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From: ladkin@KESTREL.ARPA (Peter Ladkin)
Newsgroups: mod.ai
Subject: Re: The Analog/Digital Distinction
Message-ID: <14134@kestrel.ARPA>
Date: Mon, 3-Nov-86 18:47:34 EST
Article-I.D.: kestrel.14134
Posted: Mon Nov  3 18:47:34 1986
Date-Received: Thu, 6-Nov-86 21:34:29 EST
References: <1701@Diamond.BBN.COM>
Sender: daemon@ucbvax.BERKELEY.EDU
Organization: Kestrel Institute, Palo Alto, CA
Lines: 19
Keywords: analog, digital, continuous, discrete, quantization, density, Goodman
Approved: ailist@sri-stripe.arpa

In article <1701@Diamond.BBN.COM>, aweinste@Diamond.BBN.COM
  (Anders Weinstein) writes:
> The upshot of Goodman's requirement is that if a symbol system is to count as
> "digital" (or as "notational"), there must be some finite sized "gaps",
> however minute, between the distinct elements that need to be distinguished.

I'm not sure you want this definition of the  distinction.

There are *finite-sized gaps, however minute* between rational
numbers, and if we use the pairs-of-integers representation to
represent the syntactically dense scheme, (which must be
isomorphic to some subrange of the rationals if countable)
we may use the integers and their gaps to distinguish the gaps 
in the syntactically dense scheme, in a quantifier-free manner.

Thus syntactically dense schemes would count as *digital*, too.

Peter Ladkin
ladkin@kestrel.arpa