ONT Re: Category Theory
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CAT. Discussion Note 3
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JS = John Sowa
JS: 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.
JS: 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.
JS: 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.
JS: 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.
JS: 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.
JS: 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.
JS: 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.
JS: 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
Everthing you say is quite apt and I join in recommending all the goodies
on your web pages. I am operating on the principle that the IFF proposal
is our only current starter document, and so I am looking for ways that
I can add some value to it. I will have my criticisms down the road,
but I think that one of the big futilities that we've had over the
past few years is wrangling about the finer facets before we've
roughed out or even mined the stone. So I will stick for the
time being with the basic category theory, which along with
naive set theory needs no apology, as it used on a routine
basis to carry on the everyday business of mathematics --
the original "upper ontology" if anything ever was one --
not to mention computer science, and even more and more
engineering these days via the systems theory connection.
And it's the main way that I ever learned for talking about
lattices and all kinds of other orders. So this common core
of category theory will probably have to be a central part of
the scientific components of any standard upper ontology, if not
necessarily the commonsense classification, naive ontology modules.
Jon Awbrey
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