Chris and Pat, (01)
These notes get into fundamental issues about the nature of logic,
ontology, and applications. I'll start with the following point: (02)
CP
> As I know you [Pat] know the first (?) real logical formulation
> of number by Frege is as the extension of a concept
> http://plato.stanford.edu/entries/frege/#NatNum . (03)
Frege had some very strong and very sharp views about a single
universal ontology that was truly *true*. His views were extremely
controversial in the 19th century, and they still are. (04)
From a more modern (20th c) point of view, one could say that Frege
used set theory to create a *model* that was isomorphic to the natural
numbers. But it's wrong (or at least highly misleading) to say that
any model *is* the the thing that is being modeled. (05)
Another view, which is preferred by "intuitionism", is based on
counting as the "intended" model of the integers. Any integer
can be reached in a finite time by counting. The nonstandard
models cannot be generated by counting. (06)
PH
>> the abstract/physical is probably the most intuitively secure, but
>> even there one rapidly gets into difficulties in particular cases. (07)
CP
> I'm intrigued by your [Pat's] comment "the abstract/physical is
> probably the most intuitively secure. (08)
Pat was only claiming that it's more secure than the notion of
'individual'. But note the second line: He isn't willing to
assume *any* notion as sufficiently secure for all purposes. (09)
CP
> Furthermore, I'm a little surprised at your taking intuition as
> any kind of guide. Given how easy it is to train and fool, I'd
> be wary about raw intuition without some backing. (010)
I completely agree with the second sentence. But intuition always
has been and always will be our *primary* guide for everything. (011)
In Peirce's terms, intuition is the basis for abduction. But he
was very clear that you had to test your abductions (intuitions)
by observation (gathering data), induction (generalizations from
data) and deduction (checking consistency and coherence). (012)
CP
> It is true that if one aims for a consistent organisation over a large
> amount of data, one is faced with situations where the local fit can be
> difficult. (013)
Not just difficult, but *impossible* -- and least until all possible
questions of science have been asked and answered. Furthermore, even
if we had a perfect fit globally, we would still need different and
*mutually contradictory* local approximations. (014)
I keep giving examples from physics, which is the hardest of the hard
sciences. We still do not have a consistent global theory, but we do
have some theories that are more general than others. The best we
have today is QCD (quantum chromo-dynamics). (015)
But nobody uses QCD for any practical application. Applied physics is
a hodge-podge of mutually contradictory approximations. As the slogan
goes, "All models are wrong, but some are useful." (016)
CP
> When a top ontology has been introduced, the turnaround has reduced
> significantly. The top ontology gives a framework for focusing
> the discussion. (017)
I strongly agree. But that top level must be very underspecified,
and the specific ontologies for different purposes from different
points of view will inevitably be mutually inconsistent. (018)
Furthermore, there is no such thing as one ideal top level.
A 4D ontology is great for many purposes, and a 3D ontology
is better for others. (019)
For interoperability, you do not need agreement at the top level,
which is only "a framework for focusing the discussion." And you
do not need agreement at the lowest levels, which are extremely
problem specific. (020)
Where you do need agreement is at the middle level of the common
words that people use to talk about any subject. That is why I
believe that Schema.org (and the GoodRelations ontology) hit the
"sweet spot" of specifying a useful, underspecified middle level. (021)
Charles Sanders Peirce stated the fundamental principles of ontology
design and development in the simplest and most general way:
> It is easy to speak with precision upon a general theme.
> Only, one must commonly surrender all ambition to be certain.
> It is equally easy to be certain. One has only to be sufficiently vague.
> It is not so difficult to be pretty precise and fairly certain at once
> about a very narrow subject. (022)
In other words, you can do your precise reasoning at the lowest
levels (about very narrow subjects). Your upper level (general theme)
can be precise, but only as one of many possible frameworks or
guidelines. For the middle levels, such as Schema.org, it's easy
to be certain if you keep them "sufficiently vague." (023)
John (024)
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