LINGUIST List 2.758

Wed 06 Nov 1991

Disc: Are Languages Finite

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1. jj36, Re: 2.747 Are languages infinite?
2. Jacques Guy, Are languages infinite

Message 1: Re: 2.747 Are languages infinite?

At risk of belaboring the point: Kac introduces a new 'conceptual error' in
his "crucial difference between (a) what a system of rules allows as a
matter of principle and (b) what kinds of behaviors are possible... because
of the limitations on humans and the physical universe..." The distinction
is deceptive. Systems of rules and conventions presuppose the limitations
described in (b); it would be absurd to have a rule of football barring
players from turning invisible -- and through the absence of such rules the
rule system 'contains' the natural limitations, in a negative way. What is
more, the 'matters of natural law' (Kac's term) contained in (b) are
perceived and defined in conventional terms: Kac errs in stating "That it's
physically impossible for a team of human football players to score a
million points in the confines of an hour of play is a fact, but it isn't
because the rules of football either state or imply that this should be so"
-- the error is that the impossibility depends wholly and utterly upon the
convention of how a point is scored in football. If points were awarded for
each millimeter of ground a team advances the ball, scores in the millions
would suddenly become perfectly physically possible. Even the airplane and
cat & mouse analogies are dependent upon the conventional definitions of
'mile' and 'hour'.
 We could come up with less problematic examples to illustrate Kac's
point, but I think his own examples point up how truly interconnected are
the kind of natural and conventional rules he is at pains to distinguish.

I used to think the same as Michael Kac, i.e.:
"Having said that, I should go on to say that I don't in point of fact
think that it's especially productive to debate whether languages
are infinite." (His 1st Nov 91 posting)
... until I read the biography of W.Friedman (the decipherer of
many a German and Japanese code during WWII) in the latest issue
of "Cryptologia". What if whomever he depended on for funding had
said: "Languages are infinite, so your approach cannot succeed."
(Given Friedman's approach, and granted that languages are
infinite, or even only very large, it seems indeed to be condemned
to failure. But read the article: it is very well written and I
couldn't put it down.)