Re: General semantics

On May 19, 12:26 pm, Nilone <rea..._at_gmail.com> wrote:
> I did some checking and foundhttp://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 tohttp://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.

Relation logic by Peirce and Schröder hasn't been mainstream research area until Tarski. "Applications of Alfred Tarski's Ideas in Database Theory" by Jan Van Den Bussche suggests several influences including cylindric algebras and relation algebras. I'm not convinced about the latter: Codd's relational algebra and Binary relation algebra have very different look!

Also see "the origins of calculus of binary relations" by Roger Maddux. Speaking of metaphysics and philosophical reading, much of Peirce's "Logic of Relatives" is written in that style, so some paragraphs taken out of context appear like crank musings from sci.logic usenet forum. (This observation applies to the famous George Boole manuscript as well.) This is why I find it easier to read it digested via Maddux paper.

> Back to relations - fromhttp://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?

 "relations aren't domains" sounds like some dogma. In my system domains are unary relations (or predicates if the term "relation" is reserved for finite sets of tuples). Received on Thu May 20 2010 - 00:08:57 CEST