SUO: Re: Monoclonal Antebodies
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EP = Eric Peterson
JA = Jon Awbery
JA: i apollogize for being so plodding, chris, but i have deliberately
put myself in a "keep it concrete and simple" frame of mind for the
sake of my (auto-)tutorial exercises, so let me just try to think
of some of the simpler questions that have always worried me here.
JA: 1. how does one, working solely within your favorite version of fol,
express the fact that functions are special cases of relations?
EP: If all the predicates in the world died off in a plague,
what would stop the functions from agreeing among themselves
that part of the ones that returned Boolean values would fill
in as predicates? ;^)
EP: Anyway, my instincts tell me that it is actually relations
that are special cases of functions. But you are not the
only one with much more background in logic than I who
has made that claim.
EP: What am I not seeing?
eric,
that was just a practical question, and i really thought that there might be
some sort of practical answer that i had not heard about -- people should not
impute so much unintended cleverness to me, especially on a burned out friday.
i wrote a whole passel of stuff about this once, ignore it for now:
RIG. Relations In General
01. http://suo.ieee.org/ontology/msg04721.html
02. http://suo.ieee.org/ontology/msg04722.html
03. http://suo.ieee.org/ontology/msg04723.html
04. http://suo.ieee.org/ontology/msg04724.html
this is all intended for practical applications -- if it seems a little peculiar,
it's because it's from work i did in 1980 and it recounts how a combinatorialist
turned systems-theory-engineer thinks about relations.
in an ordinary math context, a function f : X -> Y is a special case
of a relation F c X x Y. there's a logical distinction of some sort,
but one tends to regard it more as interpretive than ontological, if
you are even allowed to use such words in an ordinary math context.
from ideas that go way back, to dana scott, et al. in siam j 1976,
is one nexus where i first encountered it written down, one wants
to think of the extensions as data sets that are constrained by
information, and one wants to pass from fixating so much on
the "function f" or the "relation L" to thinking more about
the "info about f" and the "info about L" that one has.
of course, with any subset W c X, in particular, a relation L c X_1 x ... x X_k,
there is associated its indicator function f_W : X -> B, in particular, there is
also the indicator function of the relation f_L : X_1 x ... x X_k -> B, and so on.
But that is precisely the point -- one wants to view things sub specie informationis,
treating the same information the same no matter what the syntactic superficialities
of its signed or signatured expression. it's a fairly standard pov in some circles.
jon awbrey
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