Barry, (01)
Although I prefer a realist position on the issue of
whether at least some types existed before anyone invented
a word for them, I also realize that there are a lot of
nominalists in the world and even among our colleagues in
this working group. Therefore, I recommend a strategy and
terminology that avoid debates of nominalism vs. realism. (02)
> Talk of types should thus not rely too much on talk of
> definitions/intensions.... (03)
I agree that it would be desirable to have a definition
of type that did not depend on definitions stated in any
language (formal or informal). But I despair of reaching
an agreement on that issue in this WG. I would be happy
just to get an acknowledgment that 'type' is better than
'class' and that we can relate types to predicates. (04)
JS>> Aristotle introduced the word 'kategoria' as his term
>> for the intension, (05)
BS> not true, I'm afraid;
> 'kategoria' means: that which is said (in the agora, or
> market); (06)
That is the etymology. Before Aristotle, the primary
use of the word was for an accusation in a court of law.
Aristotle's use was a major innovation. (07)
BS> for Aristotle the terms was used to mean something like:
> 'highest type'; Aristotle did not have our modern notion
> of intension (08)
Although Aristotle did not coin explicit terms for the
distinction between intension and extension, he definitely
observed it and commented on what is now called the
'inverse relationship between extension and intension':
the fact that the more differentiae that are added to a
definition the smaller the set of individuals to which
the term applies. (09)
This distinction was widely observed by the Scholastic
logicians. The words 'extension' and 'intension' are
Hamilton's translations of the Port-Royal terms
'étendue' and 'compréhension'. (010)
As for 'highest type', which for A. was 'to on' or Being,
Aristotle explicitly excluded that from his list of ten
(upper-level) categories. And his first book on the
categories gave many examples a lot further down. His books
on syllogisms (later called the "categorial syllogisms")
directly addressed the methods for reasoning about categories
at all levels, with examples such as vines and deciduous plants. (011)
BS> Again, when biologists (e.g.) develop large ontologies
> representing types, they do not do this by scanning their
> minds for corresponding definitions, or intensions; they
> look at the entities in reality, e.g. at patterns of DNA. (012)
Indeed. They state *definitions* based on the theories they
develop as a result of their observations. As a realist,
I believe that there exists something real behind those
theories, but any guidelines or methodology we propose for
ONTAC WG will have to be based on the definitions. (013)
In any case, I am happy with your statement of the conclusion: (014)
BS> I prefer: the distinction between type and instance, and
> thus also between type and extension (= class of instances) is
> fundamental to ontology, and I hope it will be taken as seriously
> as it deserves to be taken. The word 'class' would hopelessly
> confuse the issue. (015)
My only suggestion is to replace "(= class of instances)"
with "(= set of instances)". It's better to avoid the
word 'class' altogether. (016)
John Sowa (017)
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