The Analog/Digital Distinction: A. Weinstein quotes N. Goodman

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Stevan Harnad

Oct 29, 1986, 2:46:22 AM10/29/86
Anders Weinstein <princeton!cmcl2!harvard!DIAMOND.BBN.COM!aweinste>,
of BBN Labs, Cambridge, MA sends excerpts from Nelson Goodman on the
A/D Distinction. His message follows. I will reply in a later module.
[Will someone with access post this on sci.electronics too, please?].

Anders Weinstein:

>Philosopher Nelson Goodman has distinguished analog from digital symbol systems
>in his book _Languages_of_Art_. The context is a technical investigation into
>the peculiar features of _notational_ systems in the arts; that is, systems
>like musical notation which are used to DEFINE a work of art by dividing the
>instances from the non-instances.
>The following excerpts contain the relevant definitions: (Warning--I've left
>out a lot of explanatory text and examples for brevity)
> The second requirement upon a notational scheme, then, is that the
> characters be _finitely_differentiated_, or _articulate_. It runs: For
> every two characters K and K' and every mark m that does not belong to
> both, determination that m does not belong to K or that m does not belong
> to K' is theoretically possible. ...
> A scheme is syntactically dense if it provides for infinitely many
> characters so ordered that between each two there is a third. ... When no
> insertion of other characters will thus destroy density, a scheme has no
> gaps and may be called _dense_throughout_. In what follows, "throughout" is
> often dropped as understood... [in footnote:] I shall call a scheme that
> contains no dense subscheme "completely discontinuous" or "discontinuous
> throughout". ...
> The final requirement [including others not quoted here] for a notational
> system is semantic finite differentiation; that is for every two characters
> K and K' such that their compliance classes are not identical and every
> object h that does not comply with both, determination that h does not
> comply with K or that h does not comply with K' must be theoretically
> possible.
> [defines 'semantically dense throughout' and 'semantically discontinuous'
> to parallel the syntactic definitions].
>And his analog/digital distinction:
> A symbol _scheme_ is analog if syntactically dense; a _system_ is analog if
> syntactically and semantically dense. ... A digital scheme, in contrast, is
> discontinuous throughout; and in a digital system the characters of such a
> scheme are one-one correlated with compliance-classes of a similarly
> discontinous set. But discontinuity, though implied by, does not imply
> differentiation...To be digital, a system must be not merely discontinuous
> but _differentiated_ throughout, syntactically and semantically...
> If only thoroughly dense systems are analog, and only thoroughly
> differentiated ones are digital, many systems are of neither type.
>To summarize: when a dense language is used to represent a dense domain, the
>system is analog; when a discrete (Goodman's "discontinuous") and articulate
>language maps a discrete and articulate domain, the system is digital.
>Note that not all discrete languages are "articulate" in Goodman's sense:
>Consider a language with only two characters, one of which contains all
>straight marks not longer than one inch and the other of which contains all
>longer marks. This is discrete but not articulate, since no matter how
>precise our tests become, there will always be a mark (infinitely many, in
>fact) that cannot be judged to belong to one or the other character.
>For more explanation, consult the source directly (and not me).
>Anders Weinstein <awei...@DIAMOND.BBN.COM>
>PS: I'd be interested to see the preprints of your Searle and Category
>papers. Thanks.

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