Ockham's Razor to Wikipedia web site )
Occam's Razor (also Ockham's Razor), is a
principle attributed to the
14th century logician and
William of Ockham that forms the basis of methodological
reductionism. It is nowadays usually stated as follows:
- "Of two competing theories or
explanations, all other things being equal, the
simpler one is to be preferred."
The principle is most often expressed as Entia non sunt multiplicanda
praeter necessitatem, or "Entities should not be multiplied beyond
necessity", but this sentence was written by later authors and cannot be found
in his surviving writings. William wrote the
Latin Pluralitas non est ponenda sine neccesitate, which translate
English as "Plurality should not be posited without necessity".
Dave Beckett of the
University of Kent at
Canterbury writes: "The medieval rule of parsimony, or principle of economy,
frequently used by Ockham came to be known as Ockham's razor."
Occam's Razor has also been referred to as the "principle of parsimony" and
the "principle of simplicity" and "K.I.S.S."
(keep it simple, stupid). Another proverb expressing the idea that is often
heard in medical schools is "When you hear hoofbeats, think horses, not zebras."
Another variant of this law is Thargola's Sword from
Nightfall, written by
Isaac Asimov and
Robert Silverberg: "We must drive a sword through any hypothesis that is not
Occam's Razor has become a basic principle of the
scientific method. It is important to note that it is a
heuristic argument that does not necessarily give correct answers; it is a
loose guide to the scientific hypothesis which contains the least possible
number of unproven assumptions and is the most likely to be fruitful. Often,
several hypotheses are equally "simple" and Occam's Razor does not express any
preference in these cases.
For example, after a storm you notice that a tree has fallen. Based on the
evidence of "a storm" and "a fallen tree" a reasonable hypothesis would be that
"the storm blew down the tree" -- a hypothesis that requires only one
assumption--that it was, in fact, a strong wind that knocked over the tree,
rather than a meteor or an elephant. The hypothesis that "the tree was knocked
over by marauding 200 meter tall space aliens" requires several additional
assumptions (concerning the very existence of aliens, their ability and desire
to travel interstellar distances and the alien biology that allows them to be
200 meters tall in terrestrial gravity) and is therefore less preferable.
Occam's Razor is not equivalent to the idea that "perfection is
Einstein had this in mind when he wrote in 1933 that
"The supreme goal of all theory is to make the
irreducible basic elements as simple and as few as possible without having to
surrender the adequate representation of a single datum of experience"
often paraphrased as "Theories should be as simple as possible, but no
simpler." It often happens that the best explanation is much more
complicated than the simplest explanation because it requires fewer assumptions.
Some people have oversimplified Occam's Razor as
"The simplest explanation is the best." (or is
"the true one")
There are various papers in scholarly journals deriving versions of Occam's
probability theory and applying it in
statistical inference, and also of various criteria for penalizing
complexity in statistical inference. Recent papers have suggested a connection
between Occam's Razor and
One of the problems with the original formulation of the principle is that it
only applies to models with the same explanatory power (i.e. prefer the simpler
one of equally good models). A more general form of Occam's Razor can be derived
Bayesian inference and
Bayesian model comparison, which can be used to compare models that don't
fit the data equally well (see e.g. Duda, Hart & Stork, 2001). These methods
will optimally balance the complexity and the power of the model.
philosophy of religion Occam's Razor is sometimes used to defeat
arguments for the existence of God. None of these applications has been
considered definitive because the competing assumptions are not precisely
defined. Also, it should be added that the principle is only a guide to the best
theory based on current knowledge, not the "truth."
William may have been inspired by earlier thinkers. For example, Book V of
Aristotle's Physics has the statement "Nature operates in the
shortest way possible."
Galileo Galilei notably lampooned Occam's Razor in his Dialogue.
The principle is represented in the dialogue by Simplicio.
The telling point that Galileo Galilei presented ironically was that
if you really wanted to start from small number of entities; one could
always consider the alphabet as the fundamental entities, since you could
certainly construct the whole of human knowledge out of them. (A view that
Abraham Abulafia held much more expansively.)
Adding another layer of Irony, many modern scientists and mathematicians
seriously propose that the basic "entities" of reality may be "bits of
information", i.e. the digits of binary code, in which case the entities of
William of Occam might be seen as foreshadowing the logic of
George Boole and modern computing.
Perhaps due to the abstuse nature of medieval logic and the obscure goals of
William of Occam as a theologian and logician, discussion and application of
Ockham's Razor is frequently full of ironies.
For example, William is widely regarded as a
precursor of the Scientific Method because he argued for a degree of
intellectual freedom in an time of dogmatic belief, but he might equally be seen
as an apologist for Divine Omnipotence, since he was concerned to demonstrate
that creation was contingent and the Creator free to change the rules at will:
is free to make an infinity of worlds with completely different rules from
those which prevail in our world, then we are free to imagine such worlds and
their logical and practical consequences (within the bounds set by the
Church's infallible Dogma).
Thus Ockham's cautious answer to the sophomoric philosophy paradox "Can God
make a stone so heavy that He Himself could not lift it?" would be a qualified
yes, which is to say that God can do anything which is not a logical
contradiction or heretical.
Perhaps the best formulation of Occam's Razor is the one which states that,
of equally good explanations for a phenomenon, the best one is the simplest
explanation which accounts for all the facts.
- Richard O. Duda, Peter E. Hart, David G. Stork (2000) Pattern
classification (2nd edition), Section 9.6.5, p. 487-489, Wiley,