[Martin Taylor 940829 09:50]
Avery Andrews undated (received Sat, 27 Aug 1994 14:05:19)
I don't see any difference between what you are saying and what
I mean, and I'm happy with everything in your posting, other than
the claim that I'm saying something different!
...
So you can't say 'the CEV associated with a PIF' - there are lots
of them, and assume there is no way to enumerate or otherwise
specify all of them (whence the term 'indefinitely large collection').
That's what is the difference between what I mean and what you are saying
(note the inversion:-). My whole posting was devoted to making clear that
in my terminology "CEV" implies one and only one CEV can EVER correspond
to a particular PIF. The PIF is a function that defines the specific
CEV. The arguments to that PIF are the inputs that (at all levels but
the lowest) are mostly the outputs of other PIFs that define OTHER CEVs.
You have a situation like function F is F(G(H(I(....)))). The only
argument to function F is the output of function G, and function F is
strictly determined. Its output is whatever F does to its single argument.
In the case of PIFs, each one has several arguments, but the arguments
themselves represent scalar values, that's all. Those values may happen
to correspond to something in the outer world, and if you want to say
that they all correspond to "CEVs associated with the PIF", I suppose
you are entitled to. I tend to use the word "that support" in place of
"are associated with," because I like to think of the CEV whose physical
function is defined by the PIF as being the single one that is associated
with that PIF. However, the number of those that support any one is
finite, and determined by the fan-in of the inputs to the PIF in question.
By the way, I like your concept of ESV, but you should perhaps make it
more clear that any ESV represents a fact of the real world that is not
accessible to the organism unless there is a corresponding PIF. My
use of CEV was originally broader than your ESV, since the "C" in "CEV"
is "Complex," not "Controlled." Any function whatever of physical variables
can be a CEV, and a distinction should be made between those that are defined
by PIFs (and therefore correspond to controllable perceptions) and those
that are not (such as, presumably, the square of the number of hairs on
my cat times the number of seconds since the opening angle of the rings of
Saturn was last zero, plus the temperature in my office). That example
is of a CEV that is neither an ESV nor a "CCEV" (a CEV corresponding to a
controlled perception).
To back up--One PIF, one defined CCEV, a finite number of supporting (or
"associated" if you wish) CCEVs, and aleph-2 (at least) CEVs. How many
ESV's, who knows?
Martin