When Grice introduced his “Modified Occam’s Razor” in the third William James
lecture at Harvard he was trying to be funny. And he succeeded! But I follow
Helm in his scholastic tendencies, and it seems fascinating to trace this idea
of a razor, especially when it originates in Graeco-Roman thought (from
Aristotle onwards). The usual bibliographies do not actually dwell much with
historical material. So one has to be careful. And then there’s the
terminology: continental philosophers seem to prefer ‘lex parsimoniae.’ But,
hey, Grice is an English philosopher, and so is Occam – or Ockham, if you
mustn’t. The keyword then should be, as far as Grice is concerned, “novacula
occami.” While Grice quotes its English rendition, the Latin rendition, “Non
sunt multiplicanda entia sine necessitate” is actually not credited to Occam.
The earliest formulation of the razor is in Aristotle’s “Posterior Analytics,”
and that should not surprise us since, as Quine says, the razor is meant to
shave Plato’s beard. “We may assume,” the Stagirite notes, “the superiority
ceteris paribus of the demonstration which derives from fewer postulates or
hypotheses.” Then there’s Ptolemy (“We consider it a good principle to explain
the phenomena by the simplest hypothesis possible.”). In fact, adages such as
“It is vain to do with more what can be done with fewer” and “A plurality is
not to be posited without necessity” are commonplace in scholastic manuals.
Grosseteste, in his “Commentarius in Posteriorum Analyticorum Libros” notes
“that is better and more valuable which requires fewer, other circumstances
being equal...” “For if one thing were demonstrated from many and another thing
from fewer equally known premises, clearly that is better which is from fewer
because it makes us know quickly, just as a universal demonstration is better
than particular because it produces knowledge from fewer premises. Similarly in
natural science, in moral science, and in metaphysics the best is that which
needs no premises and the better that which needs the fewer, other
circumstances being equal." Aquinas’s “Summa Theologica” states that "it is
superfluous to suppose that what can be accounted for by a few principles has
been produced by many". Aquinas uses this principle to construct an objection
to God's existence, an objection that he refutes through an argument based on
causality. Hence, Aquinas acknowledges Occam’s razor, but prefers a causal
explanations to a simpler explanation (cf. also Correlation does not imply
causation).
But Grice chose Occam. Occam’s fame rests chiefly on the maxim attributed to
him: his razor. The noun “razor” refers to distinguishing between two
hypotheses either by “shaving away” unnecessary assumptions or cutting apart
two similar conclusions. While it has been claimed that Occam’s razor is not
found in any of his lecture notes that have been preserved (cfr. Grice’s
unpublications), one can cite statements such as “Numquam ponenda est
pluralitas sine necessitate,” plurality must never be posited without necessity
(“Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi,” i,
dist. 27, qu. 2, K). Nevertheless, the words sometimes attributed to Occam,
“Entia non sunt multiplicanda praeter necessitatem,” entities must not be
multiplied beyond necessity, and on which Grice bases his modification, are
notable absent in Occam’s extant works. The phrasing comes from John Punch, who
described the principle as a “common axiom” (“axioma vulgare”) of the
Scholastics. Occam's contribution seems to restrict the operation of this
principle in matters pertaining to miracles and God's power; so, in the
Eucharist, a plurality of miracles is possible, simply because it pleases God.
The razor is sometimes phrased as “Pluralitas non est ponenda sine
necessitate,” plurality should not be posited without necessity. In “Summa
Totius Logicae,” i. 12, Occam cites a principle of economy:“Frustra fit per
plura quod potest fieri per pauciora,” it is futile to do with more things that
which can be done with fewer (Thorburn, pp. 352–53; Kneale and Kneale, p. 243.
– Grice attended some of Kneale’s seminars at Oxford)
To quote from Newton, “We are to admit no more causes of natural things than
such as are both true and sufficient to explain their appearances. Therefore,
to the same natural effects we must, as far as possible, assign the same
causes.” In his “Critique of Pure Reason” Kant supports the maxim that
“rudiments or principles must not be unnecessarily multiplied (“entia praeter
necessitatem non esse multiplicanda”)” and argues that this is a “regulative”
idea of pure reason which underlies scientists' theorizing about nature. It is
not surprising that, Kantotle being Grice’s favourite philosopher (vide
Bennett, “In the tradition of Kantotle”), Grice takes this idea of ‘regulative’
and applies it to ‘principle,’ which is what he deems his Modified Occam’s
Razor to be. “A near platitude,” he adds, and slightly vacuous (or
definitional, as it relies on what we count as being “beyond necessity,” as
McEvoy notes). Oddly, Grice prefers to stick with the idea that his adage
depends on what counts as ‘necessity’. Grice obviously thinks that for his
Harvard audience, to overqualify his wording as all depending on what counts to
be “beyond necessity” would be a bit too much. Note that the Latin has
“præter,” followed by the accusative, meaning ‘beyond’ (“praeter necessitatem”)
and ‘sine,’ followed by the dative, as in Punch’s “sine necessitate,” “without
necessity.” I think that, with Grice, I prefer ‘beyond,’ which has a poetic
ring to it.
Both Galileo and Newton accept versions of Occam’s Razor. Indeed Newton, whom
we mentioned before, includes a principle of parsimony as one of his three
‘Rules of Reasoning in Philosophy’ at the beginning of Bk. III of “Principia
Mathematica” – his first ‘rule’ being, “we are to admit no more causes of
natural things than such as are both true and sufficient to explain their
appearances.” Newton goes on to remark that “Nature is pleased with simplicity,
and affects not the pomp of superfluous causes.” In Italy, Galileo, in the
course of making a detailed comparison of the Ptolemaic and Copernican models
of the solar system, maintains that “nature does not multiply things
unnecessarily; that she makes use of the easiest and simplest means for
producing her effects; that she does nothing in vain, and the like” (This
Galileo was the son of Galileo, a musician – not be confused (“Do not multiply
Galilei beyond necessity” – but perhaps the one to blame here is Galileo, Sr. –
as Borges once said, “Mirrors and copulation are abominable: they multiply
humanity.” But I disgress (i.e. disgrice)). Nor are scientific advocates of
simplicity principles restricted to the ranks of physicists and astronomers.
Here is Lavoisier: “If all of chemistry can be explained in a satisfactory
manner without the help of phlogiston, that is enough to render it infinitely
likely that the principle does not exist, that it is a hypothetical substance,
a gratuitous supposition. It is, after all, a principle of logic not to
multiply entities unnecessarily.”
Lord Russell offers a particular version of Occam's razor: “Whenever possible,
substitute constructions out of known entities for inferences to unknown
entities.” And Grice admired Lord Russell – vide Grice, “Definite descriptions
in Russell and in the vernacular.”). Ray Solomonoff with his theory of
universal inductive inference, assumes prediction based on observations; e.g.,
predicting the next symbol based upon a given series of symbols. The only
assumption is that the environment follows some unknown but computable
probability distribution. Solomonoff’s theory is a mathematical formalization
of Occam's razor. Another technical approach to Occam's razor is ontological
parsimony. Parsimony means spareness and is also referred to as the Rule of
Simplicity. This is considered a "strong" version of Occam's Razor. A variation
used in medicine is called the "Zebra": a doctor should reject an exotic
medical diagnosis when a more commonplace explanation is more likely, derived
from Theodore Woodward's conditional: “If you hear hoof-beats, think of horses
not zebras”. Ernst Mach formulated the stronger version of Occam's Razor into
physics which he called the principle of economy stating: "Scientists must use
the simplest means of arriving at their results and exclude everything not
perceived by the senses.” Mach’s principle goes back at least as far as
Aristotle, who wrote that “nature operates in the shortest way possible.” The
idea of parsimony or simplicity in deciding between theories, though not the
intent of the original expression of Occam's Razor, has been assimilated into
our culture as the widespread layman's formulation that "the simplest
explanation is usually the correct one."
And then comes the anti-Grice. Ranged against the principles of parsimony
discussed in previous sections is an equally firmly rooted (though less
well-known) tradition of what might be termed “principles of explanatory
sufficiency.” These principles have their origins (and the scholastic in Helm
will be pleased by this) in the SAME medieval controversies that spawned
Occam's Razor. Ockham's contemporary, Walter of Chatton, proposed the following
counter-principle to Occam's Razor: “[I]f three things are not enough to verify
an affirmative proposition about things, a fourth must be added, and so on.”
Unfortunately, this did not make the village of Chatton a pilgrimage for
anti-Griceians as Ockham in Surrey has! A related counter-principle was later
defended by Kant (that Kant’s father spelt ‘Cant’ – a Scottish surname). “The
variety of entities should not be rashly diminished.” (“Entium varietates non
temere esse minuendas.”) There is no inconsistency in the co-existence of these
two families of principles, for they are not in direct conflict with each
other. Considerations of parsimony and of explanatory sufficiency function as
mutual counter-balances, penalizing theories which stray into explanatory
inadequacy or ontological excess. Grice was well aware of this when he notes
that his System G-HP creates “no Meinongian jungle.” (“Vacuous Names”). What we
see here is an historical echo of the contemporary debate among statisticians
concerning the proper trade-off between simplicity and goodness of fit. There
is, however, a second family of principles which do appear directly to conflict
with Occam's Razor. These are so-called ‘principles of plenitude.’ Perhaps the
best-known version is associated with Leibniz, according to whom God created
the best of all possible worlds with the greatest number of possible entities.
More generally, a principle of plenitude claims that if it is possible for an
object to exist then that object actually exists. Principles of plenitude
conflict with Occam's Razor over the existence of physically possible but
explanatorily idle objects (unlike Meinong’s ‘square circle’). Our best current
theories presumably do not rule out the existence of unicorns, but nor do they
provide any support for their existence. According to Occam's Razor we ought
not to postulate the existence of unicorns. According to a principle of
plenitude we ought to postulate their existence. In “Vacuous Names,” Grice
wants to say that he can say, with a straight face, that “Pegasus flies.” He is
making a joke on Quine (and “Vacuous Names” is Grice’s contribution to “Words
and objections,” a ‘tribute’ to Quine – for Quine had used ‘pegasising’ as a
way to avoid a commitment with the existence of Pegasus. The rise of particle
physics and quantum mechanics in the 20th century led to various principles of
plenitude being appealed to by scientists as an integral part of their
theoretical framework. A particularly clear-cut example of such an appeal is
the case of magnetic monopoles. The 19th-century theory of electromagnetism
postulated numerous analogies between electric charge and magnetic charge. One
theoretical difference is that magnetic charges must always come in
oppositely-charged pairs, called “dipoles” (as in the North and South poles of
a bar magnet), whereas single electric charges, or “monopoles,” can exist in
isolation. However, no actual magnetic monopole had ever been observed – “so
far,” Grice adds. His son agreed, but as Grice’s son was only five years old
then, it might be argued that he didn’t know the _meaning_ of a ‘magnetic
monopole.’ Physicists began to wonder whether there was some theoretical reason
why monopoles could not exist. It was initially thought that the newly
developed theory of quantum mechanics ruled out the possibility of magnetic
monopoles, and this is why none had ever been detected. However, P. Dirac
showed that the existence of monopoles is consistent with quantum mechanics,
although it is not required by it. Dirac went on to assert the existence of
monopoles, arguing that their existence is not ruled out by theory and that
“under these circumstances one would be surprised if Nature had made no use of
it.” This appeal to plenitude was widely—though not universally—accepted by
other physicists. One of the elementary rules of nature is that, in the absence
of laws prohibiting an event or phenomenon it is bound to occur with some
degree of probability. To put it simply and crudely: anything that can happen
does happen. Hence physicists must assume that the magnetic monopole exists
unless they can find a law barring its existence. Others have been less
impressed by Dirac's line of argument, and have claimed that Dirac’s line of
reasoning, when conjecturing the existence of magnetic monopoles, does not
differ from 18th-century arguments in favour of mermaids. These objectors claim
that the notion of a mermaid (or a winged horse, to use Grice’s example) was
neither intrinsically contradictory nor colliding with current biological laws,
these creatures were assumed to exist. It is difficult to know how to interpret
these principles of plenitude. Quantum mechanics diverges from classical
physics by replacing of a deterministic model of the universe with a model
based on objective probabilities. According to this probabilistic model, there
are numerous ways the universe could have evolved from its initial state, each
with a certain probability of occurring that is fixed by the laws of nature.
Consider some kind of object, say unicorns, of winged horses, whose existence
is not ruled out by the initial conditions plus the laws of nature. One can
thus distinguish between a weak and a strong version of the principle of
plenitude. According to the weak version, if there is a small finite
probability of unicorns existing then given enough time and space unicorns will
exist. According to the strong version, it follows from the theory of quantum
mechanics that if it is possible for unicorns to exist then they do exist. One
way in which this latter version may be cashed out is in the ‘many-worlds’
interpretation of quantum mechanics, according to which reality has a branching
structure in which every possible outcome is realized.
It should be emphasised that Grice’s ‘Modified Occam’s Razor’ merely replaces
Occam’s ‘entities’ by ‘senses’: “Senses are not to be multiplied beyond
necessity.” This he did to joke with Strawson, who in his “Introduction to
Logical Theory” had claimed, contra Grice, that Russell is wrong and that
‘not,’ ‘and,’ ‘or,’ ‘if,’ ‘all,’ ‘some’ and ‘the,’ DIVERGE in SENSE from “~,”
“^,” “V,” “)”, “(x)”, “(Ex),” and “(ix).” And Grice is right: we don’t NEED to
multiply the ‘sense’ of ‘and,’ say, just because, to use Urmson’s example, “He
went to bed and took off his trousers” sounds odder than “He took off his
trousers and went to bed”. Positing a simple desideratum, ‘be orderly in what
you report’ does the job and you can stick, and with a straight face, too, to
‘and’ being commutative. Occam – and Ockham – would be pleased! -- Cheers –
Speranza -- REFERENCES: Grice, H. P. Studies in the Way of Words. Strawson, P.
F. Introduction to Logical Theory.
