On 3/21/2015 9:41 AM, William Frank wrote:
> The idea that our concepts are organized in HIERARCHIES. This is
> false. The analogy with biological hierachies has been the pied
> piper of engineering ontology since its beginnings in 0-0
> programming, ignoring the real advances in the area made in
> library science and in enterprise data modelling. (01)
If by hierarchy you mean a tree, that is certainly true.
Aristotle's primary example of science was biology, and that
was the inspiration for his ontology. Nobody knows whether
he drew trees, since there are no diagrams in his manuscripts. (02)
Some people use the term 'tangled hierarchy' for a tree with
cross references. Others use the word 'hierarchy' as a generic
term for any partial ordering. Then they define special cases of
partial orderings as trees, lattices, chains (AKA linear order). (03)
Aristotle's syllogisms actually support lattices with all possible
combinations. In the 17th century, Leibniz represented primitive
concepts with prime numbers. For the full lattice, he used products
of primes to define complex concepts: Concept A is a supertype of B
iff the number for A divides the number for B. (04)
For history and examples: http://www.jfsowa.com/talks/aristo.pdf (05)
> So this below, is absolutely right:
>
> On Fri, Mar 20, 2015 at 3:20 PM, Chris Mungall wrote:
>
> "Different aspects are
> being described in each hierarchy. You may dislike this separation
> philosophically, but it serves a purpose. We're quite simple minded
> at the end of the day, and prohibiting someone attaching a "mass" or
> "width" property to a fruit ripening process appeals to us, and the
> benefits of abandoning this aren't clear." (06)
I agree. But there is a clear, precise distinction that is easy
to understand and consistent with common sense: (07)
1. All mathematical structures are abstract. They have no
weight, mass, taste, etc. (08)
2. But those structures can be used to describe or characterize
physical structures, which do have weight, mass, taste, etc. (09)
Plato said that the physical things are imperfect imitations
of the ideal forms. Aristotle said that the physical things
came first, and the mathematical forms are abstractions from
them. For more, see aristo.pdf. (010)
> These general 'axioms' are logical, in the broader sense,
> and can be used in any domain, while scientific principles
> of biology are the special knowledge of the biologist. (011)
Yes, but it's more general to use the distinction between
mathematics and physics. All axioms are (or can be) stated in
logic. Axioms for mathematics specify abstract forms, and axioms
for physical domains describe concrete things and processes. (012)
> [In] modern philosophy... we have learned to stop talking about
> what something 'really' is, vs. how we are looking at it, and
> have learned to see scientific theories themselves not as things
> that are 'true' or 'false', but more or less effective and
> insightful, that can only approach that asymptote of what is
> really out there. (013)
I agree. But you can summarize the point in a way that any
programmer or engineer could understand: A mathematical
structure such as a circle or a cube is abstract. Those
abstractions can be used to describe or specify some physical
embodiment. But errors and approximations are inevitable in
any physical measurement or engineering tolerance. (014)
This philosophy, by the way, is as old as Aristotle. In his
logic, he used top-down definitions. But in his biological
writings, he said that you should start by describing actual
specimens. And he emphasized that you may need to change
the definitions when you get new data. (015)
John (016)
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