Fabian, Alan, and Matthew, (01)
This is related to problems of omniscience in theories about knowledge
and belief (epistemic logic). The simplest theoretical method is also
the most unrealistic for any practical purpose: assume omniscience. (02)
FN
> I don't see the need to explicitly talk about all inferences from
> the axioms as long as we are concerned with ontology languages that
> are based on truth-preserving deductive inference systems like
> Common Logic or OWL. If all the axioms in X are true it follows
> that all inferences from the axioms in X are true. (03)
That is monotonic logic. It's fine for classical mathematics. (04)
But it is impossible for any application to the physical world
to use classical monotonic logic for anything beyond a very narrow
special-purpose task. (05)
Physicists use mathematics very heavily as a *tool*, but they are
very careful to note that their starting assumptions (AKA axioms)
are fallible. They realize that local consistency and approximate
accuracy are the most that they can ever hope for. (06)
Practicing physicists, even most theoretical physicists, have
a very clear and simple slogan: (07)
Physicists don't do axioms. (08)
Some physicists have indeed proposed axioms for quantum mechanics
and other subjects. But practicing physicists consider them
irrelevant *toys*. (09)
When you get to medicine, business, engineering, etc., *everything*
is fallible -- i.e., nonmonotonic and emphatically incomplete. (010)
AR
> [Fabian's statement] is theoretically true but seriously misleading
> in practice. Belief in it has led to serious harm - e.g. potentially
> life-threatening errors in medical ontologies... (011)
Yes indeed. All practical reasoning *must be* fallible & nonmonotonic. (012)
AR
> Do we need to be careful about the word "completeness" to avoid confusion
> with the meaning in computational logic in "complete and decidable".
> Would we be better using a word such as "sufficient" or "comprehensive"
> or similar? (013)
MW
> A better approach I think would be to use qualifiers when the senses might
> be inferred. So logically complete vs factually complete or some such. (014)
AR
> Fine, as long as we are aware of and careful to avoid the potential ambiguity. (015)
I strongly recommend that we expunge the word 'complete' when talking
about any ontology that makes any reference to anything outside of
pure mathematics. Adjectives are too easy to forget or omit. (016)
For more about these issues, please talk to Alan Bundy and his students
and colleagues at the U. of Edinburgh. Bundy has been working on logic
and theorem provers for many decades, and he has applied his theorem
provers to many applications in physics. (017)
Bundy can provide abundant evidence to dash any hopes for a globally
complete and consistent theory of ontology. The best you can have are
theories that are locally consistent, but known to be *false* on a
global scale. Any global (upper or even middle) ontology *must* be
very incomplete and underspecified. (018)
MW
> One thing I have learnt is that writing good logic is a skill, like
> writing good English. (019)
Yes indeed. Writing good axioms is an *art*, not a science. (020)
Alfred North Whitehead was a pretty good logician -- and physicist.
But he emphasized that you can't use logic to determine your axioms.
A theorem prover may be useful to help debug your axioms, but the
source of the axioms is *always* prior to any deduction. (021)
John (022)
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