Re: Lowenheim-Skolem-Ockham Theorem


David C. Ullrich wrote:

> I don't recall the original Latin, but what Occam
> actually said was "entities should not be multiplied
> without necessity", or words to that effect. That's
> _not_ "the simplest explanation is most likely" -
> it says nothing whatever about which explanation
> is most likely!

> I don't recall the original Latin, but what Occam
> actually said was "entities should not be multiplied
> without necessity",

I never said that (at least as far as anyone knows). The Latin maxim
"non sunt multiplicanda entia praeter necessitatem" ("entities are not
to be multiplied beyond necessity.") W. M Thorburn ("The Myth of
Ockhams Razor." Mind (1918) 345-353) argues that it was invented by
John Ponce of Cork and says it appeared for the first time in 1639.

Other versions of the principle are

"Pluralitas non est ponenda sine neccesitate"
"non est ponenda pluritas sine necessitate",
"si duae res sufficient ad ejus veritatem, superfluum est ponere aliam
(tertiam) rem". (If two things are sufficient to explain its truth, it
is superfluous to posit a third thing).

Similar principles of parsimony were current before my time (in the
late thirteenth century). Aquinas says "If a thing can be done
adequately by means of one, it is superfluous to do it by means of
several; for we observe that nature does not employ two instruments
where one suffices. (*Basic Writings of St. Thomas Aquinas*, trans.
Pegis, 1945, p. 129)

I DID say "Frustra fit per plura quod potest fieri per pauciora" "it is
in vain to bring about through several ways what can be brought about
through fewer". This is in 12.6 of my Summa Logicae. I also said,
anticipating Wittgenstein, we should not look for a substance wherever
we see a substantive. We shouldn't imagine every word that is
grammatically a name, is the name of something. "Radix est
multiplicare entia secundum multitudinem terminorum, et quod quilibet
terminus habet quid rei; quod tamen abusivum est et a veritate maxime
abducens. (The root [of the error] is to multiply entities according to
the multiplicity of terms and [to suppose] that every term has
something real [corresponding to it]. This, however, is erroneous and
leads far from the truth.) (Summa c.51)

The expression "Ockham's Razor" was coined in the 19c. The spelling of
my name in Latin texts is "Ocham". In the 19c it was "Ockham" (I
prefer this). Computer programmers and the like seem to prefer
"Occam".

"Ockham" is the spelling of a village in Surrey where it is supposed I
grew up. This is a beautiful place in the country with an old church.
However some people think my name comes from "Oak Ham" i.e. Woking,
which is a hideous place with a Tesco superstore.

Another thing to bear in mind is that there should only be one
explanation for anything, if it is truly an explanation.

.