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Re: [ontolog-forum] Current Semantic Web Layer Cake

To: Kathryn Blackmond Laskey <klaskey@xxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 2 Aug 2007 11:42:32 -0500
Message-id: <p06230900c2d7b51b29bc@[]>
>>The set D can *be* a set of horses. Sets can be
>>sets of anything.
>>To say that the universe is a set is, literally, to
>>say nothing whatever about what kinds of thing are in the universe,
>True.  But to say that the universe is a set does imply that it is
>composed of "things".    (01)

In a VERY broad sense of "thing", yes.    (02)

>  That is not a vacuous assumption    (03)

I agree, but it is about as close to vacuous as 
we currently know how to get without giving up on 
the idea of using a language at all. Are there 
any human languages that are noun-free?    (04)

>, and it's not
>shared by all cultures.
>Let me give an example.    (05)

good :-)    (06)

>  Suppose I tell you my Aunt Jane's positive
>attitude is part of the reason she is a 20-year breast cancer
>survivor. In order to make sense of that sentence, do I need to
>believe there really *is* a set of all possible attitudes, and that
>there is a member of this set that really *is* my Aunt Jane's actual
>attitude?    (07)

That is what the sentence seems to say. Of 
course, the surface form of a NL sentence is not 
always a true guide to the ontological 
underpinnings of what the sentence is intended to 
convey, but in this case it seems reasonable to 
take the sentence at face value, at least at 
first.    (08)

>That is how I would represent this sentence if I were to construct a
>logical theory (using a probabilistic logic, of course)    (09)

:-)    (010)

>  that says a
>person's chances of surviving cancer are higher if the person has a
>positive attitude.  The natural way to do this would be to define a
>function that maps a person x to the person's attitude Attitude(x).
>The domain of the Attitude function is the set of all persons, and
>the range is the set of all attitudes.    (011)

Right. (My only worry here is the possibility 
that one might have several attitudes 
simultaneously, but that could be formalized 
similarly.)    (012)

>I'm willing to accept the following assertions: (1) There is a set of
>all people; (2) There is an attribute of persons that we label
>attitude; (3) To some degree, we can ascertain whether a person has a
>positive attitude; (4) There are interventions we can make to affect
>a person's attitude.    (013)

OK. A quick remark: the 'being able to ascertain' 
isn't necessary, in order to accept that 
attitudes exist.    (014)

>  But I'm not at all sure I agree that the
>universe really contains a set of consisting of all the possible
>attitudes    (015)

But it seems to me that you have already accepted 
that. Persons exist, and persons have attitudes: 
surely it follows that attitudes exist, does it 
not? Assuming at least that "attributes" exist 
(which CL has as a built-in.) One has to accept 
that 'exist' may be more generous than physical 
existence.    (016)

>, and that there really is a function that maps each person
>to an element of the set of all attitudes, and that the value of this
>function *is* the person's attitude.    (017)

That just seems to me to be a mathematical way of 
saying exactly what you already said in (1)-(4) 
above.    (018)

>  Maybe there is and maybe there
>isn't a real set of all possible attitudes.  I don't know.  From what
>I know of psychology and neurophysiology, I think we're a very long
>way from a theory of attitude to which I would give cre    (019)

Oh, sure. Attitudes are part of a folk 
psychology, just as entities like 'pool of water' 
are part of folk physics. But that is a different 
kind of distinction. Do mirages exist? In a sense 
yes, in another sense no. But we can certainly 
talk about them.    (020)

>  I think it's
>fairly likely that today's notion of attitude will go the way of
>phlogiston, the non-existent component that was once thought to be
>the part of all flammable substances that caused them to burn.
>Fortunately, I don't think it is necessary to believe there really
>*is* a set of all possible attitudes, and that each person really
>*does* have an attitude that is an element of this set, in order to
>accept the above theory as a useful representation of reality for
>some purposes.    (021)

Quite. I think you are taking phrases like 
"really" too seriously here. The point I was 
making was that (in your example) the fact that 
the ontology is formalized and has a formally 
described semantic theory is not a sufficient 
grounds in itself for claiming that the worlds it 
describes aren't real. If one believes that 
attitudes are real, then one can speak of sets of 
them; also, in fact, if one believes they are not 
real.    (022)

>  We can design questionnaires to measure attitude. We
>can correlate questionnaire responses to cancer survival rates. We
>can define a conditional probability distribution for cancer survival
>given positive attitude and given negative attitude, and estimate the
>parameters of this distribution to ascertain the degree to which
>attitude affects survival. We can design interventions, measure the
>impact of the interventions both on responses to the attitude
>questionnaire and on cancer survival rates.  We can use the results
>of these studies to design clinical interventions aimed at improving
>survival rates. Teams of healthcare professionals and statisticians
>do this sort of thing all the time.  They end up with logical
>theories / mathematical models / representations of reality that are
>very useful for the practice of medicine.
>The theory of attitudes I sketched above is mathematically equivalent
>to defining a probability distribution on Tarski interpretations of a
>set of logical axioms.  In each of these Tarski interpretations,
>there is a set of people and a set of possible attitudes and a
>function mapping persons to attitudes.  Each sentence about attitudes
>makes an assertion about elements of or subsets of this set of
>possible attitudes.   The logical theory is *about* (among other
>things) the set of all possible attitudes.
>But I can make perfectly good use of this theory, while thinking that
>the idea of a set of all possible attitudes is utter nonsense.    (023)

Yes. Ontologies can be wrong and yet still useful.    (024)

>I may
>find this theory very useful for the purpose of representing the
>effect of attitude on cancer survival and recommending clinical
>interventions that improve survival rates.  I can believe this theory
>makes assertions that are approximately correct about the real world.
>Yet I may think that literally treating these assertions as being
>*about* an actual set of attitudes that really exists in the world is
>absurd.    (025)

I tend to think that if the theory accurately 
describes observable phenomena, then that's about 
as real as one can hope to get in practice. But 
we are straying from semantics to philosophy of 
science at this point.    (026)

>It may very well be that our ontologies represent classes of "things"
>that do not correspond to real "things" in the world.  Maybe some of
>our assertions, although they are phrased as sentences about these
>"things," are not actually about "real" things. Maybe that's just the
>best we can do with language, but our language doesn't map very well
>onto what is really there. I don't think one needs to believe that
>the Universe really is a set in order to make effective use of
>logical theories that represent the Universe as a set.    (027)

True, but my original point was rather the 
inverse: one can believe the universe is a set, 
without thereby being obliged to abandon ones 
belief that it is populated with real things. I 
think we agree on this as well.    (028)

Pat    (029)

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