Subject: Re: Computing Functions & Boehm-Jacopini
From: "William J. Rapaport" <rapaport@buffalo.edu>
Date: Tue, 16 Feb 2010 09:06:13 -0500 (EST)

In response to the discussion archived at
http://www.cse.buffalo.edu/~rapaport/584/S10/EMAIL/20100211-CompgFns-Boehm-Jacopini.txt
Bill Duncan (wdduncan@buffalo.edu) writes (with my replies interpolated):

"I'd like to follow up on some of your responses.
For convenience, I'll list them as numbered points.

"1. The definitions I listed are taken from the BFO
(http://www.ifomis.org/bfo). I do not have control over them.
Unfortunately, the definitions do contain a number of technical terms,
and it would take quite a bit of work to explain them fully.
I will I have to forgo this."

Reply:
That's fair, but is there a place where those terms
("inhere", "bear", etc.) are defined?

"2. To recap, in BFO a function is "A realizable entity the
manifestation of which is an essentially end-directed activity of a
continuant entity in virtue of that continuant entity being a specific
kind of entity in the kind or kinds of contexts that it is made for."
You have suggested that by "end-directed activity" the BFO is referring
to a function's purpose. I am unsure why the designers of BFO decided
to use the phrase "end-directed activity" instead of "purpose", but I
will speculate that the following two considerations may have played
role:

"a. The term "purpose" may too strongly suggest that the reason for a
function's behavior is due to an intelligent designer. Much of BFO's
application has been in the area of bio-medical sciences, and the
suggestion of intelligent design would not be applicable to many of
these areas of research."

Reply:
Sounds plausible.

"b. The term "purpose" may be too narrow to define all functions.
Consider that it is a function of the heart to pump blood.
It sounds odd (to me at least) say that this is the heart's purpose."

Reply:
Another good point: I think I'm willing to agree that all purposes are
functions in this sense, but not the other way around
(not all functions in this sense are purposes). So, to echo your point (a),
"end-directed activity" certainly seems like the more general term.

"3. There may be a sense of "purpose" which may apply to programming
languages. For modern programming languages (at least in the sense of
artifacts) are intentionally designed entities. Their grammar rules
have been intentionally designed for the generation of sequences of
statements. This "purpose" is not a temporal entity. However, it is
actualized when one does actually generate a sequence of statements."

Reply:
Here's where I think the major distinction reveals itself. I agree that
algorithms/programs **have** purposes. After all, we have defined an
algorithm as an algorithm **for solving a particular problem** or
**for computing a particular mathematical function**. So the "end" that
an algorithm's "activity" is "directed to" is the solution of a problem
or the computation of a mathematical function. But that's very different
from saying that an algorithm **is** a purpose and that it should be
categorized in the BFO ontology *as* a function (in the end-directed
activity sense): It *has* a function (in that sense) but *isn't* one
(in that sense). (And, to repeat, it *computes* a function in the
*mathematical* sense.)