Re: General semantics

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? Received on Wed May 19 2010 - 22:26:42 CEST