Pat, (01)
In response to my suggestion that "Most authors who write biology text books
don't know about, or aren't thinking about Taskian models." You said: (02)
They may not know about them, but they can still be thinking about
them. Just as someone who knows nothing of botany can think about
plants. (03)
This snapped my mind back to yoir exchange below with John (04)
JS>> I agree that formal model theorists tend to talk that way, but
.> that is not how scientists work. The model comes first, and
JS>> the axioms are derived from the model. (05)
Pat>First, I wonder how you can possibly know this. (06)
I'm sure that you, like John, have a good reason for knowing this, but it would
help me to understand a (07)
little bit more of why you say this. Is it that biologist understand something
about the biological language under discussion (there biologocal object
language) BL, and ther are thinking that any biological definitions have to be
expressed in another language a meta BL? What is that metalanguage that they
are tinking of? (08)
And do they intuite that set theory is involved etc..? Do you mean that
Biology as written in text books is a formal system? (09)
Well the title of this tread is about being confused about models so perhaps
this fits right in. :-} (010)
Gary Berg-Cross, Ph.D.
Spatial Ontology Community of Practice (SOCoP)
http://www.visualknowledge.com/wiki/socop
<http://www.visualknowledge.com/wiki/socop>
Executive Secretariat
Semantic Technology , EM&I (011)
Herndon VA 20170 703-742-0585 (012)
________________________________ (013)
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx on behalf of Pat Hayes
Sent: Mon 7/16/2007 6:44 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] confounded models (014)
On Jul 16, 2007, at 5:20 PM, Gary Berg-Cross wrote: (015)
> Pat, Barry
>
> Most authors who write biology text books don't know about, or
> aren't thinking about Taskian models. (016)
They may not know about them, but they can still be thinking about
them. Just as someone who knows nothing of botany can think about
plants. (017)
> They are thinking about real cells as know through theory and
> related biological models.
>
>> So that a full model of the sentences in the biology textbook would
>> have two kinds of cells, real ones and model ones?
>> BS
>
> No more or less , it seems to me, than two different biology books
> with slightly different sentences featuring certain aspects of
> cells could be said to have to different models. Or take a book
> from 1970 and one from 2000, They have differences based on
> advancement. They both are about real cells, just reflecting the
> author's different understanding of the field at the time. (018)
Agreed. You are talking about what the authors have in mind. But one
might also take a more, er, analytical perspective and ask the
following question: Given the ontologies they have produced, what
could these ontologies *possibly* be about? Hopefully what their
authors had in mind is one such topic, but there could be others. In
particular, if you produce a very 'thin' ontology with very little
content, it *could* be about a wider range of things, perhaps things
you didn't have in mind at all. The Tarskian formal semantic theory
gives this idea flesh, and provides a way to even construct these
'nonstandard' models. Thy are often very useful as they provide a way
to identify weak points in a formal ontology. (019)
BTW, the terminology 'nonstandard' comes from mathematics, where
people realized a while ago that no matter how many axioms you write
for arithmetic, there are going to be models of them that aren't like
the integers (the 'standard model' that we all have in mind).
Investigating such nonstandard arithmetics turns out to be very
useful and interesting, for example there are such arithmetics with
infinitesimals in them, providing for the first time a rigorous
foundation of Newton's intuitions. (020)
Pat (021)
>
> Gary Berg-Cross, Ph.D.
> Spatial Ontology Community of Practice (SOCoP)
> http://www.visualknowledge.com/wiki/socop <http://
> www.visualknowledge.com/wiki/socop>
> Executive Secretariat
> Semantic Technology
> EM&I
> Suite 350 455 Spring park Place
> Herndon VA 20170
> 703-742-0585
>
>
> ________________________________
>
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx on behalf of Pat Hayes
> Sent: Mon 7/16/2007 1:30 PM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] confounded models
>
>
>
>
> On Jul 16, 2007, at 4:10 AM, Smith, Barry wrote:
>
>> At 12:14 AM 7/16/2007, Jon Awbrey wrote:
>>> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>>>
>>> BS: If we have a sentence in a biology textbook, say "blood cells
>>> are non-nucleated",
>>> then is this about cells in reality (as I, and I guess common sense,
>>> would assume)
>>> or about cells in the biology model?
>>>
>>> If by "about" we mean something like "applies to" or "true of",
>>> is there any harm in saying that the sentences are about both?
>>
>>
>> So that a full model of the sentences in the biology textbook would
>> have two kinds of cells, real ones and model ones?
>> BS
>>
> Or, a more charitable interpretation might be that one model of the
> sentences might have real cells in it, while another model might have
> model cells in it. Which does indeed seem to be an accurate statement
> about how Tarskian semantics captures a lack of information, by
> allowing more models than may have been intended. The 'model cells'
> might well be called, following mathematical precedent, 'non-
> standard' cells.
>
> Pat
>
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