian Statistics.
American Scientist 1991
80: 64–7 or Scott Needham and David L. Dowe,
Message Length as an Effective Ockham's Razor
in Decision Tree Induction.(2001)

Now, Sober discusses some of the conceptual
problems with this - for a starter, Bayesians
don't deal in "explanations" to start with,
so you need to reformulate the principle
from the word go.

More problematically, in the general case
it simply does not work, there are numerous
prima facie counter examples where the more
complex theory is also the more probable.

So what people who followed this approach had
to do was
a) come up with a good, objective notion of
"simplicity" that is also amenable to a
probabilistic analysis - which turned
out to be quite difficult.
b) they had to find a way to deal with all the
counter examples.

As a result, you get an exceedingly complex theory
of what the razor actually says, with very elaborate
definitions of "simplicity" and lots of ad hoc
restrictions to certain applications. The end
result is something that looks suspiciously like a
circular definition to many (you smuggle the
"probabilities" into your definition of simplicity.

Lots of commentators noticed this nice self-
contradiction, that the theory of parsimony
turned out to be not parsimonious at all.

Personally, i'd say from the failed or almost
failed attempts to find a new ontological
justification for parsimony, we should
tentatively conclude that there is no such
thing and treat it merely as a useful,
pragmatic tool. That is also
the conclusion of amongst others
Steven Hales, (1997). “Ockham’s Disposable Razor.”
The Role of Pragmatics in Contemporary Philosophy.
356-361 or, from the "practitioner side",
Steven Weinberg (in his "Dreams of a Final Theory",
with lots of examples from physics, as one would
guess)