SUO: Re: Mapping from one notation to another
Jon,
Yes, there is more to be said. But getting the point
across with just one instance is sufficient to dispell
many of the confusions about notation.
JA> And no matter how you syntacticize the description
> or graphicize the depiction of that single triple, which
> latter task CG's naturally do beautifully, that triple
> is not the 3-adic relation "Gives", but only a single
> instance of it.
Actually there is no single "best" way to show a
relation. A table of all instances is only possible
for a finite relation, and even then, it only shows
the extension, not the intension. For most relations
that one encounters in ordinary language, the intension
is far more important than the extension.
In any case, any syntactic representation of the
issues for a single instance can be generalized
to a similar representation for any axioms that
define the intension.
John