[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

QUIPS.  Discussion Note 57

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

JA = Jon Awbrey
JW = Jim Willgoose

QUIPS-DIS 56.  http://stderr.org/pipermail/inquiry/2005-May/002757.html
QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

JW: You say:

JA: In loose speech, we often say "relation" when we really mean
    "elementary relation", that is, one k-tuple or one element of
    the whole collection of k-tuples that constitute the relation.
    But we will have to cure ourselves of that habit if we want to
    get beyond the confusions of loose speech.

JW: We would want to cure ourselves of loose speech if we have no
    name for "one k-tuple".  You call it "elementary relation".
    You call the parts of an elementary relation "components".
    I proposed "member" for one k-tuple so as to clarify the
    difference.  The usage is standard.  Thus, we have

    1.  set of k-tuples
    2.  member of the set of k-tuples
    3.  components of the members of the set of k-tuples
    4.  N = cardinal of #1
    5.  w = ordinal of #2

Jim,

I used that usage because it was the usage that Peirce used.
He described the single k-tuples of a k-adic relation as its
"elementary/individual relatives/relations".  He recognized
a number of further distinctions at various times depending
on the extensional versus intensional approaches, but those
can be put off for the time being.  Of course we can always
say "element (or member) of a k-adic relation", but there's
some convenience in having a more succinct phrase, and here
Peirce's "elementary relation" seems to do nicely enough in
most circumstances.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o