Defined classes vs Universals
Chris Mungall
I think the defined-class vs universal dichotomy is confusing on
multiple different levels. It mixes separate orthogonal concerns -
information artefacts vs mind-independent things, primitive vs
complex, defined vs undefined, asserted vs inferred hierarchies.
Everyone I've met who has been exposed to the distinction seems
confused. A major part of the confusion is overriding the perfectly
simple term "defined class" to mean something other than "a class that
is defined". I would like the terminology to be changed.
The following OBI document is confused and will lead to further
confusion:
http://obi-ontology.org/page/Defined_classes
It seems to suggest things like using protege to determine whether
something is a universal?
I think there is a potentially useful distinction that is being lost:
the distinction between classes representing patterns repeated in
nature (and thus of interest to science) and classes that are somewhat
arbitrary grouping classes, or grouping classes made for some specific
purpose. But this distinction is tricky, and should not be mixed with
other mundane yet important distinctions.
Let me try and clarify this with two diagrams. The first hierarchy is
of mind-dependent representational artifacts:
Representational Unit
Class
Defined Class
Defined Class, definition specified in formal language
Defined Class, definition specified in FOL or subset of FOL
Defined Class, definition specified in OWL
Defined Class, definition specified in unrestricted FOL
Defined Class, definition specified in natural language or semi-
controlled subset
Undefined Class
Primitive Class
Potentially definable class, definition not specified yet
This isn't necessarily pairwise disjoint (e.g. BFO classes may have
NL, FOL and OWL definitions), nor is it exhaustive (we're not
concerned with extensional vs intensional definitions, or with
partially specified definitions, this is just for illustration). These
are all within the scope of the IAO, and the distinctions made here
are all of some relevance to ontology construction, but of little
relevance outside this field. Hopefully these are reasonably boring
and uncontroversial, and don't involve taking a philosophical stance
about reality or science. There is one point of terminological
confusion, in that "defined class" means "class that has owl
equivalence axiom" to Protege users; however, I think it's important
to recognize other ways of specifying definitions, and to use the term
in the generic sense, and qualify it for added specificity if necessary.
The second hierarchy is of mind-independent entities. Please _don't_
think of this an an ontology or meta-ontology, it's just a diagram to
attempt to clarify some things:
Representation-independent entity
Instance
Instantiation pattern
Universal
Arbitrary pattern
I'm taking the realist position here whereby universals/types exist,
as this is consistent with BFO. Anti-realists may scoff at the notion
of a universal existing outside our minds, but hopefully they will at
least go along with the notion that there are some patterns in nature
that arise through scientific laws. Perhaps not - but the very fact
that this is contentious is one of the reasons we must separate these
two hierarchies.
The implicitly exclusive disjunction "defined class vs universal"
mixes these two hierarchies and conflates numerous unstated
assumptions about what kinds of things in hierarchy 1 can represent
what kinds of things in hierarchy 2.
By separating these hierarchies we can explore certain questions more
coherently:
* Is any undefined class necessarily intended to represent a universal?
* Should reference ontologies contain only classes that represent
universals, or can we have classes that are arbitrary groupings?
* Are universals definable? If so, are there constraints or guidelines
(e.g. genus-differentia style positive conjunction of a named class
and 1 or more differentia)?
* Does the single asserted inheritance hierarchy dictum apply only to
classes representing universals? what about inferred?
Different people will have different opinions on these - others may
think these are all irrelevant points of dogma. These discussions have
been happening, and the confusions arising from these discussions are
clouding the very simple, mundane yet important notion of "defined
class". I suggest we reserve the term "defined class" to mean "a class
that has been defined", as this is how it is understood by the
majority of people outside this esoteric discussion -- and it's
completely obvious!! If we wish to draw separate orthogonal
distinctions then we should make these distinctions apparent in the
name and not pollute existing terminology. For example, something like
"universal class" vs "grouping class" or "arbitrary grouping class".
This all seems fairly obvious, sorry for belaboring the point.
One remaining difficultly is that "defined class" has been pressed
into action to cover cases where a BFO representation is non-obvious.
For example, OGMS places "phenotype" under defined class and there has
been discussion on using "defined class"es to represent "qualities of
processes" such as heartbeats. I wouldn't say these are arbitrary, and
I think any theory of universals that excludes phenotypes or
heartbeats would not be much a theory. I believe that ultimately we'll
have a way of doing justice to these in BFO that renders them as
universals, but this is a bit harder than the simple terminological
suggestion above.
Michel Dumontier
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Michel Dumontier
Associate Professor of Bioinformatics
Carleton University
http://dumontierlab.com
Albert Goldfain
Thanks for the detailed examination of the use of 'defined class'.
I agree that the way OGMS uses it is confusing, so I have opened up
this issue on the OGMS tracker:
http://code.google.com/p/ogms/issues/detail?id=41
I propose we use a better term:
'nonuniversal class' to denote a class that is not a universal in the BFO
sense...i.e., not repeatable in nature
OR, perhaps
'named class' to denote a class that science gives a name to, but
whose status as a
universal has not been determined
-Albert
Bjoern Peters
I very much like your writeup. I have had a hard time personally to make the distinction between a universal and 'arbitrary pattern' in many cases, and confusing that tricky distinction with having the ability to express N&S conditions in OWL has not helped. So your writeup nicely separates those issues.
I am less clear if you are only proposing a terminology which makes it clearer to discuss these issues, or if you are proposing an implementation how we would specify these in OWL. Specifically, were you proposing to create the different 'representational units' as owl:classes in IAO when you said they are in IAO's scope? If so, how would that be referenced by other ontologies such as OBI/OGMS?
Finally: Much of the reason for the confusion in the OBI document you referred to is that this issue is linked with opinions on when is_a assertions should be made. Barry et al asked for a single asserted is_a hierarchy limited to universals. Robert Stevens et al asked not to assert under a class with N&S conditions. There are good reasons for both approaches, but it once again puts philosophy vs. technology. I have been advocating sticking to the Barry approach, and asserting freely under classes with N&S conditions that I consider 'nice' which is a weak way of saying that when challenged I can still not say what a universal is. I can say though that I feel comfortable to assert something under e.g. 'assay', because it is a nice class that I think I fully understand.
- Bjoern
Bjoern Peters
Assistant Member
La Jolla Institute for Allergy and Immunology
9420 Athena Circle
La Jolla, CA 92037, USA
Tel: 858/752-6914
Fax: 858/752-6987
http://www.liai.org/pages/faculty-peters
Bill Hogan
http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
Of course, the OWL usage to refer to something with specified N&S conditions may predate that.
I read something recently that used the labels 'class' and 'category' to refer to what that paper lables 'universals' and 'defined classes'.
I think universal is fine, maybe category is a good term for the latter.
Bill
Pat Hayes
I understand the reasons for confusion around defined classes, but the usage of defined class in the "BFO sense" goes back at least to 2006:
http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
Of course, the OWL usage to refer to something with specified N&S conditions may predate that.
Chris Mungall
On Dec 10, 2009, at 4:28 PM, Bjoern Peters wrote:
> Chris,
>
> I very much like your writeup. I have had a hard time personally to
> make the distinction between a universal and 'arbitrary pattern' in
> many cases, and confusing that tricky distinction with having the
> ability to express N&S conditions in OWL has not helped. So your
> writeup nicely separates those issues.
>
> I am less clear if you are only proposing a terminology which makes
> it clearer to discuss these issues, or if you are proposing an
> implementation how we would specify these in OWL. Specifically, were
> you proposing to create the different 'representational units' as
> owl:classes in IAO when you said they are in IAO's scope? If so, how
> would that be referenced by other ontologies such as OBI/OGMS?
using "defined class" to denote a class that is defined somehow. Then
if we want to ask a question such as "how many defined classes are
there in my ontology" there is no ambiguity in what we're asking.
The natural place to enshrine these would be the ontology-metadata
subset of IAO. But I'm not pushing for that at the moment as there are
probably negative consequences in having metaclasses that are part of
a standard import chain. A reasonable compromise would be an
additional OWL file that is not typically part of an import chain
containing metaclasses such as:
Class: 'defined class'
AnnotationProperties: IAO:definition "A class that is defined by
either an EquivalentClasses axioms, a textual definition (e.g
IAO:definition) or a definition in some other formal language."
For most purposes this file would serve as a kind of formalized
documentation. You might be able to reason with these in OWL full but
that's not really required.
The important thing for me is to stop using "defined class" in an
undefined, confusing way.
> Finally: Much of the reason for the confusion in the OBI document
> you referred to is that this issue is linked with opinions on when
> is_a assertions should be made. Barry et al asked for a single
> asserted is_a hierarchy limited to universals.
universals should be defined in genus-differentia form i.e. X is_a G
that D. Here we have both an asserted is_a hierarchy (X is_a G) and
defined classes (in the simple sense that I have defined).
> Robert Stevens et al asked not to assert under a class with N&S
> conditions. There are good reasons for both approaches, but it once
> again puts philosophy vs. technology. I have been advocating
> sticking to the Barry approach, and asserting freely under classes
> with N&S conditions that I consider 'nice' which is a weak way of
> saying that when challenged I can still not say what a universal is.
> I can say though that I feel comfortable to assert something under
> e.g. 'assay', because it is a nice class that I think I fully
> understand.
Chris Mungall
On Dec 10, 2009, at 12:19 PM, Michel Dumontier wrote:
> Chris,
> First, thanks for this useful contribution!
>
> Second, can you elaborate on "arbitrary pattern" in contrast to
> "universal" with an example?
planet). The class has an extension but the individuals share no
properties other than the trivial one of being in the set union of
cheeseburgers, monkeys and planets.
Less trivial examples arise when we consider real-life ontology
engineering challenges such as when to pre-coordinate and when to post-
coordinate. Most scientists involved in ontology development have an
intuition that "epithelial cell" is a fine named class in an ontology
but "epithelial cell of ulnar side of left pinky" is not, because this
specific type of epipthelial cell as no specific properties other than
the trivial one of being part of the ulnar side of the left pinky. You
can't make interesting statements that would not be applicable at a
more general level. There are also cases where for historical reasons
people have grouped things together somewhat arbitrarily - e.g. the
limbic system. There exist circumstances where it's convenient to name
classes such as these, in which case it can be nice to tag the class
somehow, e.g. as a grouping class. This to me seems to align with what
the original defined class / universal distinction was aiming at.
Pat Hayes
On Dec 11, 2009, at 7:10 PM, Chris Mungall wrote:
>
> On Dec 10, 2009, at 4:28 PM, Bjoern Peters wrote:
>
>> Chris,
>>
>> I very much like your writeup. I have had a hard time personally to
>> make the distinction between a universal and 'arbitrary pattern' in
>> many cases, and confusing that tricky distinction with having the
>> ability to express N&S conditions in OWL has not helped. So your
>> writeup nicely separates those issues.
>>
>> I am less clear if you are only proposing a terminology which makes
>> it clearer to discuss these issues, or if you are proposing an
>> implementation how we would specify these in OWL. Specifically, were
>> you proposing to create the different 'representational units' as
>> owl:classes in IAO when you said they are in IAO's scope? If so, how
>> would that be referenced by other ontologies such as OBI/OGMS?
>
> Primarily I'd like us to standardize on the terminology and agree on
> using "defined class" to denote a class that is defined somehow.
not defined *somehow*, so this would seem to include all classes. If
on the other hand you want to restrict this to some particular form
for the definition, I doubt if the concept will be of much use (and
will in any case be hostage to which way the 'definitions' are read.
If I simply assert that two classes are each N&S for inclusion in the
other (owl:EquivalentClass) then which of them is the definer and
which the definee?)
I have a larger question about this. What does it matter? Suppose for
a moment we simply ignore the distinction between non-defined classes
and defined classes, and eliminate it from the ontology. What other
entailments would we no longer be able to make, or would give the
wrong answer? I suspect that the answer is, none. In which case, let
us simply ignore this issue as a timewasting irrelevance. (And if
there is a meaningful answer, it might help us to clarify what the
intended distinction really is.)
> Then
> if we want to ask a question such as "how many defined classes are
> there in my ontology" there is no ambiguity in what we're asking.
more class definitions to an ontology, or to recast it with more or
fewer definitions, but with no essential change.
Pat
Chris Mungall
On Dec 11, 2009, at 4:50 AM, Bill Hogan wrote:
> I understand the reasons for confusion around defined classes, but
> the usage of defined class in the "BFO sense" goes back at least to
> 2006:
>
> http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
exception of the paragraph on defined classes.
> Of course, the OWL usage to refer to something with specified N&S
> conditions may predate that.
http://www.google.com/search?q=%22defined+class%22+ontology&btnG=Search&hl=en
But I think the usage goes way beyond OWL, OWL doesn't have exclusive
rights over the terms "defined" and "class"
> I read something recently that used the labels 'class' and
> 'category' to refer to what that paper lables 'universals' and
> 'defined classes'.
I think the principle of least surprise is a good one. Barry advocates
the use of the word "universal" because it is so alien to most people
they will not be surprised to hear it used to mean something they
didn't expect. By the same principle we should reject surprising
definitions of "defined class", "class" or "category".
> I think universal is fine, maybe category is a good term for the
> latter.
http://plato.stanford.edu/entries/aristotle-categories/
Chris Mungall
On Dec 11, 2009, at 5:41 PM, Pat Hayes wrote:
>
> On Dec 11, 2009, at 7:10 PM, Chris Mungall wrote:
>
>>
>> On Dec 10, 2009, at 4:28 PM, Bjoern Peters wrote:
>>
>>> Chris,
>>>
>>> I very much like your writeup. I have had a hard time personally to
>>> make the distinction between a universal and 'arbitrary pattern' in
>>> many cases, and confusing that tricky distinction with having the
>>> ability to express N&S conditions in OWL has not helped. So your
>>> writeup nicely separates those issues.
>>>
>>> I am less clear if you are only proposing a terminology which makes
>>> it clearer to discuss these issues, or if you are proposing an
>>> implementation how we would specify these in OWL. Specifically, were
>>> you proposing to create the different 'representational units' as
>>> owl:classes in IAO when you said they are in IAO's scope? If so, how
>>> would that be referenced by other ontologies such as OBI/OGMS?
>>
>> Primarily I'd like us to standardize on the terminology and agree on
>> using "defined class" to denote a class that is defined somehow.
>
> The problem I have with this idea is, I cannot imagine a class that is
> not defined *somehow*, so this would seem to include all classes.
the definition is explicitly stated. There are many classes in many
ontologies whose definitions are not explicitly stated.
> If
> on the other hand you want to restrict this to some particular form
> for the definition, I doubt if the concept will be of much use (and
> will in any case be hostage to which way the 'definitions' are read.
> If I simply assert that two classes are each N&S for inclusion in the
> other (owl:EquivalentClass) then which of them is the definer and
> which the definee?)
> I have a larger question about this. What does it matter? Suppose for
> a moment we simply ignore the distinction between non-defined classes
> and defined classes, and eliminate it from the ontology. What other
> entailments would we no longer be able to make, or would give the
> wrong answer? I suspect that the answer is, none. In which case, let
> us simply ignore this issue as a timewasting irrelevance. (And if
> there is a meaningful answer, it might help us to clarify what the
> intended distinction really is.)
distinction is useful, the term "defined class" is quite clearly in
common use. One group of people are using it one way, and another is
using it another way, and another larger group is picking up bits and
pieces of both and getting confused. My initial email was just an
attempt to eliminate some of that confusion.
As it happens I think that making a distinction between defined and
undefined classes is plainly useful. We don't have to ontologize the
distinction, or use a reasoner to make entailments. There are simpler
ways of checking if a class is defined.
>> Then
>> if we want to ask a question such as "how many defined classes are
>> there in my ontology" there is no ambiguity in what we're asking.
>
> True, but that is a very silly question to ask. It is trivial to add
> more class definitions to an ontology, or to recast it with more or
> fewer definitions, but with no essential change.
undefined classes from a bunch of different ontologies I use
regularly. Can you quickly recast them for me?
Pat Hayes
Actually, the CLASSIC literature I have, and most of the following DL literature including the DL handbook, all talk about concepts and descriptions and even structured descriptions (where the latter two seem to refer to logical axioms about concepts that specify necessary plus/minus sufficient conditions).
Even the syntax in those languages used concept, e.g., operators like def-concept or def-prim-concept.
The switch to the usage of 'class' seems to me to have occurred with OWL, but I could be wrong.
Bill
Bill Hogan
Pat Hayes
When I looked up the word 'class' in the index of the DL Handbook, it was in the context of entity relationship modeling. That, UML, and object-oriented programming languages' use of the word, is my best guess. Some of the original RDFS W3C standards reference UML....
Jonathan Rees
same question came up in a fight I had with the OWL 2 WG. They wanted
a "class" to be a symbol (something that is written in one particular
way, can be upper or lower case, is used in formulas, etc.), and I
wanted it to be what the symbol referred to (something that has
members, might be infinite, etc.). They won, and one WG member
dismissed me by asserting that no one would be confused by the
overloading. This thread proves them wrong.
So, to reexpress Chris's hierarchy, if "class1" is the former and
"class2" the latter, then a class1 might have the property that
ontology O (1) gives it a definition or not, and (2) if it does,
whether the definition is prose or formally necessary and sufficient
conditions. A class2 might have the property that it is a subclass of
some other class, and so on. And a class1 would be "about" or would
"refer to" or "name" (etc.) a class2, in O. (The purpose of using URIs
for class1s is to remove the annoyance of having to provide the
qualifier "in O".)
If I were to try to characterize the two communities that use the word
"class" in these two different ways, I'd say the former are logicians
while the latter are mathematicians. I cannot claim to be either but I
think I have more affinity with the mathematicians.
Jonathan
Pat Hayes
philosophical debates. Certainly I have never come across any
discussion of the issue in any other ontology forum. DL-based
ontologies define classes all over the place without making any fuss
about the distinction.
> One group of people are using it one way, and another is
> using it another way, and another larger group is picking up bits and
> pieces of both and getting confused. My initial email was just an
> attempt to eliminate some of that confusion.
at hand, viz. building an ontology, why does anyone really care?
>
> As it happens I think that making a distinction between defined and
> undefined classes is plainly useful.
being a syntactic accident. Hence my meta-question.
> We don't have to ontologize the
> distinction, or use a reasoner to make entailments.
care about it at all?
> There are simpler
> ways of checking if a class is defined.
>
>>> Then
>>> if we want to ask a question such as "how many defined classes are
>>> there in my ontology" there is no ambiguity in what we're asking.
>>
>> True, but that is a very silly question to ask. It is trivial to add
>> more class definitions to an ontology, or to recast it with more or
>> fewer definitions, but with no essential change.
>
> If only it were a silly question. I can give you a list of some 100k
> undefined classes from a bunch of different ontologies I use
> regularly. Can you quickly recast them for me?
expect I could, yes. For example, If An subclass Bn, both undefined,
then invent a C with An equal (Bn intersect C). (C is the union over n
of the relative complement of Bn with An, assuming some disjointness
conditions on the Bn.) Now the An are defined classes. Of course,
nothing has really changed. Which was my point.
Pat
Barry Smith
there will be certain reference ontologies, roughly corresponding to
the basic biological sciences, with terms like 'cell', 'organ',
'protein', 'population', 'glucose', and so forth, and then certain
application ontologies, which will as far as possible create their
terms through compositions from the reference ontologies and through
terms referring to instances in reality, such as 'population of
Buffalo residents on 1/1/2010 with elevated blood glucose'.
The latter we know how to define; for them it seems clear that the
corresponding extensions (sets of instances) are what is primary ; so
we have been calling them, provisionally, 'defined classes'. I, too,
still have worried about the latter term, but we are working on an
improved framework.
For the former it seems equally clear that the extensions are NOT primary:
[A] a instance_of cell
does not hold because a is a member of the set of cells. Rather a is
a member of that set, because [A] is true. [A], we say, asserts a
relation between a certain instance and a certain type or universal.
The OBO reference ontologies concern themselves with types in given
domains, just as physics, for instance, concerns itself with types
such as force or matter.
> >
> > As it happens I think that making a distinction between defined and
> > undefined classes is plainly useful.
>
>I disagree. I think the distinction has no real import and is close to
>being a syntactic accident. Hence my meta-question.
>
> > We don't have to ontologize the
> > distinction, or use a reasoner to make entailments.
>
>But if *no* entailments are affected by the distinction, why do we
>care about it at all?
such a way that we can distinguish the basic from the non-basic (just
as it is a very fruitful way to organize medical education by having
everyone learn molecular biology and anatomy, but have only some
people use their knowledge of those things in order to learn, say,
pediatric oncology or orthodontology).
> > There are simpler
> > ways of checking if a class is defined.
> >
> >>> Then
> >>> if we want to ask a question such as "how many defined classes are
> >>> there in my ontology" there is no ambiguity in what we're asking.
> >>
> >> True, but that is a very silly question to ask. It is trivial to add
> >> more class definitions to an ontology, or to recast it with more or
> >> fewer definitions, but with no essential change.
> >
> > If only it were a silly question. I can give you a list of some 100k
> > undefined classes from a bunch of different ontologies I use
> > regularly. Can you quickly recast them for me?
>
>I have better things to do, but if there is any regularity to them I
>expect I could, yes. For example, If An subclass Bn, both undefined,
>then invent a C with An equal (Bn intersect C). (C is the union over n
>of the relative complement of Bn with An, assuming some disjointness
>conditions on the Bn.) Now the An are defined classes. Of course,
>nothing has really changed. Which was my point.
on treating A, B, C as extensions, from the start. Distinguishing
universals/types from defined classes precisely denies the
appropriateness of this treatment. See, again, the discussion here:
http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
BS
Chris Mungall
standard tutorial for Protege OWL makes the distinction quite prominent.
>> One group of people are using it one way, and another is
>> using it another way, and another larger group is picking up bits and
>> pieces of both and getting confused. My initial email was just an
>> attempt to eliminate some of that confusion.
>
> Fair enough, but if this confusion has no bearing on the actual
> matter at hand, viz. building an ontology, why does anyone really
> care?
>> As it happens I think that making a distinction between defined and
>> undefined classes is plainly useful.
>
> I disagree. I think the distinction has no real import and is close
> to being a syntactic accident. Hence my meta-question.
>> We don't have to ontologize the
>> distinction, or use a reasoner to make entailments.
>
> But if *no* entailments are affected by the distinction, why do we
> care about it at all?
classes have textual definitions because if they do not then people
will use them in different ways leading to inconsistent data. If the
classes have N+S conditions in languages like OWL or FOL then we can
leverage reasoners more. It's as simple as that.
>> There are simpler
>> ways of checking if a class is defined.
>>
>>>> Then
>>>> if we want to ask a question such as "how many defined classes are
>>>> there in my ontology" there is no ambiguity in what we're asking.
>>>
>>> True, but that is a very silly question to ask. It is trivial to add
>>> more class definitions to an ontology, or to recast it with more or
>>> fewer definitions, but with no essential change.
>>
>> If only it were a silly question. I can give you a list of some 100k
>> undefined classes from a bunch of different ontologies I use
>> regularly. Can you quickly recast them for me?
>
> I have better things to do, but if there is any regularity to them I
> expect I could, yes. For example, If An subclass Bn, both undefined,
> then invent a C with An equal (Bn intersect C). (C is the union over
> n of the relative complement of Bn with An, assuming some
> disjointness conditions on the Bn.) Now the An are defined classes.
> Of course, nothing has really changed. Which was my point.
loopholes involving trivially defined classs, e.g. definitions should
not be circular, or at least certain types of definitions should not
be circular. Fairly trivial but this is straying from the point.
Chris Mungall
know how to define precisely, and for others we at least make attempts
at natural language definitions, as can be seen in existing
ontologies. And given that 'cell', 'organ', 'protein', 'glucose' and
so on all have representations as owl:Classes, we end up with confusion.
I'm glad that 'defined class' in the sense you are using it here is
provisional, I hope we can find a better alternative term soon to
avoid more discussions like this one..
Pat Hayes
[A], are exactly equivalent, by definition, assuming the usual formal
semantics for our formalisms. To claim that one of the is the cause of
the other is meaningless. 7= 3 + 4, but it does not make sense to ask
whether 7 is 7 because it is 3 more than 4, or 4 is 4 because it is 3
less than 7.
> [A], we say, asserts a
> relation between a certain instance and a certain type or universal.
> The OBO reference ontologies concern themselves with types in given
> domains, just as physics, for instance, concerns itself with types
> such as force or matter.
science. And in any case, I do not believe that physics thinks of
force and matter as 'types'.
>
>>>
>>> As it happens I think that making a distinction between defined and
>>> undefined classes is plainly useful.
>>
>> I disagree. I think the distinction has no real import and is close
>> to
>> being a syntactic accident. Hence my meta-question.
>>
>>> We don't have to ontologize the
>>> distinction, or use a reasoner to make entailments.
>>
>> But if *no* entailments are affected by the distinction, why do we
>> care about it at all?
>
> Because it proves to be a very fruitful way to organize ontologies in
> such a way that we can distinguish the basic from the non-basic
distinction between basic (undefined) and non-basic (defined), that
the distinction is artificial and arbitrary. It is no reply to simply
use this very distinction in arguing against my claim.
> (just
> as it is a very fruitful way to organize medical education by having
> everyone learn molecular biology and anatomy, but have only some
> people use their knowledge of those things in order to learn, say,
> pediatric oncology or orthodontology).
upon knowledge gained in the more general ones. (Or at any rate, that
is the assumption: in practice, this is often somewhat of an
idealization, as any educator will attest.) But what has this got to
do with ontologies? (Unless you are presuming that ontologies will be
used in education? That is an interesting idea, but a novel one to me.)
>
>>> There are simpler
>>> ways of checking if a class is defined.
>>>
>>>>> Then
>>>>> if we want to ask a question such as "how many defined classes are
>>>>> there in my ontology" there is no ambiguity in what we're asking.
>>>>
>>>> True, but that is a very silly question to ask. It is trivial to
>>>> add
>>>> more class definitions to an ontology, or to recast it with more or
>>>> fewer definitions, but with no essential change.
>>>
>>> If only it were a silly question. I can give you a list of some 100k
>>> undefined classes from a bunch of different ontologies I use
>>> regularly. Can you quickly recast them for me?
>>
>> I have better things to do, but if there is any regularity to them I
>> expect I could, yes. For example, If An subclass Bn, both undefined,
>> then invent a C with An equal (Bn intersect C). (C is the union
>> over n
>> of the relative complement of Bn with An, assuming some disjointness
>> conditions on the Bn.) Now the An are defined classes. Of course,
>> nothing has really changed. Which was my point.
>
> On the strategy we are taking this trick won't work, since it rests
> on treating A, B, C as extensions, from the start.
(like RDFS), provided that it allows the definition of classes using
'and' and 'union' and exclusion.
Look, as far as the formalisms are concerned, all classes are simply
classes. Chris appeared to be arguing that some classes are
distinguished from others by virtue of being 'defined'. My point was
that this distinction is largely accidental, and that trivial re-
compositions, amounting to a slightly different choice of
formalization style, will change 'defined' to 'not-defined'. Hence,
the argument goes, this distinction as stated has very little merit or
utility.
It appears that being defined is not, however, of primary importance:
rather, the key distinction is between 'universals' and mere classes.
On this more philosophical point, I actually disagree: I simply don't
believe in 'universals'. But my present point is that whatever the
merits of this distinction, it is not one that is reflected in
anything in the formal axioms of any ontology, or that has any
consequences for any entailments. So, purely on these grounds, I
suggest, it is not a matter that should be being discussed here.
> Distinguishing
> universals/types from defined classes precisely denies the
> appropriateness of this treatment.
I will be happy to do, precisely rejects that denial.
Yes, I have read that, and disagree with much of it. Indeed, it may be
that we are not agreeing on the very definition of what an ontology
is, since the definition given there refers to 'universals', a notion
I find quite uncongenial. I prefer Gruber's original definition of
'ontology' : a formalization of a conceptualization.
Pat
Pat Hayes
simply because the Protege interface provides a handy way to create an
N&S definition. But it defines its notion crisply and unambiguously,
and provides no exegesis of it as being a terribly significant
distinction. I would also add, that this notion makes sense only
within a given ontology. A class may be N&S-defined in one ontology
but not in another, even though the two ontologies are formally
equivalent. Which was what I meant by 'syntactic accident', by the way.
(I have not checked, but if I simply assert that :A
owl:equivalentClass :B, does Protege consider them both to be defined
classes? That would seem to follow from what the tutorial says.)
But maybe this is irrelevant to your original terminological point, in
which case I apologize for muddying the water.
Pat
Barry Smith
formalisms to define the domain over which
variables x, y, z, ... range to include both
individuals (this cell, that cell) and the
universals (cell, cell membrane, ...) which these
individuals instantiate. Let us embrace this
view, defended at length here:
<http://ontology.buffalo.edu/bfo/Against_Fantology.pdf>http://ontology.buffalo.edu/bfo/Against_Fantology.pdf.
(1) 'a instance_of cell' then has the logical form: instance_of(a, cell)
(2) 'a member-of the set of cells' has the
logical form: a € {x | x instance_of(a, cell)}
and you are right that the two are equivalent.
And to understand either you need to understand
what it means to say that a is an instance of the universal cell.
Note that in other cases, to say that 'a
member-of B' does not have that logical form. For instance
(3) 1 member-of {1, 2, 3}
>>[A], we say, asserts a
>>relation between a certain instance and a certain type or universal.
>>The OBO reference ontologies concern themselves with types in given
>>domains, just as physics, for instance, concerns itself with types
>>such as force or matter.
>
>Bad analogy. Physics is science. Ontologies are not themselves
>science.
>And in any case, I do not believe that physics thinks of
>force and matter as 'types'.
>>>>As it happens I think that making a distinction between defined and
>>>>undefined classes is plainly useful.
>>>
>>>I disagree. I think the distinction has no real import and is close
>>>to
>>>being a syntactic accident. Hence my meta-question.
>>>
>>>>We don't have to ontologize the
>>>>distinction, or use a reasoner to make entailments.
>>>
>>>But if *no* entailments are affected by the distinction, why do we
>>>care about it at all?
>>
>>Because it proves to be a very fruitful way to organize ontologies in
>>such a way that we can distinguish the basic from the non-basic
>
>This is a circular answer. I am claiming that there is no useful
>distinction between basic (undefined) and non-basic (defined), that
>the distinction is artificial and arbitrary. It is no reply to simply
>use this very distinction in arguing against my claim.
>>(just
>>as it is a very fruitful way to organize medical education by having
>>everyone learn molecular biology and anatomy, but have only some
>>people use their knowledge of those things in order to learn, say,
>>pediatric oncology or orthodontology).
>
>Because in these cases, the more specialized areas presume and rely
>upon knowledge gained in the more general ones. (Or at any rate, that
>is the assumption: in practice, this is often somewhat of an
>idealization, as any educator will attest.) But what has this got to
>do with ontologies? (Unless you are presuming that ontologies will be
>used in education? That is an interesting idea, but a novel one to me.)
favored reference ontology for anatomy, currently being refactored in OWL:
>The FMA, by contrast, is a hybrid between ...
>traditional sources of anatomical information:
>its intent is to encode anatomical knowledge
>that can be reused for any application to serve
>the needs of any user group. Moreover, it is
>qualitatively distinct from traditional sources
>in that it encodes anatomical knowledge in a way
>that can support machine-based inference, a
>requirement for the development of
>next-generation, “smart” applications in
>education, clinical practice and research.
The whole idea is developed at length here:
<http://sigpubs.biostr.washington.edu/archive/00000204/01/FMA_Chapter_final.pdf>http://sigpubs.biostr.washington.edu/archive/00000204/01/FMA_Chapter_final.pdf
>>>>There are simpler
>>>>ways of checking if a class is defined.
>>>>
>>>>>>Then
>>>>>>if we want to ask a question such as "how many defined classes are
>>>>>>there in my ontology" there is no ambiguity in what we're asking.
>>>>>
>>>>>True, but that is a very silly question to ask. It is trivial to
>>>>>add
>>>>>more class definitions to an ontology, or to recast it with more or
>>>>>fewer definitions, but with no essential change.
>>>>
>>>>If only it were a silly question. I can give you a list of some 100k
>>>>undefined classes from a bunch of different ontologies I use
>>>>regularly. Can you quickly recast them for me?
>>>
>>>I have better things to do, but if there is any regularity to them I
>>>expect I could, yes. For example, If An subclass Bn, both undefined,
>>>then invent a C with An equal (Bn intersect C). (C is the union
>>>over n
>>>of the relative complement of Bn with An, assuming some disjointness
>>>conditions on the Bn.) Now the An are defined classes. Of course,
>>>nothing has really changed. Which was my point.
>>
>>On the strategy we are taking this trick won't work, since it rests
>>on treating A, B, C as extensions, from the start.
>
>No, it would work even in a theory which treats classes intensionally
>(like RDFS), provided that it allows the definition of classes using
>'and' and 'union' and exclusion.
full-fledged entities in the domain of variables
x, y, z, ... (normally, but we can now see overly
restrictedly, referred to as 'individual
variables') is that we can do justice to the idea
that, while classes can be trivially defined
using 'union', etc., this is not so for
universals; there is no universal 'rabbit or molecule'.
>Look, as far as the formalisms are concerned, all classes are simply
>classes.
>Chris appeared to be arguing that some classes are
>distinguished from others by virtue of being 'defined'. My point was
>that this distinction is largely accidental, and
>that trivial re- compositions, amounting to a slightly different choice of
>formalization style, will change 'defined' to 'not-defined'. Hence,
>the argument goes, this distinction as stated has very little merit or
>utility.
>
>It appears that being defined is not, however, of primary importance:
>rather, the key distinction is between 'universals' and mere classes.
>On this more philosophical point, I actually disagree: I simply don't
>believe in 'universals'. But my present point is that whatever the
>merits of this distinction, it is not one that is reflected in
>anything in the formal axioms of any ontology, or that has any
>consequences for any entailments. So, purely on these grounds, I
>suggest, it is not a matter that should be being discussed here.
(4) some universal exists
Not however from (3).
>>Distinguishing
>>universals/types from defined classes precisely denies the
>>appropriateness of this treatment.
>
>And denying the distinction between universals and defined classes, as
>I will be happy to do, precisely rejects that denial.
>
>>See, again, the discussion here:
>>http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
>
>Yes, I have read that, and disagree with much of it. Indeed, it may be
>that we are not agreeing on the very definition of what an ontology
>is, since the definition given there refers to 'universals', a notion
>I find quite uncongenial. I prefer Gruber's original definition of
>'ontology' : a formalization of a conceptualization.
Gruber, by the biologists (Michael Ashburner et
al.) in 1999, they fortunately did not make the
Gruberite mistake of supposing that ontology
terms refer to concepts (whatever they are). (I
do not believe that Gruber himself made this
mistake, incidentally.) It would indeed be odd to
suppose, for instance, that when we say that
TLR2 -MyD88 ligand binding precedes TLR2 -MyD88
binding in the TLR2 signalling pathway
which is the sort of thing bio-ontologists do
say, then they are talking about some sort of temporal order among concepts.
BS
Pat Hayes
Indeed, let us do so. (I have to interpret 'universal' here as meaning
'relation', but am then happy to agree.)
> defended at length here: <http://ontology.buffalo.edu/bfo/Against_Fantology.pdf
> >http://ontology.buffalo.edu/bfo/Against_Fantology.pdf.
>
> (1) 'a instance_of cell' then has the logical form: instance_of(a,
> cell)
>
> (2) 'a member-of the set of cells' has the logical form: a • {x | x
> instance_of(a, cell)}
I think it is: a member {x | instance_of(x, cell) )
>
> and you are right that the two are equivalent.
And they are *necessarily* equivalent, if the first is understood in
the standard Tarskian way (ie if the formalism which appears to be FOL
is in fact FOL.) And, by the way, this has nothing at all to do with
instance_of: it would apply to any other atomic sentence.
> And to understand either you need to understand what it means to say
> that a is an instance of the universal cell.
Well, no, I disagree. Or rather, I think I disagree; because I believe
I do understand instance_of(a, cell), but I have no idea what a
universal is.
>
> Note that in other cases, to say that 'a member-of B' does not have
> that logical form. For instance
>
> (3) 1 member-of {1, 2, 3}
But it is easy to re-cast this into the required form:
1 member { x | (x=1 or x=2 or x=3 )
The logical form itself conveys nothing of importance.
>
>>> [A], we say, asserts a
>>> relation between a certain instance and a certain type or universal.
>>> The OBO reference ontologies concern themselves with types in given
>>> domains, just as physics, for instance, concerns itself with types
>>> such as force or matter.
>>
>> Bad analogy. Physics is science. Ontologies are not themselves
>> science.
>
> Not yet.
:-) They never will be. They may be of help in science, but I rather
think not, actually, as scientists are usually somewhat ahead of the
formalizers when it comes to thinking their ideas through carefully.
I defer to your more intimate acquaintance with universals. Never
having come across any, I wouldn't know. I'd be interested to know how
you recognize them and distinguish them from mere classes. Is it
something about the way they are described?
>
>> Look, as far as the formalisms are concerned, all classes are simply
>> classes.
>
> See above.
>
>> Chris appeared to be arguing that some classes are
>> distinguished from others by virtue of being 'defined'. My point was
>> that this distinction is largely accidental, and that trivial re-
>> compositions, amounting to a slightly different choice of
>> formalization style, will change 'defined' to 'not-defined'. Hence,
>> the argument goes, this distinction as stated has very little merit
>> or
>> utility.
>>
>> It appears that being defined is not, however, of primary importance:
>> rather, the key distinction is between 'universals' and mere classes.
>> On this more philosophical point, I actually disagree: I simply don't
>> believe in 'universals'. But my present point is that whatever the
>> merits of this distinction, it is not one that is reflected in
>> anything in the formal axioms of any ontology, or that has any
>> consequences for any entailments. So, purely on these grounds, I
>> suggest, it is not a matter that should be being discussed here.
>
> From (2) we can infer:
>
> (4) some universal exists
? How? (2) doesn't mention universals. But in any case, if the only
thing that can be inferred, by inserting a theory of fongles into our
ontology, is that fongles exist, then I would view this as prima facia
evidence that the notion of fongledom is not especially useful.
>
> Not however from (3).
>
>
>>> Distinguishing
>>> universals/types from defined classes precisely denies the
>>> appropriateness of this treatment.
>>
>> And denying the distinction between universals and defined classes,
>> as
>> I will be happy to do, precisely rejects that denial.
>>
>>> See, again, the discussion here:
>>> http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
>>
>> Yes, I have read that, and disagree with much of it. Indeed, it may
>> be
>> that we are not agreeing on the very definition of what an ontology
>> is, since the definition given there refers to 'universals', a notion
>> I find quite uncongenial. I prefer Gruber's original definition of
>> 'ontology' : a formalization of a conceptualization.
> When ontology was re-invented, independently of Gruber, by the
> biologists (Michael Ashburner et al.) in 1999
FOFL. Ontology was invented by biologists in 1999?? No wonder BFO is
such a shambles.
> , they fortunately did not make the Gruberite mistake of supposing
> that ontology terms refer to concepts (whatever they are). (I do not
> believe that Gruber himself made this mistake, incidentally.)
Of course he did not, and neither did anyone else back in the 1970s
when all this work was being started. I have no idea where you get
this idea from, or why you describe it as 'Gruberite'. The point of
Gruber's definition is that any ontology must be based upon, and be a
formalization of, a particular way of thinking and describing the
world. From which it is a small step to the realization that no
ontology is a definitive description of reality as such; all
ontologies admit of alternatives, which have (at least a priori) an
equal claim to be veridical descriptions of the same reality. This is
not to say that these alternative descriptions are descriptions OF
concepts, of course. Surely you, who expound this very idea in your
SNAP/SPAN papers, would agree with Gruber here.
> It would indeed be odd to suppose, for instance, that when we say that
>
> TLR2™-MyD88 ligand binding precedes TLR2™-MyD88 binding in the TLR2
> signalling pathway
>
> which is the sort of thing bio-ontologists do say, then they are
> talking about some sort of temporal order among concepts.
Of course, that would be ridiculous. Nobody has ever suggested such an
idea, AFAIK.
Pat
> BS
Barry Smith
yes
> >
> > and you are right that the two are equivalent.
>
>And they are *necessarily* equivalent, if the first is understood in
>the standard Tarskian way (ie if the formalism which appears to be FOL
>is in fact FOL.) And, by the way, this has nothing at all to do with
>instance_of: it would apply to any other atomic sentence.
Yes
> > And to understand either you need to understand what it means to say
> > that a is an instance of the universal cell.
>
>Well, no, I disagree. Or rather, I think I disagree; because I believe
>I do understand instance_of(a, cell), but I have no idea what a
>universal is.
[B] universal(x) =def. for some y, instance_of(y, x)
> >
> > Note that in other cases, to say that 'a member-of B' does not have
> > that logical form. For instance
> >
> > (3) 1 member-of {1, 2, 3}
>
>But it is easy to re-cast this into the required form:
>
>1 member { x | (x=1 or x=2 or x=3 )
Let me rephrase. Not every
a member_of B
has the unpacked form:
[A] a € {x | instance_of(x, u)}
for some universal u.
>The logical form itself conveys nothing of importance.
Whatever you call the form of [A] the stuff after
the '|' conveys something of importance to this
argument. If you think that it does not, then YOUR argument is of the form:
There are no such things as universals because
whenever you attempt to talk about them I will
say that what you say conveys nothing of
importance. And you can do better than that. I would have hoped.
> >
> >>> [A], we say, asserts a
> >>> relation between a certain instance and a certain type or universal.
> >>> The OBO reference ontologies concern themselves with types in given
> >>> domains, just as physics, for instance, concerns itself with types
> >>> such as force or matter.
> >>
> >> Bad analogy. Physics is science. Ontologies are not themselves
> >> science.
> >
> > Not yet.
>
>:-) They never will be. They may be of help in science, but I rather
>think not, actually, as scientists are usually somewhat ahead of the
>formalizers when it comes to thinking their ideas through carefully.
I think that we can shoot for ontology being a
science in something like the way computer
science is a science. But my point is in fact
more trivial than that. It is that bio-ontologies
such as the Gene Ontology are already a part of
biological science in something like the way
textbooks of biology are a part of biological
science. (The established part, of course.)
> >> development of next-generation, „smart‰ applications in in education,
Take any textbook in a natural science and look
at the common nouns in the index. Most of them
name universals. If you know some science, you
know some students. And imagine, you have been
speaking prose all your life without knowing it.
> >
> >> Look, as far as the formalisms are concerned, all classes are simply
> >> classes.
> >
> > See above.
> >
> >> Chris appeared to be arguing that some classes are
> >> distinguished from others by virtue of being 'defined'. My point was
> >> that this distinction is largely accidental, and that trivial re-
> >> compositions, amounting to a slightly different choice of
> >> formalization style, will change 'defined' to 'not-defined'. Hence,
> >> the argument goes, this distinction as stated has very little merit
> >> or
> >> utility.
> >>
> >> It appears that being defined is not, however, of primary importance:
> >> rather, the key distinction is between 'universals' and mere classes.
> >> On this more philosophical point, I actually disagree: I simply don't
> >> believe in 'universals'. But my present point is that whatever the
> >> merits of this distinction, it is not one that is reflected in
> >> anything in the formal axioms of any ontology, or that has any
> >> consequences for any entailments. So, purely on these grounds, I
> >> suggest, it is not a matter that should be being discussed here.
> >
> > From (2) we can infer:
> >
> > (4) some universal exists
>
>? How? (2) doesn't mention universals.
See [B] above. (Admittedly added later, here, but
present everywhere in the published versions of the above argument.)
>But in any case, if the only
>thing that can be inferred, by inserting a theory of fongles into our
>ontology, is that fongles exist, then I would view this as prima facia
>evidence that the notion of fongledom is not especially useful.
'... or that has any consequences for any
entailments ...' the man said. And I was rather
hoping that the man would agree that one
counterexample to a universal claim would suffice
to refute it. But now I see that you take refuge
in the 'not important' argument. Why so many
names for universals in the indexes of scientific
texts, I wonder. And why so many giant
bio-ontologies which claim to be representing universals ...
> >
> > Not however from (3).
> >
> >
> >>> Distinguishing
> >>> universals/types from defined classes precisely denies the
> >>> appropriateness of this treatment.
> >>
> >> And denying the distinction between universals and defined classes,
> >> as
> >> I will be happy to do, precisely rejects that denial.
> >>
> >>> See, again, the discussion here:
> >>> http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
> >>
> >> Yes, I have read that, and disagree with much of it. Indeed, it may
> >> be
> >> that we are not agreeing on the very definition of what an ontology
> >> is, since the definition given there refers to 'universals', a notion
> >> I find quite uncongenial. I prefer Gruber's original definition of
> >> 'ontology' : a formalization of a conceptualization.
> > When ontology was re-invented, independently of Gruber, by the
> > biologists (Michael Ashburner et al.) in 1999
>
>FOFL. Ontology was invented by biologists in 1999?? No wonder BFO is
>such a shambles.
I said 're-invented'.
google 'ontology' and the 3rd and 4th items on
page 1 are both bio-ontologists, the first first
put together in 1999, the second put together by
the same people a couple of years later. The next
named ontology, much further down the list, is
the Plant Ontology, from the same shop, and so it goes.
> > , they fortunately did not make the Gruberite mistake of supposing
> > that ontology terms refer to concepts (whatever they are). (I do not
> > believe that Gruber himself made this mistake, incidentally.)
>
>Of course he did not, and neither did anyone else back in the 1970s
>when all this work was being started. I have no idea where you get
>this idea from, or why you describe it as 'Gruberite'.
'twas you who introduced Gruber. I use
'Gruberite' to bundle together those views which
see ontologies as representations of concepts (in
a sense still, in my view, not coherently
explained), views which often cite Gruber
(incorrectly in my view). I will use
pseudo-Gruberian in future if this will make you happy.
>The point of
>Gruber's definition is that any ontology must be based upon, and be a
>formalization of, a particular way of thinking and describing the
>world.
If you like, yes.
> From which it is a small step to the realization that no
>ontology is a definitive description of reality as such;
no science, either, my lad
>all
>ontologies admit of alternatives, which have (at least a priori) an
>equal claim to be veridical descriptions of the same reality.
true of scientific theories, too, I guess
>This is
>not to say that these alternative descriptions are descriptions OF
>concepts, of course. Surely you, who expound this very idea in your
>SNAP/SPAN papers, would agree with Gruber here.
I agree. My fight is with the pseudo-Gruberians.
> > It would indeed be odd to suppose, for instance, that when we say that
> >
> > TLR2™-MyD88 ligand binding precedes TLR2™-MyD88 binding ig in the TLR2
> > signalling pathway
> >
> > which is the sort of thing bio-ontologists do say, then they are
> > talking about some sort of temporal order among concepts.
>
>Of course, that would be ridiculous. Nobody has ever suggested such an
>idea, AFAIK.
There are government standards which say exactly
such things. I could give you a long, long list, but let these suffice:
Geographic Area isa Idea or Concept
Body Space or Junction isa Idea or Concept
Amino Acid Sequence isa Idea or Concept
Body Location or Region isa Idea or Concept
Body System isa Idea or Concept
While the cardiovascular system is an idea or
concept; the heart, you'll be reassured to learn
(or perhaps not, given your eventist tendencies, is a physical object)
From http://www.nlm.nih.gov/pubs/factsheets/umlssemn.html
If you hadn't heard about these pseudo-Gruberian
monsters before today, you should get out more.
BS
Larry Hunter
On Dec 16, 2009, at 8:27 PM, Barry Smith wrote:
> At 09:42 PM 12/16/2009, Pat Hayes wrote:
>> On Dec 14, 2009, at 3:26 PM, Barry Smith wrote:
>>> At 10:37 PM 12/13/2009, Pat Hayes wrote:
>>>> On Dec 13, 2009, at 10:43 AM, Barry Smith wrote:
>>
>>>> Bad analogy. Physics is science. Ontologies are not themselves
>>>> science.
>>>
>>> Not yet.
>>
>> :-) They never will be. They may be of help in science, but I rather
>> think not, actually, as scientists are usually somewhat ahead of the
>> formalizers when it comes to thinking their ideas through carefully.
>
> I think that we can shoot for ontology being a
> science in something like the way computer
> science is a science. But my point is in fact
> more trivial than that. It is that bio-ontologies
> such as the Gene Ontology are already a part of
> biological science in something like the way
> textbooks of biology are a part of biological
> science. (The established part, of course.)
Anything with "science" in the name, isn't one (computer science, political science, christian science).
Ontologies are a (so far, modestly) useful tool in understanding life. I would posit that ontologies are only useful instrumentally to computer systems being a useful tool in understanding life. http://genomebiology.com/2002/3/6/INTERACTIONS/1002
Larry
Pat Hayes
On Dec 16, 2009, at 9:27 PM, Barry Smith wrote:
> At 09:42 PM 12/16/2009, Pat Hayes wrote:
...
>>
>> Well, no, I disagree. Or rather, I think I disagree; because I
>> believe
>> I do understand instance_of(a, cell), but I have no idea what a
>> universal is.
>
> [B] universal(x) =def. for some y, instance_of(y, x)
But again, that seems completely trivial to me. Since
instance_of(A, B)
is simply a longwinded way of writing
B(A)
(because they *necessarily* have *exactly* the same truth conditions,
as I believe you agreed in the last response), this is just saying
that B is a universal when B is a property, or maybe when B is denoted
by a predicate symbol.
I think the basic reason we are not communicating here is because you
actually do have a pre-theoretical intuitive sense of what "universal"
means, and all the formal machinery is just a way to capture that. But
I don't have this pre-theoretical intuition; in fact, I genuinely do
not believe in these things; I am close to being an unreconstructed
nominalist in my personal philosophy. Hence, the only way I can
interpret your responses is that you are giving me a formal
*definition* of what 'universal' means; and these 'definitions' don't
hold up: they are too fragile, they don't survive trivial
reformulations between logically equivalent alternatives.
I guess my methodological position would be: why do we even NEED to
talk about universals? I have never seen any actual utility from
having notions at this extreme level of generality included in an
ontology. It does not make the biology clearer or increase its
explanatory power to be told that something is a universal or not; and
debates about whether something should be so classified can become
interminable, so the net utility of having the distinction is likely
to be negative.
>>> Note that in other cases, to say that 'a member-of B' does not have
>>> that logical form. For instance
>>>
>>> (3) 1 member-of {1, 2, 3}
>>
>> But it is easy to re-cast this into the required form:
>>
>> 1 member { x | (x=1 or x=2 or x=3 )
>
> Let me rephrase. Not every
>
> a member_of B
>
> has the unpacked form:
>
> [A] a € {x | instance_of(x, u)}
>
> for some universal u.
They can all be put into this syntactic form, if required. Now, of
course, you may not consider the resulting U to be a universal; but
then that decision must be being made on other grounds, not on the
form of the definitions involved, on pains of circularity. And as I do
not know what a universal is or how to recognize one, this
classification must remain opaque to me.
>
>> The logical form itself conveys nothing of importance.
>
> Whatever you call the form of [A] the stuff after
> the '|' conveys something of importance to this
> argument. If you think that it does not, then YOUR argument is of
> the form:
>
> There are no such things as universals because
> whenever you attempt to talk about them I will
> say that what you say conveys nothing of
> importance.
No, my point is that *the logical form itself* cannot (I hope) be the
defining characteristic that makes these universal-thingies actually
be what you say they are. That is what I meant by the above remark.
> And you can do better than that. I would have hoped.
>
>>>
>>>>> [A], we say, asserts a
>>>>> relation between a certain instance and a certain type or
>>>>> universal.
>>>>> The OBO reference ontologies concern themselves with types in
>>>>> given
>>>>> domains, just as physics, for instance, concerns itself with types
>>>>> such as force or matter.
>>>>
>>>> Bad analogy. Physics is science. Ontologies are not themselves
>>>> science.
>>>
>>> Not yet.
>>
>> :-) They never will be. They may be of help in science, but I rather
>> think not, actually, as scientists are usually somewhat ahead of the
>> formalizers when it comes to thinking their ideas through carefully.
>
> I think that we can shoot for ontology being a
> science in something like the way computer
> science is a science.
Seems like we agree. I wouldn't say that CS was a science, either. As
the director of one of them once remarked to me, if you see anything
called a "Center for XX Science" then you know immediately (a) that XX
is not a science and (b) that you are on the edge of the campus.
> But my point is in fact
> more trivial than that. It is that bio-ontologies
> such as the Gene Ontology are already a part of
> biological science in something like the way
> textbooks of biology are a part of biological
> science. (The established part, of course.)
OK, fair enough.
...
>>>
>>> One feature of the treatment of universals as full-fledged entities
>>> in the domain of variables x, y, z, ... (normally, but we can now
>>> see overly restrictedly, referred to as 'individual variables') is
>>> that we can do justice to the idea that, while classes can be
>>> trivially defined using 'union', etc., this is not so for
>>> universals; there is no universal 'rabbit or molecule'.
>>
>> I defer to your more intimate acquaintance with universals. Never
>> having come across any, I wouldn't know. I'd be interested to know
>> how
>> you recognize them and distinguish them from mere classes. Is it
>> something about the way they are described?
>
> Take any textbook in a natural science and look
> at the common nouns in the index. Most of them
> name universals.
And how do you know this, pray tell? Look, there are clearly (even to
a nominalist like me) relations and properties that things have and
bear to one another. And it is obviously useful to give these names
and even to talk as though they exist and have a reality of their own.
Maybe it is even essential to talk and think like this. But none of
this leads me to distinguish a special category of 'universals' which
are somehow demarcated as being more... well what? correct?
scientific? widely applicable? real? ... than others. There are many
different kinds of relation and property, and they can be classified
in all sorts of ways, for various purposes. Still, I don't see any
central, basic distinction that warrants being put at the very core of
a basic foundational ontology. On the contrary: it seems that
classifications and distinctions and relationships that are central to
one science are irrelevant or even in-principle invisible to other
sciences. (Even using your rough-and-ready criterion, surely I will
get very different results for a textbook of astrophysics from one on
ethnography.) And classifications that are useful, even central, to
areas such as commerce, or reasoning about shipping routes, or
banking, or planning military sorties, or searching for images, or
literary analysis, are *completely* different in kind to those that
science treats as 'universal'. So it seems to me that any such
division is almost guaranteed to be more wrong than right; and that it
will only contribute negatively to any attempt to interoperate with
different ontologies, which will of necessity not agree on what is
"universal". And, as with so many other essentially philosophical
debates, none of this makes the slightest difference to anything of
any practical importance. Nothing turns on whether a given set is a
'universal'. What does matter is, what its elements are and what being
in it signifies. And all of that is about the set itself.
OK, got that now. BUt see my response.
>
>> But in any case, if the only
>> thing that can be inferred, by inserting a theory of fongles into our
>> ontology, is that fongles exist, then I would view this as prima
>> facia
>> evidence that the notion of fongledom is not especially useful.
>
> '... or that has any consequences for any
> entailments ...' the man said. And I was rather
> hoping that the man would agree that one
> counterexample to a universal claim would suffice
> to refute it.
I should have spoken more carefully. To be achingly precise. Suppose
that an ontology O has a predicate Fongle in its vocabulary. Consider
the simplified ontology OF got by removing that term from the
vocabulary and deleting it from all axioms that contain it (eg if they
had quantifiers restricted to Fongles, then they are now vacuous,
etc..). If every sentence *in the vocabulary of OF* which is entailed
by O is also entailed by OF, then the concept Fongle is of no utility
other than in making the very distinction that it purports to explain.
I maintain that "universal" is such a notion. The need for the
asterisked condition is precisely to avoid the inescapable fact that
virtually any addition of some vocabulary, however pointless, does
enable new entailments in that very vocabulary.
> But now I see that you take refuge
> in the 'not important' argument. Why so many
> names for universals in the indexes of scientific
> texts, I wonder. And why so many giant
> bio-ontologies which claim to be representing universals ...
Of course the things you call universals are often important. My gripe
is not with concepts of broad scope, but with the insistence upon
their classification as Universals (and hence the status of non-
universals, those mere sets that can be defined so carelessly.)
...
> I agree. My fight is with the pseudo-Gruberians.
>
>>> It would indeed be odd to suppose, for instance, that when we say
>>> that
>>>
>>> TLR2™-MyD88 ligand binding precedes TLR2™-MyD88 binding ig in the
>>> TLR2
>>> signalling pathway
>>>
>>> which is the sort of thing bio-ontologists do say, then they are
>>> talking about some sort of temporal order among concepts.
>>
>> Of course, that would be ridiculous. Nobody has ever suggested such
>> an
>> idea, AFAIK.
> There are government standards which say exactly
> such things. I could give you a long, long list, but let these
> suffice:
>
> Geographic Area isa Idea or Concept
> Body Space or Junction isa Idea or Concept
> Amino Acid Sequence isa Idea or Concept
> Body Location or Region isa Idea or Concept
> Body System isa Idea or Concept
Ah, I stand refuted, indeed. I should never have said "Nobody...",
forgetting the ubiquity of use/mention confusions in the wider world.
But certainly Tom (and the rest of us in AI/KR) never suffered from
this particular problem, as you can easily check by reading our
writings (and some of the archived email discussions about reality and
model theory, if you have the stomach for it.) So I don't think they
are relevant to his definition of ontology.
BTW, one can treat such nonsenses with a little generosity, instead of
taking them literally. They are obvious use/mention confusions, and
can be repaired by a judicious use of something like quasi-quotation.
If our formal logics were a little more accommodating, we should be
able to take in stuff like this and make sense of it.
Pat
Barry Smith
>On Dec 16, 2009, at 9:27 PM, Barry Smith wrote:
>
>>At 09:42 PM 12/16/2009, Pat Hayes wrote:
>...
>>>
>>>Well, no, I disagree. Or rather, I think I disagree; because I
>>>believe
>>>I do understand instance_of(a, cell), but I have no idea what a
>>>universal is.
>>
>>[B] universal(x) =def. for some y, instance_of(y, x)
>
>But again, that seems completely trivial to me. Since
>
>instance_of(A, B)
>
>is simply a longwinded way of writing
>
>B(A)
You (Pat) still don't get it, I'm afraid. There
are many cases where you would write
B(A)
where there is no instance_of relation. Examples
1. has_headache(John)
2. suntanned(Mary)
3. running(Jim)
4. well_known_in_Witwatersrand(Herman)
5. such_that_2+2=4(Roderick)
6. not_represented_in_any_Mickey_Mouse_cartoon(Eva Braun)
For you 'B(A)' (or, as I prefer, 'F(a)') can be
used for all of these, since 'F(a)' can be used
wherever we have a sentence with a noun or
noun-phrase in it, just by substituting 'F' for
the open sentence which results from removing the
noun, and 'a' for the noun. It's that easy.
This fact about open sentence substitutability
does not go far enough for ontological purposes
(we hold), since it is woefully unconstrained.
>(because they *necessarily* have *exactly* the same truth conditions,
>as I believe you agreed in the last response), this is just saying
>that B is a universal when B is a property, or maybe when B is denoted
>by a predicate symbol.
>
>I think the basic reason we are not communicating here is because you
>actually do have a pre-theoretical intuitive sense of what "universal"
>means, and all the formal machinery is just a way to capture that. But
>I don't have this pre-theoretical intuition; in fact, I genuinely do
>not believe in these things; I am close to being an unreconstructed
>nominalist in my personal philosophy. Hence, the only way I can
>interpret your responses is that you are giving me a formal
>*definition* of what 'universal' means; and these 'definitions' don't
>hold up: they are too fragile, they don't survive trivial
>reformulations between logically equivalent alternatives.
You think they are trivial reformulations, but I
am still optimistic that I can show that there is
more to it than that. See below.
>I guess my methodological position would be: why do we even NEED to
>talk about universals? I have never seen any actual utility from
>having notions at this extreme level of generality included in an
>ontology.
My view is that the very enterprise of ontology,
in the natural science field at least, makes
sense only if we recognize that ontologies, like
scientific theories, are representations of
universals and the relations between them. There
is no Bill Clinton represented in a textbook of
biology; rather there are organisms, cells,
molecules, etc. The instances of these universals
are what biologists perform experiments on, in
order to test their hypotheses about what holds
on the level of universals or types or kinds.
>It does not make the biology clearer or increase its
>explanatory power to be told that something is a universal or not; and
>debates about whether something should be so classified can become
>interminable, so the net utility of having the distinction is likely
>to be negative.
Biologists, the evidence shows, need ontologies.
For this, the evidence also shows, it is useful
to have a clear understanding of what these
ontologies represent, and how they ought properly
to be used in annotating data in consistent ways
to promote integration: http://www.biomedcentral.com/1471-2105/9/S5/S2
You are right that we will not increase the
explanatory power of the biology in this way, but
we will improve the success with which biologists
build their ontologies consistently. The nonsense
talked about 'concepts', and the success we have
had gaining relative clarity by formulating
matters more carefully in terms of universals and
their instances, suggests also that you are for
other reasons wrong in holding that there is no
net utility in the approach we take. See, e.g.:
>Concepts, also known as classes, are used in a
>broad sense. They can be abstract or concrete,
>elementary or composite, real or fictious (sic).
>In short, a concept can be anything about which
>something is said, and, therefore, could also be
>the description of a task, function, action,
>strategy, reasoning process, etc. (Oscar Corcho
>and Asuncion Gomez-Perez “A Roadmap to Ontology
>Specification Languages”, from Knowledge
>Engineering and Knowledge Management, Springer, Berlin, 2000.)
There are, as you well know, different approaches
to building a basic foundational ontology. You
take the 4D-ist, nominalist approach. We take the
combined 3D-ist/4D-ist approach (we believe that
there are both objects and processes) and the
realist approach when it comes to universals (we
believe that there is a reason why aspirin works
so reliably in curing headaches, that we can't
understand unless we see aspirin pills and
headaches as instances of the same kinds of,
respectively, independent continuants and dependent continuants).
It may be that everything that can be done on
your approach can also be done by BFO and
vice-versa. Haven't seen a formalization of your
upper-level ontology, yet, though, and so haven't
seen it being used by actual biologists. This
puts BFO ahead, at least in this one respect. We
have actual users. Two respects: BFO also exists already.
> On the contrary: it seems that
>classifications and distinctions and relationships that are central to
>one science are irrelevant or even in-principle invisible to other
>sciences. (Even using your rough-and-ready criterion, surely I will
>get very different results for a textbook of astrophysics from one on
>ethnography.) And classifications that are useful, even central, to
>areas such as commerce, or reasoning about shipping routes, or
>banking, or planning military sorties, or searching for images, or
>literary analysis, are *completely* different in kind to those that
>science treats as 'universal'. So it seems to me that any such
>division is almost guaranteed to be more wrong than right; and that it
>will only contribute negatively to any attempt to interoperate with
>different ontologies, which will of necessity not agree on what is
>"universal". And, as with so many other essentially philosophical
>debates, none of this makes the slightest difference to anything of
>any practical importance. Nothing turns on whether a given set is a
>'universal'. What does matter is, what its elements are and what being
>in it signifies. And all of that is about the set itself.
Yes, life is hard. But BFO seems to work, in its
still clunky, for many areas of biomedicine, at
least. And your argument above seems to be that,
because cross-domain ontology interoperability is
so hard to do, perhaps even impossible, we should
give up doing it. And this, just when we are beginning to show results.
Yes. I am aware of this fongle fact. And am aware
also that I need to give you examples of genuine
entailments gained by adding the distinction
between universals and instances. But for the
moment, perhaps the idea can be elucidated most
easily (for you) by reference to Davidson's
treatment of events and adverbs. How, Davidson
asked, can we capture the entailment from
D1. John buttered the toast slowly
to
D2. John buttered the toast?
If we follow the F(a) approach, as above, (call
it 'fantology', for short), then we get for D1.
D1*. F(John)
and for D2
D2*. G(John)
and thereby lose the entailment relation.
Instead, says Davidson, we need to see D1. and D2. as short for
D1**. there is some e, buttering_event(e) & agent_of(John,e) & slow(e)
D2**. there is some e, buttering_event(e) & agent_of(John,e)
respectively. The entailment is then clear.
Care to fongle this?
>>But now I see that you take refuge
>>in the 'not important' argument. Why so many
>>names for universals in the indexes of scientific
>>texts, I wonder. And why so many giant
>>bio-ontologies which claim to be representing universals ...
>
>Of course the things you call universals are often important. My gripe
>is not with concepts of broad scope, but with the insistence upon
>their classification as Universals (and hence
>the status of non- universals, those mere sets
>that can be defined so carelessly.)
>
>...
Good. Progress. We choose to use 'universal' in
part because, in the ontology engineering world,
at least, it has a short tail of associated
meanings, and thus is associated with fewer
confusions than, e.g., 'concept', 'class',... We
could use 'type' or 'kind' instead.
They are relevant to the phenomenal influence of
an (admittedly confused) reading of his
definition. Maybe you and he should join the
fight against the pernicious influence of this
confused reading, and against the use-mention
confusions in ontology circles which it promotes.
Consider e.g. the Disease Ontology, which is an
open source ontology derived from the WHO's
international classification of diseases (ICD),
and contains dozens of terms like:
senility without mention of psychosis
acute gastritis without mention of hemorrhage
acute monocytic leukemia without mention of remission
measles without mention of complication
toxic multinodular goiter with mention of thyrotoxic crisis or storm
ICD itself is far worse even than this, though
it, I suppose, can defend itself by pointing out
that it is not aiming to be an ontology.
>BTW, one can treat such nonsenses with a little generosity, instead of
>taking them literally. They are obvious use/mention confusions, and
>can be repaired by a judicious use of something like quasi-quotation.
>If our formal logics were a little more accommodating, we should be
>able to take in stuff like this and make sense of it.
Clever logicians can make sense of near-nonsense
in clever ways. Not, however, your standard
working scientist ontology user. Moreover, there
will often be multiple such clever ways; and so
allowing near-nonsense in through the front door
will promote precisely the sorts of forking which
ontologies, in science, are designed to prevent.
I prefer, therefore, to do it right the first
time, and not have to distinguish, e.g. two sorts
of part relation: physical_part_of between atrium
and heart, and conceptual_part_of, between heart and cardiovascular system.
There are virtues, in ontology, of imposing a
certain degree of constraint on what people
should be allowed to say. (Just as, when building
an international standard for telephone networks
it is good to impose certain constraints on
Sprint and Verizon technical people.) I think,
for instance, that it should be impossible for
people to say, e.g., 'aspirin treats concept'
(thousands of such assertions follow
axiomatically from SNOMED, which defines all diseases as concepts).
BFO is, indeed, a still ramshackle constraint;
but it is, I believe, improvable, and its users
seem to think it is better than existing
alternatives (though I am sure that there are
multiple non-existing alternatives which are way better).
BS
Barry Smith
>At 12:18 AM 12/17/2009, Pat Hayes wrote:
>
>>
>>>At 09:42 PM 12/16/2009, Pat Hayes wrote:
>>...
>>>>
>>>>Well, no, I disagree. Or rather, I think I disagree; because I
>>>>believe
>>>>I do understand instance_of(a, cell), but I have no idea what a
>>>>universal is.
>>>
>>>[B] universal(x) =def. for some y, instance_of(y, x)
>>
>>But again, that seems completely trivial to me. Since
>>
>>instance_of(A, B)
>>
>>is simply a longwinded way of writing
>>
>>B(A)
>
>are many cases where you would write
>
>B(A)
>
>where there is no instance_of relation. Examples
>
>1. has_headache(John)
>2. suntanned(Mary)
>3. running(Jim)
>4. well_known_in_Witwatersrand(Herman)
>5. such_that_2+2=4(Roderick)
>6. not_represented_in_any_Mickey_Mouse_cartoon(Eva Braun)
>
>For you 'B(A)' (or, as I prefer, 'F(a)') can be
>used for all of these, since 'F(a)' can be used
>wherever we have a sentence with a noun or
>noun-phrase in it, just by substituting 'F' for
>the open sentence which results from removing
>the noun, and 'a' for the noun. It's that easy.
>
>This fact about open sentence substitutability
>does not go far enough for ontological purposes
>(we hold), since it is woefully unconstrained.
>
>
>>as I believe you agreed in the last response), this is just saying
>>that B is a universal when B is a property, or maybe when B is denoted
>>by a predicate symbol.
>>
>>I think the basic reason we are not communicating here is because you
>>actually do have a pre-theoretical intuitive sense of what "universal"
>>means, and all the formal machinery is just a way to capture that. But
>>I don't have this pre-theoretical intuition; in fact, I genuinely do
>>not believe in these things; I am close to being an unreconstructed
>>nominalist in my personal philosophy. Hence, the only way I can
>>interpret your responses is that you are giving me a formal
>>*definition* of what 'universal' means; and these 'definitions' don't
>>hold up: they are too fragile, they don't survive trivial
>>reformulations between logically equivalent alternatives.
>
>am still optimistic that I can show that there
>is more to it than that. See below.
>
>>talk about universals? I have never seen any actual utility from
>>having notions at this extreme level of generality included in an
>>ontology.
>
>in the natural science field at least, makes
>sense only if we recognize that ontologies, like
>scientific theories, are representations of
>universals and the relations between them. There
>is no Bill Clinton represented in a textbook of
>biology; rather there are organisms, cells,
>molecules, etc. The instances of these
>universals are what biologists perform
>experiments on, in order to test their
>hypotheses about what holds on the level of universals or types or kinds.
>
>>explanatory power to be told that something is a universal or not; and
>>debates about whether something should be so classified can become
>>interminable, so the net utility of having the distinction is likely
>>to be negative.
>
>approaches to building a basic foundational
>ontology. You take the 4D-ist, nominalist
>approach. We take the combined 3D-ist/4D-ist
>approach (we believe that there are both objects
>and processes) and the realist approach when it
>comes to universals (we believe that there is a
>reason why aspirin works so reliably in curing
>headaches, that we can't understand unless we
>see aspirin pills and headaches as instances of
>the same kinds of, respectively, independent
>continuants and dependent continuants).
>
>It may be that everything that can be done on
>your approach can also be done by BFO and
>vice-versa. Haven't seen a formalization of your
>upper-level ontology, yet, though, and so
>haven't seen it being used by actual biologists.
>This puts BFO ahead, at least in this one
>respects: BFO actually exists, already.
>
>> On the contrary: it seems that
>>classifications and distinctions and relationships that are central to
>>one science are irrelevant or even in-principle invisible to other
>>sciences. (Even using your rough-and-ready criterion, surely I will
>>get very different results for a textbook of astrophysics from one on
>>ethnography.) And classifications that are useful, even central, to
>>areas such as commerce, or reasoning about shipping routes, or
>>banking, or planning military sorties, or searching for images, or
>>literary analysis, are *completely* different in kind to those that
>>science treats as 'universal'. So it seems to me that any such
>>division is almost guaranteed to be more wrong than right; and that it
>>will only contribute negatively to any attempt to interoperate with
>>different ontologies, which will of necessity not agree on what is
>>"universal". And, as with so many other essentially philosophical
>>debates, none of this makes the slightest difference to anything of
>>any practical importance. Nothing turns on whether a given set is a
>>'universal'. What does matter is, what its elements are and what being
>>in it signifies. And all of that is about the set itself.
>
>
>still clunky, for many areas of biomedicine, at
>least. And your argument above seems to be that,
>because cross-domain ontology interoperability
>is so hard to do, perhaps even impossible, we
>should give up doing it. And this, just when we are beginning to show results.
>
>between universals and instances. But for the
>moment, perhaps the idea can be elucidated most
>easily (for you) by reference to Davidson's
>treatment of events and adverbs. How, Davidson
>asked, can we capture the entailment from
>
>D1. John buttered the toast slowly
>
>to
>
>D2. John buttered the toast
>
>
>D1*. F(John)
>
>and for D2
>
>D2*. G(John)
>
>and thereby lose the entailment relation.
>Instead, says Davidson, we need to see D1. and
>
>D1**. there is some e, buttering_event(e) & agent_of(John,e) & slow(e)
>
>D2**. there is some e, buttering_event(e) & agent_of(John,e)
>
>respectively. The entailment is then clear.
>
>Care to fongle this?
>
>>>in the 'not important' argument. Why so many
>>>names for universals in the indexes of scientific
>>>texts, I wonder. And why so many giant
>>>bio-ontologies which claim to be representing universals ...
>>
>>Of course the things you call universals are often important. My gripe
>>is not with concepts of broad scope, but with the insistence upon
>>their classification as Universals (and hence
>>the status of non- universals, those mere sets
>>that can be defined so carelessly.)
>>
>>...
>
>part because, in the ontology engineering world,
>at least, it has a short tail of associated
>meanings, and thus is associated with fewer
>confusions than, e.g., 'concept', 'class',... We
>could use 'type' or 'kind' instead.
>
>
>an (admittedly confused) reading of his
>definition. Maybe you and he should join the
>fight against the pernicious influence of this
>confused reading, and against the use-mention
>confusions in ontology circles which it promotes.
>
>Consider e.g. the Disease Ontology, which is an
>open source ontology derived from the WHO's
>international classification of diseases (ICD),
>and contains dozens of terms like:
>
>senility without mention of psychosis
>acute gastritis without mention of hemorrhage
>acute monocytic leukemia without mention of remission
>measles without mention of complication
>toxic multinodular goiter with mention of thyrotoxic crisis or storm
>
>ICD itself is far worse even than this, though
>it, I suppose, can defend itself by pointing out
>
>>BTW, one can treat such nonsenses with a little generosity, instead of
>>taking them literally. They are obvious use/mention confusions, and
>>can be repaired by a judicious use of something like quasi-quotation.
>>If our formal logics were a little more accommodating, we should be
>>able to take in stuff like this and make sense of it.
>
>in clever ways. Not, however, your standard
>working scientist ontology user. Moreover, there
>will often be multiple such clever ways; and so
>allowing near-nonsense in through the front door
>will promote precisely the sorts of forking
>which ontologies, in science, are designed to
>prevent. I prefer, therefore, to do it right the
>first time, and not have to distinguish, e.g.
>two sorts of part relation: physical_part_of
>between atrium and heart, and
>conceptual_part_of, between heart and cardiovascular system.
>
>There are virtues, in ontology, of imposing a
>certain degree of constraint on what people
>should be allowed to say. (Just as, when
>building an international standard for telephone
>networks it is good to impose certain
>constraints on Sprint and Verizon technical
>people.) I think, for instance, that it should
>be impossible for people to say, e.g., 'aspirin
>treats concept' (thousands of such assertions
>follow axiomatically from SNOMED, which defines all diseases as concepts).
>
P. Def
Universals are that which is general or abstract in reality. They are the philosophical explanation of the structure, order and regularity that is to be found in nature, and they are what all members of a natural kind, grouping or species (for example the kind “feline” or “mammal”) have in common. Universals are repeatable in the sense that they can be instantiated by more than one object and at more than one time..
Every universal has a corresponding class, but not every class corresponds to a universal. A class can be defined as a collection of particulars falling under a term in such a way that the term applies to every member of the collection, and every particular to which the term applies is a member of the collection. For example, the class corresponding to the universal “cat” will be designated by the term ‘cat’ and will contain all and only the particular cats that exist in reality.
However, there are many classes that do not correspond to any universal, and these fall into two general kinds:
(1) The first are classes designated by arbitrary general terms (e.g. Nelson Goodman's "grue" category, tuberculosis of unspecified bones and joints, normal pregnancy, injury due to war operations by lasers, railway accident involving collision with rolling stock and injuring pedal cyclist, etc)
(2) The second kinds of classes that do not correspond to universals in reality are classes created by using a general term to make reference to particulars existing at a specific time or in a specific place (e.g. the class of all women currently living on the north coast of Germany, the class of all athletes over the age of 30, or the class of all individuals currently infected by HIV on the Continent of Africa)
At the 2007 summer workshop it was decided to allow defined classes in OBI, for two principal reasons
- To allow the definitions of terms that were in use by the community but were not "universals" as determined by the group.
- To facilitate organization of OBI as a single asserted hierarchy while allowing for polyhierarchy where appropriate.
Barry Smith
>Hi all, I think I am a little bit confused by the universal /
>defined-class dichotomy as well
>
'Fur' comes close to designate a universal. Thus "animal with fur"
demarcates a subclass of the extension of the universal "animal"
which consists of all those animals with coverings made of fur.
>
>another problem is that if I wanted to add the Cat into the category
>of "Furry animals" I wouldn't know where to insert the category in
>the taxonomy because:
>1. the Furry Animal category goes beyond the Cat and the Feline
>category (e.g. a Bear also qualify as a Furry Animal)
This is exactly as we should predice, given that 'furry animal' does
not designate a universal
>2. but it is also true that not all Felines and not all Cats
>actually qualify as Furry Animals (e.g. the Sphynx cat)
>
>so I believe I should rather define the Furry Animal category as a
>class which would basically comprise any Animal without a fur
without?
>however, I am not sure about what the consequences of introducing
>this new defined class would be..
>
>
>In particular,
><http://obi-ontology.org/page/Defined_classes>http://obi-ontology.org/page/Defined_classes
>states that:
>At the 2007 summer workshop it was decided to allow defined classes
>in OBI, for two principal reasons
> * To allow the definitions of terms that were in use by the
> community but were not "universals" as determined by the group.
> * To facilitate organization of OBI as a single asserted
> hierarchy while allowing for polyhierarchy where appropriate.
>
>
>With regard to the 2nd point, I thought the BFO was strongly
>supporting the idea that every node in the taxonomy may not have
>more than one parent.
Once you allow classes like the designatum of 'furry animal' in your
ontology you will inevitable be able to infer multiple parents, e.g.
furry animal is_a animal, furry animal is_a furry organism
the idea is that while we can infer multiple parents, we will ASSERT
only those child-parent relations which obtain between universals.
>Would it be possible for anyone to elaborate on how the concept of
>polyhierarchy is implemented in the OBI by virtue of the defined classes ?
>and how is this implementation still consistent with the basic
>principles of the BFO?
>
>Earlier in the thread, Bjoern said that "Barry et al asked for a
>single asserted is_a hierarchy limited to universals."
>This make sense, but how can a multiple is_a hierarchy be
>implemented in such a way as to remain consistent with the whole framework?
>
>
>Also, if universals are limited to a single is_a hierarchy, is it
>not possible to make the multiple assertion that a Cat is_a Feline
>and a Cat is_a Furry Animal?
>
>
>Finally, I am not sure whether things which have been created by man
>(such as e.g. houses, cars, books) can also be regarded as universals or not ?
>
>- in case they do, then where should the line be drawn between what
>can be regarded as a universal and what not:
> eg. would the categories of "summer house" "cabriolet" or
> "hard-cover books" qualify as a universal or as an arbitrary defined class?
>
We are advancing BFO as an ontology to support data integration in
the natural sciences. No claims are made as concerns artifacts of
these sorts. Most of them, I guess, do not refer to universals.
>- and in case they do not, would the various breeds which have been
>created by man (e.g. pugs, pitbulls) also not qualify as universals ?
>
There are (I am still guessing) borderline cases. Clear cases of
universals are, e.g., organism, cell; clear cases of non-universals,
organism owned by Primavera, organism of a type not mentioned in
Kleist's novel Michael Kohlhaas.
BS
>
>
>Thanks for your attention and looking forward to your answer.
>
>--
>informatio...@googlegroups.com
>To change settings, visit
><http://groups.google.com/group/information-ontology>http://groups.google.com/group/information-ontology
Pat Hayes
On Dec 17, 2009, at 8:07 PM, Barry Smith wrote:
> At 02:24 PM 12/17/2009, P. Def wrote:
>> Hi all, I think I am a little bit confused by the universal /
>> defined-class dichotomy as well
>>
>
...
> Once you allow classes like the designatum of 'furry animal' in your
> ontology you will inevitable be able to infer multiple parents, e.g.
> furry animal is_a animal, furry animal is_a furry organism
>
> the idea is that while we can infer multiple parents, we will ASSERT
> only those child-parent relations which obtain between universals.
To me, this sounds completely crazy. I *must* be misunderstanding
this, surely. Is there an assumption here that universals have only a
single parent category? So that if something is a universal then it
can be generalized in only one way, and so the generalization
hierarchy of universals is a pure tree? What *possible* theoretical
justification can there be for such an idea?
Or do I have this completely wrong?
Pat
Pat Hayes
Um... the embedding seems to be getting jumbled. Your reply to me was
formatted as though it was a reply to your reply. And the topics seem
to be getting mixed up, as well. I will try to stick to the point in
this thread, which is the matter of distinguishing universals from
mere predicates. (Not the 4D/ continuant debate, which belongs in a
different thread.)
I see no reason, myself, to not write any of these using instance_of,
if someone prefers that way of expressing themselves. In RDF they
would all be written using rdf:type, for example. But I gather that
this would clash with your intuitions, so read on.
>>
>> For you 'B(A)' (or, as I prefer, 'F(a)'
I actually prefer (B a), but whatever.
>> ) can be
>> used for all of these, since 'F(a)' can be used
>> wherever we have a sentence with a noun or
>> noun-phrase in it, just by substituting 'F' for
>> the open sentence which results from removing
>> the noun, and 'a' for the noun. It's that easy.
>>
>> This fact about open sentence substitutability
>> does not go far enough for ontological purposes
>> (we hold), since it is woefully unconstrained.
And it is so because, I gather, you see some predicates as being
universals, and others (like the above) as not being. OK, fair enough:
but then, just as a matter of exposition, you should not confuse the
universal/not-universal distinction with any distinction based on
logical syntax, such as being defined/not being defined. I believe
that was the very point that Chris made that gave rise to this thread
in the first place. So thus far, I am simply echoing Chris' original
point. However, I wish to take it further. I simply do not accept that
this category, which you find so obvious, of 'universals', is useful
or even completely meaningful. So let us ignore the questions of
logical syntax for now and concentrate on this notion of 'universal'.
>>> (because they *necessarily* have *exactly* the same truth
>>> conditions,
>>> as I believe you agreed in the last response), this is just saying
>>> that B is a universal when B is a property, or maybe when B is
>>> denoted
>>> by a predicate symbol.
>>>
>>> I think the basic reason we are not communicating here is because
>>> you
>>> actually do have a pre-theoretical intuitive sense of what
>>> "universal"
>>> means, and all the formal machinery is just a way to capture that.
>>> But
>>> I don't have this pre-theoretical intuition; in fact, I genuinely do
>>> not believe in these things; I am close to being an unreconstructed
>>> nominalist in my personal philosophy. Hence, the only way I can
>>> interpret your responses is that you are giving me a formal
>>> *definition* of what 'universal' means; and these 'definitions'
>>> don't
>>> hold up: they are too fragile, they don't survive trivial
>>> reformulations between logically equivalent alternatives.
>>
>> You think they are trivial reformulations, but I
>> am still optimistic that I can show that there
>> is more to it than that. See below.
OK. The trivial reformulation is expressed in the CLIF axiom
(forall (x y)((iff (x y)(y instance_of x) ))
which I believe you would reject in favor of something like
(forall ((x Universal) y)(if (y instance_of x)(y x) ))
using a restriction on the first quantifier and no 'only if'
>>
>>> I guess my methodological position would be: why do we even NEED to
>>> talk about universals? I have never seen any actual utility from
>>> having notions at this extreme level of generality included in an
>>> ontology.
>>
>> My view is that the very enterprise of ontology,
>> in the natural science field at least, makes
>> sense only if we recognize that ontologies, like
>> scientific theories, are representations of
>> universals and the relations between them.
Well, I can disagree with this even though I don't really know what it
means, because ontologies can be, and are, used for many purposes, and
any a priori constraint of this kind is anathema to the whole
enterprise of ontological engineering. But having stated that general
position, I will simply observe that since I have told you that I
don't know what you mean by 'universal', it is little help to me to be
told that ontologies must represent them.
>> There
>> is no Bill Clinton represented in a textbook of
>> biology; rather there are organisms, cells,
>> molecules, etc. The instances of these
>> universals are what biologists perform
>> experiments on, in order to test their
>> hypotheses about what holds on the level of universals or types or
>> kinds.
If one simply deletes the word 'universal' from this paragraph and
replaces it with 'property', it seems to express exactly the same
content. Of course a biology textbook concerns itself with matters
that are important in biology. So what? A textbook of political
science will refer to different entities and relationships, of physics
yet another different world of entities and relationships. Where in
all this does one find the notion of a 'universal'?
>>
>>> It does not make the biology clearer or increase its
>>> explanatory power to be told that something is a universal or not;
>>> and
>>> debates about whether something should be so classified can become
>>> interminable, so the net utility of having the distinction is likely
>>> to be negative.
>>
>> Biologists, the evidence shows, need ontologies.
>> For this, the evidence also shows, it is useful
>> to have a clear understanding of what these
>> ontologies represent, and how they ought
>> properly to be used in annotating data in
>> consistent ways to promote integration:
>> http://www.biomedcentral.com/1471-2105/9/S5/S2
>>
>> You are right that we will not increase the
>> explanatory power of the biology in this way,
>> but we will improve the success with which
>> biologists build their ontologies consistently.
I am not convinced. At any rate, there is not nearly enough evidence
to support any such general claim yet.
>> The nonsense talked about 'concepts', and the
>> success we have had gaining relative clarity by
>> formulating matters more carefully in terms of
>> universals and their instances, suggests also
>> that you are for other reasons wrong in holding
>> that there is no net utility in the approach we take.
My point is not that clarity is not useful; it obviously is. My point
is that no extra clarity is gained by insisting upon this distinction
between universals and non-universals.
>> See, e.g.:
>>
>>> Concepts, also known as classes, are used in a
>>> broad sense. They can be abstract or concrete,
>>> elementary or composite, real or fictious
>>> (sic). In short, a concept can be anything
>>> about which something is said, and, therefore,
>>> could also be the description of a task,
>>> function, action, strategy, reasoning process,
>>> etc. (Oscar Corcho and Asuncion Gomez-Perez “A
>>> Roadmap to Ontology Specification Languages”,
>>> from Knowledge Engineering and Knowledge Management, Springer,
>>> Berlin, 2000.)
Im not sure of your point in quoting this. I could have written this
myself. See the introductory sections of http://www.ihmc.us/users/phayes/ikl/guide/guide.html
, for example. So, is this to illustrate the utility, or the problem
that is solved, by your approach? And what bearing does anything in
this quote have to the notion of universal?
For the record, so do I. But I also believe that the categories
overlap, and that both kinds of thing can be described either way, and
that there are some indeed that can only be understood properly by
being described in both ways. And I do not believe in continuants, in
the technical sense. The objects I know are definitely not
continuants. They have temporal parts. In particular, I myself am not
a continuant.
>> ) and the realist approach when it
>> comes to universals (we believe that there is a
>> reason why aspirin works so reliably in curing
>> headaches
I agree with that, of course.
>> , that we can't understand unless we
>> see aspirin pills and headaches as instances of
>> the same kinds of, respectively, independent
>> continuants and dependent continuants).
If you *really* believe that, then good luck, as we are clearly on
different planets. For myself, I certainly don't need to know anything
at all about 'continuants' in order to grasp the essentials of how
aspirin blocks neurotransmission.
>>
>> It may be that everything that can be done on
>> your approach can also be done by BFO and
>> vice-versa. Haven't seen a formalization of your
>> upper-level ontology, yet, though, and so
>> haven't seen it being used by actual biologists.
>> This puts BFO ahead, at least in this one
>> respect. We have actual users. Oh. Sorry. Two
>> respects: BFO actually exists, already.
Had I realized we were counting brownie points, I would have put my
game hat on. :-)
On the contrary. It is that we should take interoperation seriously,
and not try to impose one idiosyncratic ontological perspective on an
entire scientific discipline.
I am of course aware of Davidson's treatment. It is widely used in KR
work. It works very well for capturing simple English tensed sentences
describing actions. It sees to not have anything to do with the topic
at hand, however.(?)
>> How, Davidson
>> asked, can we capture the entailment from
>>
>> D1. John buttered the toast slowly
>>
>> to
>>
>> D2. John buttered the toast
>>
>> ? If we follow the F(a) approach, as above,
>> (call it 'fantology', for short), then we get for D1.
>>
>> D1*. F(John)
Actually, you get Buttered(John, toast, slowly)
>>
>> and for D2
>>
>> D2*. G(John)
and Buttered(John, toast)
Still Davidson's point holds; there is no logical entailment. But in
response, I can now write (in CL) axioms about kinds of action, for
example
(Mode slowly)
(forall (x (y Mode) ...)(if (x ... y)(x ...)))
which systematically restores the entailments. Moreover, this has the
merit over the uniform case-based form suggested by Davidson, of
allowing more nuanced entailments, by for example classifying
different kinds of qualifier. But I will concede that Davidson's
construction is widely used and often very natural.
>> and thereby lose the entailment relation.
>> Instead, says Davidson, we need to see D1. and
>> D2. as having what he calls the following logical forms:
>>
>> D1**. there is some e, buttering_event(e) & agent_of(John,e) &
>> slow(e)
>>
>> D2**. there is some e, buttering_event(e) & agent_of(John,e)
>>
>> respectively. The entailment is then clear.
>>
>> Care to fongle this?
What has ANY of this got to do with what we were talking about?
>>
>>>> But now I see that you take refuge
>>>> in the 'not important' argument. Why so many
>>>> names for universals in the indexes of scientific
>>>> texts, I wonder. And why so many giant
>>>> bio-ontologies which claim to be representing universals ...
>>>
>>> Of course the things you call universals are often important. My
>>> gripe
>>> is not with concepts of broad scope, but with the insistence upon
>>> their classification as Universals (and hence
>>> the status of non- universals, those mere sets
>>> that can be defined so carelessly.)
>>>
>>> ...
>>
>> Good. Progress. We choose to use 'universal' in
>> part because, in the ontology engineering world,
>> at least, it has a short tail of associated
>> meanings, and thus is associated with fewer
>> confusions than, e.g., 'concept', 'class',... We
>> could use 'type' or 'kind' instead.
No no, that will not do. Because you have insisted that 'universal'
does NOT mean simply 'class' or 'concept'. If it did, then we would
not be arguing here, and the trivial transformations described earlier
would serve to eliminate instance_of in favor of simple application.
Apparently your use of 'universal' is not merely a simply choice of an
intuitive vocabulary for a lay audience, but rather has real meaning.
And you still have not told me what that meaning is.
Pat
<Remainder belongs on another thread>
Barry Smith
There are two heuristic justifications. 1., as experience shows, when
bio-ontologies (for example) build ontologies using multiple
inheritance, then they make a larger number of mistakes than if they
are constrained to use single inheritance (the constraint forces them
to think); 2. imposing single inheritance creates a very easy way of
formulating definitions, which people find very useful.
BS
>Pat
>
>
>
Barry Smith
Predicates, as I use this term, are never universals, or classes, or
objects, or properties. Predicates are pieces of language. In the
view I embrace, called FOLWUT (for: first-order logic with universal
terms), there would be a very restricted number of predicates modeled
on '=' and 'element-of', and including: 'instance_of', 'part_of',
'has_part' and a few others. Most of the predicates we have been
working with so far are binary, some are ternary (e.g. the has_part
relation for continuants, since continuants can have different parts
at different times).
Instead of saying 'F(a)', which can mean so many different things,
because what 'F' can stand for is almost entirely unconstrained
(practically all we need is an open sentence), we say things like:
instance_of(a, u) -- Socrates is a man
for some q, quality(q) & instance_of(q, suntan) & inheres_in(q, a) --
Socrates is suntanned
for some e, action(e) & instance_of(e, buttering) & agent_of(a, e) --
Socrates is buttering
The strategy is to get rid of adjectives as far as possible and leave
only nouns, plus =, inheres, etc.
> OK, fair enough:
>but then, just as a matter of exposition, you should not confuse the
>universal/not-universal distinction with any distinction based on
>logical syntax, such as being defined/not being defined.
I agree. No argument here.
The only point I would make is that, since universals are not
linguistic entities, they do not allow themselves to be defined e.g.
via unions or intersections (there is no universal 'rabbit or
molecule' -- proof: show me a science text with this noun-phrase in
the index). In this sense, and in this sense only, universals are not
definable (i.e. they cannot be created through definitions, as [some
think] classes can)
Yes.
>>>>I guess my methodological position would be: why do we even NEED to
>>>>talk about universals? I have never seen any actual utility from
>>>>having notions at this extreme level of generality included in an
>>>>ontology.
>>>
>>>My view is that the very enterprise of ontology,
>>>in the natural science field at least, makes
>>>sense only if we recognize that ontologies, like
>>>scientific theories, are representations of
>>>universals and the relations between them.
>
>Well, I can disagree with this even though I don't really know what it
>means, because ontologies can be, and are, used for many purposes, and
>any a priori constraint of this kind is anathema to the whole
>enterprise of ontological engineering.
Except the more successful parts of this enterprise, when it comes to
actual users, uses, ... This
<http://genomebiology.com/2005/6/5/R46>http://genomebiology.com/2005/6/5/R46
has been accessed some 40,000 times, and cited some 300 times in the
bio-ontological literature.
>But having stated that general
>position, I will simply observe that since I have told you that I
>don't know what you mean by 'universal', it is little help to me to be
>told that ontologies must represent them.
Try: ontologies built to support scientific research should consist
exclusively of singular nouns found in the indexes of scientific textbooks.
>>>There
>>>is no Bill Clinton represented in a textbook of
>>>biology; rather there are organisms, cells,
>>>molecules, etc. The instances of these
>>>universals are what biologists perform
>>>experiments on, in order to test their
>>>hypotheses about what holds on the level of universals or types or
>>>kinds.
>
>If one simply deletes the word 'universal' from this paragraph and
>replaces it with 'property',
a cell is not an instance of property
properties are things like sphericality, spongiform
(as I use this term, which you may view as idiosyncratic, but when I
was a philosopher everyone in that discipline, at least, seemed to
use it in ways corresponding to the way I am proposing here)
John has the property of being suntanned
John is an instance of human being
John's suntan is an instance of the universal suntan
John's headache is an instance of the universal headache
John's foot is an instance of the universal foot
John's foot part_of John
John's headache inheres_in John
>it seems to express exactly the same
>content. Of course a biology textbook concerns itself with matters
>that are important in biology. So what? A textbook of political
>science will refer to different entities and relationships, of physics
>yet another different world of entities and relationships. Where in
>all this does one find the notion of a 'universal'?
As I explained earlier, we use 'universal' in part because it is not
(any longer) much used -- which means that it is not surrounded by a
detritus of conflicting associations; but if you prefer, use 'kind'
or 'natural kind' or 'type'.
>>>>It does not make the biology clearer or increase its
>>>>explanatory power to be told that something is a universal or not;
>>>>and
>>>>debates about whether something should be so classified can become
>>>>interminable, so the net utility of having the distinction is likely
>>>>to be negative.
>>>
>>>Biologists, the evidence shows, need ontologies.
>>>For this, the evidence also shows, it is useful
>>>to have a clear understanding of what these
>>>ontologies represent, and how they ought
>>>properly to be used in annotating data in
>>>consistent ways to promote integration:
>>>http://www.biomedcentral.com/1471-2105/9/S5/S2
>>>
>>>You are right that we will not increase the
>>>explanatory power of the biology in this way,
>>>but we will improve the success with which
>>>biologists build their ontologies consistently.
>
>I am not convinced. At any rate, there is not nearly enough evidence
>to support any such general claim yet.
Yes. So we should stop seeking such evidence, because there isn't enough yet?
>>>The nonsense talked about 'concepts', and the
>>>success we have had gaining relative clarity by
>>>formulating matters more carefully in terms of
>>>universals and their instances, suggests also
>>>that you are for other reasons wrong in holding
>>>that there is no net utility in the approach we take.
>
>My point is not that clarity is not useful; it obviously is. My point
>is that no extra clarity is gained by insisting upon this distinction
>between universals and non-universals.
You often criticize philosophers who attempt to do work in ontology.
I agree with these criticisms.
Ontologists, I like to think, should not care about any philosophical
foundations of what they do. Rather, they should examine different
alternatives, and test them violently to see which ones work. You
seem to want us not to test one particular alternative approach, the
one based on BFO. For what reason? Some would say: because you have
philosophical prejudices against talk of 'universals'.
Me, I prefer to take the more practical, empirical, comparative
approach, and with an open mind.
I hope that we will have the opportunity to measure the results, and
see who is right, in the end.
So far, BFO seems to be winning, in biomedicine at least.
>>>See, e.g.:
>>>
>>>>Concepts, also known as classes, are used in a
>>>>broad sense. They can be abstract or concrete,
>>>>elementary or composite, real or fictious
>>>>(sic). In short, a concept can be anything
>>>>about which something is said, and, therefore,
>>>>could also be the description of a task,
>>>>function, action, strategy, reasoning process,
>>>>etc. (Oscar Corcho and Asuncion Gomez-Perez "A
>>>>Roadmap to Ontology Specification Languages",
>>>>from Knowledge Engineering and Knowledge Management, Springer,
>>>>Berlin, 2000.)
>
>Im not sure of your point in quoting this. I could have written this
>myself. See the introductory sections of
>http://www.ihmc.us/users/phayes/ikl/guide/guide.html ,
You do not use the word 'concept' there, at all, and so also you do
not misuse it.
As I suggested earlier, you have been speaking, and are still
speaking, prose all your life without knowing it.
One day, if I am right, it will not appear idiosyncratic, not even to you.
At the same time I look forward to you proving me wrong by building
an ontology to support cross-domain interoperability and convincing
some scientists to use it.
The approach is a generalization of Davidson's treatment, to include
not just occurrents (events) but also dependent continuants (suntans,
headaches, ...), too.
>>>How, Davidson
>>>asked, can we capture the entailment from
>>>
>>>D1. John buttered the toast slowly
>>>
>>>to
>>>
>>>D2. John buttered the toast
>>>
>>>? If we follow the F(a) approach, as above,
>>>(call it 'fantology', for short), then we get for D1.
>>>
>>>D1*. F(John)
>
>Actually, you get Buttered(John, toast, slowly)
>
>>>
>>>and for D2
>>>
>>>D2*. G(John)
>
>and Buttered(John, toast)
>
>Still Davidson's point holds; there is no logical entailment. But in
>response, I can now write (in CL) axioms about kinds of action, for
>example
>
>(Mode slowly)
>(forall (x (y Mode) ...)(if (x ... y)(x ...)))
>
>which systematically restores the entailments. Moreover, this has the
>merit over the uniform case-based form suggested by Davidson, of
>allowing more nuanced entailments, by for example classifying
>different kinds of qualifier. But I will concede that Davidson's
>construction is widely used and often very natural.
Axioms about 'kinds of action', forsooth (see 10 lines back). Perhaps
you truly have been believing in universals all your life without knowing it.
>>>and thereby lose the entailment relation.
>>>Instead, says Davidson, we need to see D1. and
>>>D2. as having what he calls the following logical forms:
>>>
>>>D1**. there is some e, buttering_event(e) & agent_of(John,e) &
>>>slow(e)
>>>
>>>D2**. there is some e, buttering_event(e) & agent_of(John,e)
>>>
>>>respectively. The entailment is then clear.
>>>
>>>Care to fongle this?
>
>What has ANY of this got to do with what we were talking about?
See above.
Since you seem to like 'kind' I will try to formulate the main point
by using this term. Not every predicate 'F' is such that 'F(a)' is
sensibly translated as meaning: a is an instance of kind F. Consider
is_missing(John's gardenhose)
is_taller_than_John(Fred)
is_such_that_Socrates_is_wise(Roderick)
and so on, ad nauseam. There is no kind represented by 'missing
items', or 'taller than John items', or 'such that Socrates is wise'
items. So not all predicates correspond (even in your
set-theory-derived) sense. Geddit?
Until I get you to agree with this, I also will not be at the point
where you will understand what I mean by 'universal' and what I hope
you mean when you use 'kind'.
BS