harnad@mind.UUCP (Stevan Harnad) (10/29/86)
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 <aweinste@DIAMOND.BBN.COM> > >PS: I'd be interested to see the preprints of your Searle and Category >papers. Thanks.