Re: General semantics

From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 20 May 2010 02:59:43 GMT
Message-ID: <zA1Jn.4255$Z6.1870_at_edtnps82>


Nilone wrote:
> On May 19, 5:12 pm, paul c <toledobythe..._at_oohay.ac> wrote:

>> Eg., I'd be curious as to who first talked about unary relations, which
>> seem an essential part of Codd's breakthrough.  Seems to me that
>> anything 'new' needs to be compared to what Codd wrote (though
>> apparently he had such a practical bent that he saw no need for nullary
>> relations).

>
> I did some checking and found http://fair-use.org/bertrand-russell/the-principles-of-mathematics/s27,
> from which I snip and paste liberally:
>
> "Peirce and Schröder have realized the great importance of the
> subject ... their method suffers technically ... from the fact that
> they regard a relation essentially as a class of couples, thus
> requiring elaborate formulae of summation for dealing with single
> relations. ... it was certainly from the opposite philosophical
> belief, which I derived from my friend Mr G. E. Moore, that I was led
> to a different formal treatment of relations."
>
> Am I correct in thinking that Russell's 'single relations' refer to
> unary relations? Although I didn't follow up all the references, some
> further checking makes it seem as if Peirce first developed the idea.
> According to http://en.wikipedia.org/wiki/Charles_Sanders_Peirce#Mathematics_of_logic,
> Codd studied under Burks who strongly advocated the ideas of Peirce,
> so it seems likely that Codd would build on that foundation.
>
> Searching on Burks netted me this paper:
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.4104&rep=rep1&type=ps
> (Peirce's Late Theory Of Abduction), which explores some of Peirce's
> phenomenology.
>
> Back to relations - from http://fair-use.org/bertrand-russell/the-principles-of-mathematics/s30,
> "If u be any class which is not null, there is a relation which all of
> its terms have to it, and which holds for no other pairs of terms."
> If a unary relation describes a relation between a class and its
> terms, and classes equate to the domains of relations, then can we /
> should we allow the direct use of relations as domains? For example:
>
> Carnivore = [x : Animal]
> Wolf
> Lion
>
> PredatorPrey = [y : Carnivore, z : Animal]
> Wolf, Rabbit
> Lion, Deer
>
> This goes against the adage "relations aren't domains", and we can
> achieve the same via referential constraint expressions, which can
> also express more complex relationships between the domains of
> relations, but do we need the extra concept?

I think it is just as important to avoid circular definitions as it is to minimize concepts. At least, as far as implememters are concerned because otherwise we can tie ourselves into knots, paint into corners, etc., eg., when is an implementation dealing with a set and when is it dealing with a relation? This is a practical reason, maybe some future progress will able to discount it.

(If we do think by means of language, then we start with givens such as noun and verb symbols, pick something else if you like. I remember reading a few books by Edward de Bono, recommended to me by a marriage counselor of all people! He coined the term 'lateral thinking' and invented a few products which some find pointless and others find intriguing. Lateral thinking prompts alternative conclusions but doesn't demonstrate them, it allows circular thinking but at some point one must put its possible 'conclusions' to some test or other. I'd say it comes down to being a means to an end, eg., I came to the conclusion that lateral thinking is just an aid towards better linear thinking. If that's apt, then treating relations as domains is sort like saying the means justifies the end.) Received on Thu May 20 2010 - 04:59:43 CEST

Original text of this message