Hi John, (01)
A couple of points .... (02)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
> Sent: 22 December 2012 15:35
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Fwd: Ontologies and individuals
>
> Chris and Pat,
>
> These notes get into fundamental issues about the nature of logic,
ontology,
> and applications. I'll start with the following point:
>
> 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 .
>
> 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.
>
> 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. (03)
Sure, one can go that way, but my reading of the neo-Fregeans (e.g. Wright,
Crispin, 1983, Frege's Conception of Numbers as Objects, Aberdeen: Aberdeen
University Press) and structuralists (e.g. Shapiro, Stewart, 1997,
Philosophy of Mathematics: Structure and Ontology, Oxford: Oxford University
Press) is that they did not. Field also has interesting things to say
(Field, H., 1989, Realism, Mathematics and Modality, Oxford: Blackwell) but
anticipating Pat - while this is interesting, I'm not sure that it is
totally relevant. I raised this to make the point that there are established
positions where numbers are taken as having instances. (04)
>
> 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.
>
> PH
> >> the abstract/physical is probably the most intuitively secure, but
> >> even there one rapidly gets into difficulties in particular cases.
>
> CP
> > I'm intrigued by your [Pat's] comment "the abstract/physical is
> > probably the most intuitively secure.
>
> 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. (05)
I had assumed he meant the individual-type distinction. I guess you might
mean that here.
I thought he was not willing to assume *any* philosophical notion was
sufficiently secure for *any* practical purpose :-) (06)
>
> 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.
>
> I completely agree with the second sentence. But intuition always has
been
> and always will be our *primary* guide for everything. (07)
I agree that one can argue things bottoms out with intuition; but I guess we
definitely agree it should not start with raw intuition. (08)
>
> 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).
>
> 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.
>
> 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. (09)
I think you might be mistaking the nature of the exercise here. In the
enterprise, where a standard is mandated, in practice people usually make a
local fit but there is a cost. The goal is not that to find a perfect
ontology, but one that meets the constraints set. The question is what
constraints to set. (010)
>
> 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).
>
> 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."
>
> CP
> > When a top ontology has been introduced, the turnaround has reduced
> > significantly. The top ontology gives a framework for focusing the
> > discussion.
>
> 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. (011)
I think I agree. I certainly find using a very (what I would call) sparse
top level is helpful. A baroque top ontology seems to get in the way. But
this may be a feature of the relative immaturity of the area. (012)
>
> 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.
>
> 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. (013)
Umm. I think this is too simple, too black or white. For internal
interoperability it may be more cost-effective to mandate a single top
level. When agreeing message types to exchange, it certainly helps
interoperability to have a common top ontology. BTW messages are a good
example where universal conformity is a given - often, if the message is not
in the right format, it is not read. (014)
>
> 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.
>
> 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.
>
> 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."
>
> John
>
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