Re: SUO: Category Theory
Jon,
When a reader with the expected level of prerequisites finds it
difficult to read a text, even after making several diligent
attempts, the fault is the author's.
> I have tried to get through the IFF proposal several times now,
> and even though I have a basic acquaintance with category theory
> as used in math and computer science, it's been pretty rough going.
> I thought of trying to start an online review of this material, but
> second thought tells me that it won't be possible for us to evaluate
> this work unless we sort it out by layers of complexity and usability.
Although I have been sympathetic to the IFF efforts, I have repeatedly
pointed out that the current document is not suitable as a standard.
It should be considered the developers' first attempt at writing a
technical report that could be used (by them) as the basis for a
standard. Readers are expected to meet an author halfway, but the
author is also expected to meet the readers halfway.
As an example of the level of formality that is appropriate for the
IFF, I recommend any decent textbook of computer science for first-year
computer science graduate students. Anything that is unreadable by
students who have been accepted for a CS graduate program at a good
university is inappropriate as a standards document.
Those excerpts that you extracted from textbooks on category theory
are intended to be read by advanced undergraduates and beginning
graduate students -- i.e., by the kind of people who might be
expected to read the IFF document. Yet they are much more readable
than the IFF document.
I recognize that the IFF developers have tackled a very large complex
task, and they are trying to state the standard at a very high level
of generality and abstraction. I commend them for their ambition.
But I believe that it is now time to scale back the project to
something that is more easily (1) readable by people who have a BS
degree in computer science, (2) salable to people who see the need
for ontology but not the need for an opaque formalism, and last but
not least, (3) implementable.
For several years now, I have been arguing for a lattice of theories
as a framework for relating various ontologies. The IFF developers have
assured me that their framework is general enough to accommodate the
lattice I would like to see as a special case. I believe that is
probably true. I also believe that category theory is the proper
formalism to use for what the IFF is supposed to do.
But if the IFF developers cannot write a readable document that
presents their ideas, I suggest that they scale back version 1.0
of the proposed standard to something that isn't much more than
the simple lattice I have been proposing. Then at some point
in the future, after people have started using and implementing
version 1.0, they can develop version 2.0 with all the power
and glory that they are now trying to document.
As an example of the level of readability and formality that I
believe would be appropriate for the IFF standard, I recommend
my tutorial on math and logic:
http://www.jfsowa.com/logic/math.htm
John Sowa