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Re: Operationalize orthogonality

From: paul c <toledobythesea_at_oohay.ac>
Date: Wed, 07 Jun 2006 01:35:35 GMT
Message-ID: <H3qhg.250420$WI1.9111@pd7tw2no>


Pickie wrote:
> Booleans don't in themselves convey order. Marshall elsewhere in this
> thread said "The RM doesn't have anything about order as part of its
> definition; one defines order on top of it." and I don't think there
> was any controversy over that.
>
> Individual bits can represent booleans, but where is the concept of
> order coming from that turns a set of bits into a coded string of bits?
> If Marshall's statement quoted above is true, then it cannot come from
> relations, therefore Tony's contention that it is possible to "model
> everything from there on up in terms of relations and booleans" is
> untrue.
>
> So, to answer your question. Not only do I not see it, I do not
> acknowledge it is possible. Obviously there are systems that do it,
> but _not_ by building _solely_ on booleans and relations (even
> theoretically).
>

At the end of the day, order is in your head and doesn't seem to be necessary to the rm though you could choose to express it with a relation. Even physical machines fake it, eg., opcodes that return 'greater than' are usually just subtraction circuits in disguise. There is a big difference between slavishly emulating such a relation and taking a short-cut to get its logical equivalent. Even though I'm not one of them I'll stick my neck out and state that that's part of what rm's deep thinkers have in mind when they talk about implementing an abstraction, which is not at all about emulation or imitation (which were certainly part of the motivation for C++, plus maybe other oo languages). You don't need to materialize a relation in order to adhere to it (which some of the oo people seem to forget, can't comment about the pickies). My impression is that the rm people consider the "coded string of bits" as a mere representation, ie. carrying meaning only in the eyes of the beholder.

p Received on Tue Jun 06 2006 - 20:35:35 CDT

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