thanks for this, John and Mathew, Avril, Doug, and the other partakers in this discussion
I learn alot from participating in this forum, and especially every now and again when I see things I vaguely know come looming out of the fog organized in a lovely fashion. I am even sure this helps me in my business, so a recreation in the root sense.
Wm
On Fri, Sep 28, 2012 at 12:54 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
Dear Matthew, Avril, William, and Doug,
MW
> I do not see set theory and mereology as alternatives that you choose
> one from for your ontology, rather I see them as being appropriate
> in different circumstances. One of the tests I use to determine which
> is appropriate is whether I am or could be interested in the weight
> of the collection. Sets are abstract and so do not have a weight.
> A mereological sum on the other hand does.
That's a very good, one-paragraph summary of the difference. Formally,
I would emphasize that set theory has two operators (subset and isIn),
but mereology has only one operator (partOf).
The partOf operator need not change the ontological category: a car
and a mereological sum of cars are both physical. That's also the
reason why mereology is better suited to plurals in NLs. A single
person, say Bob, can be an animate agent of an action, and a plural
such as Bob and Sue can be the agents of the same verb.
But the isIn or elementOf operator always treats the second operand
as abstract. Even if the first operand is a set, the second belongs
to the category 'set of sets'. That formalism does not have a simple
mapping to natural languages, in which plurals do not change category.
AS
> ... as a definition of what is continuous, continuous mereology is
> a lot simpler than set theory which can be used as a foundation
> continuous point-sets, and thus mereology is better. A better question
> is why do we need 'continuity' in the first place in modeling finite
> and discrete phenomena?
To answer your second question, set theory is fine for those phenomena.
But Matthew gave a good answer for physical things, and the use of
mereology for plurals is a good answer for applications to NLP.
AS
> set theory can be used in modeling granular structures that are found
> all around in nature.
I agree that you can use set theory for those purposes. And set
theory can be used in conjunction with continuous math in physics.
Furthermore, the method of partitioning and projection by Bittner
et al. can be adapted just as easily to set theory as to mereology.
WF
> I feel it is important to distinguish between what some formal ontology
> says, however excellent that may be, and the domain concepts of groups
> of domain practitioners.
This point should always be considered in any ontology. Formalism is
necessary for computer processing, but it's not the ultimate goal.
I put more faith in the judgment of practitioners who know the subject
than in some programmer or philosopher who proposes a clever encoding.
JFS
>> The point Rom was trying to make is that the word 'body' is not
>> synonymous with 'person'. Those words are never used in ways
>> that are interchangeable.
DF
> Fine. But Rom was discussing parthood, not whether they are
> synonymous or interchangeable. If he claimed that a body was
> only a (proper) part of a person, that would mean that the concepts
> were not synonymous or interchangeable.
Rom was criticizing the way parthood was used in some applications
of mereology. I believe that he was emphasizing the phrase "in the
relevant sense". He used the word 'part' only because it was used
in the writings he was criticizing.
Rom cited Wittgenstein's later philosophy as a basis for his approach.
As a guideline for making an ontological decision, LW and RH would
both give high priority to the following sentences:
Bob thinks that the sky is blue.
Bob's body thinks that the sky is blue.
Bob was walking to the store.
Bob's body was walking to the store.
Note that you can't attribute walking or thinking to Bob's body
by itself. That's a clue that there is a category mistake in
any attempt to identify Bob with his body.
But note that the following two sentences are both acceptable:
Bob weighs 165 lbs.
Bob's body weighs 165 lbs.
These examples show that Bob and his body have certain physical
properties that are identical. But English speakers don't consider
the body by itself as the agent of actions (mental or physical).
I have more faith in the common sense of English speakers than
in the claims of philosophers who are trying to defend a theory.
John
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