Re: Prototypes

John F. Sowa (
Sat, 20 Dec 1997 07:36:55 -0500

Some comments on John McCarthy's note:

>When there is a division into non-overlapping species, a few of the
>characteristics of a species can serve to distinguish it from the
>others that exist. We can often have an if-and-only-if definition
>that will work for all species that exist, even if we can imagine and
>maybe genetic engineering could create new species not distinguished
>by the definition. In a limited domain of experience, e.g a child's
>experience or even the experience of farmers working a particular
>region, if-and-only-if definitions work even if they would fail when
>the flora of Sumatra had to be taken into account.

Yes, I agree. Wittgenstein, Waismann, and others have emphasized the point
that new instances keep cropping up to spoil any classification. But if we
have exhausted the domain or closed the door to any new candidates, it is
possible to find iff-style definitions.

>2. Sowa has hinted that logic likes (and maybe requires)
>if-and-only-if definitions. This isn't so. We can have sufficient
>conditions expressed as logical formulas for regarding something as a
>rose and also necessary conditions without the two having to co-incide
>into a necessary and sufficient condition. Theories based on
>prototypes can also be expressed logically.

I agree. That discussion I circulated was from a preliminary part of the
chapter on "Knowledge Soup" which summarizes various difficulties and
criticisms of a logic-based approach. Later in the chapter, I summarize
the discussion with a quote from Whitehead: "We must be systematic,
but we must keep our systems open."

>3. Biology tells us that all roses have in common important properties that
>no-one has discovered yet. Geology doesn't tell us that all hills
>have in common important undiscovered properties differentiating them,
>on the one hand from hillocks, and on the other hand from mountains.
>Moreover, there are no committees of geologists trying to formalize
>these particular distinctions. There is no truth waiting to be
>discovered about what distinguishes hills from hillocks.

These are the kinds of things that a terminological ontology will have to
leave partially, if not mostly undefined. It may give some necessary
conditions for both hills and mountains, but different subdomains,
applications, and discussions may specialize or tailor the definitions
differently for different purposes.

>4. I am working on a theory of "approximate concepts" for which
>if-and-only-if definitions are inappropriate, and where there isn't
>even a truth of the matter to be approximated. The slogan is to build
>solid logical structures on conceptual foundations of quicksand.
>Example: it is definite that Mount Everest was climbed in 1953 even
>though it is not well defined what rocks and ice are parts of Mount
>Everest. Maybe there will be a paper soon.

Purpose is essential. There is no need to make the definitions more
precise than the application. If the goal is to get an honorable mention
in the Guinnes Book of Records, the deails are irrelevant as long as
the climber got his or her head above the surrounding debris. But if
you are trying to set an olympic record skiing against other top contenders,
they use artificially precise standards to break the ties. The purpose of
all those decimal points in the record books is not to determine who is
the better athlete, but to decide who gets the medal.

>5. HPKB and other projects need to tolerate loose ontologies, i.e. use
>necessary conditions and sufficient conditions without supposing that
>necessary and sufficient conditions are to be had.

Yes. And there are going to be many special-purpose, "nonce" ontologies
that will only be used for a single application, or even just a single
email note. They all have to be accommodated somehow.

John Sowa