For example, a calculation process has an output of a number.
Numbers are one of the simplest forms of information, so if we can't do
numbers, then information in general is a problem.
The two options here are straight-forward; either we have numbers
because they are useful or, we don't have them because they introduce
more confusion than their utility. It's a cost-benefit issue.
Phil
Janna Hastings <janna.h...@gmail.com> writes:
> I'm not sure I understand. Why would you like 'number' to be included in
> BFO? Is 'number' a class in an ontology you wish to align with BFO? Or do
> you mean that you wish to include properties such as mass which have numeric
> values?
>
> Thanks, Janna
>
>
Measurement unit datum does not use numeral. Michel pointed out in a
previous mail that it uses a datatype property with a float value. Of
course, in OWL floats aren't numbers either ;-)
But we borrow (sort of) numbers from OWL rather than representing them
in IAO explicitly. This is cheating. But useful cheating for the
moment.
You point about alternate representations of numbers it interesting,
though, and deserves some thought. Please consider filing an issue.
http://code.google.com/p/information-artifact-ontology/issues/list
> Likewise, it has "conclusion textual entity"; conclusion is apparently,
> like number, hard, but text about it is okay.
We're more able to identify the textual entities and be clear about
identity criteria for them. Still waiting for a good proposal on how
to handle conclusions in general. I haven't been impressed by any so
far.
What's your strategy for dealing with hard things? My worry is that a
common way of dealing with hard things is to add a term to the
ontology with a label and no definition, and hope for the best. I
haven't found that to work very well.
> IAO demonstrates the problem with BFO. Barry argues that BFO clearly
> differentiates between numbers and numerals; I say, that by considering
> numbers out-of-scope, we are left with representing numerals instead, so
> BFO is actually forcing us to conflate the two.
Do you have an alternative that we should look at for inspiration?
> I think that IAO is less clear than it should be as a result.
Well, it's hard to argue that it couldn't use more clarity. But
frankly, I think IAO even as it is has made progress over what already
exists, and I credit BFO for bringing a perspective that I've found
helpful.
You said: "Numbers are one of the simplest forms of information".
Perhaps this makes sense to you, but I don't happen to find it very
illuminating. What definition of information supports the idea that
number is a subclass of it?
Elsewhere you say: "Ontologies should represent our shared confusion
as well as our shared understanding." How is representing our shared
confusion going to make IAO more clear?
-Alan
>On Dec 17, 2009, at 9:13 PM, Barry Smith wrote:
>
>>At 10:02 PM 12/13/2009, you wrote:
>>
>>>On Dec 12, 2009, at 10:47 AM, Barry Smith wrote:
>>>
>>>>At 01:59 AM 12/11/2009, you wrote:
>>>>
>>>>>On Dec 10, 2009, at 8:15 AM, Barry Smith wrote:
>>>>>
>>>>>>As I say, we are doing our best to improve the definitions of BFO
>>>>>>terms. We will be releasing some better definitions soon; though
>>>>>>these, too, will still surely be imperfect. Natural language is,
>>>>>>for
>>>>>>these sorts of purposes, an imperfect vehicle. (But relying on a
>>>>>>formal language has its problems, too.) There is now a great
>>>>>>deal of
>>>>>>experience of using BFO, and enough documentation explaining how
>>>>>>it
>>>>>>is used
>>>>>
>>>>>Can you briefly point to some of this? That would be genuinely
>>>>>helpful
>>>>>for me.
>>>>
>>>>You can start digging around here:
>>>>http://www.ifomis.uni-saarland.de/bfo/
>>>>The 'manual' was put together in haste be a student of mine some
>>>>time ago, so treat it gentlily. We are preparing a thoroughly
>>>>revised version for MIT Press, and I may be able to send you the MS
>>>>in the near future. There is more , but this is probably enough to
>>>>get yous started.
>>>
>>>Thanks, but I was mostly wondering about papers reporting the
>>>*experience of using* you refer to above.
>>
>>There are several links under the users tab at the
>>
>>http://www.ifomis.uni-saarland.de/bfo/
>>
>>site
>
>OK, thanks.
>
>>
>>>Do you actually believe all this stuff about universals comprising
>>>reality, and ontologies being solely concerned with the description
>>>of
>>>universals? (Your student needs to read more about grue and bleen, by
>>>the way :-)
>>
>>I actually do believe it, though it is clear that we need facility
>>for ontology terms representing classes which are not extensions of
>>universals, in addition to the first-class terms representing
>>universals. The latter is, I'm afraid, what science is all about,
>>and that your talk of 'properties' as capturing what is general in
>>reality can properly be made sense of only by appeal to universals.
>
>It seems increasingly clear that you and I live in entirely different
>worlds. I really, really have absolutely no idea what you are talking
>about. And I do know quite a lot about (some) sciences :-)
>
>What I find so strange about much of these emails is that people quite
>frequently express puzzlement about whether something is a continuant,
>or is a universal, and you infallibly tell them the answer, but you
>never tell them what criteria you are using to make these decisions.
>Your recent reply to P.Def, for example, says that Fur is 'close to'
>being a universal, but that 'furry animal' is not. But Barry, *how* do
>you make such judgements? What thoughts or criteria are behind them?
>To me, they sound like completely arbitrary pronouncements. I have no
>idea how you are making them, even intuitively. If I were shown some
>other examples, the only way I could possibly answer such questions
>would be to ask you.
I have been trying to teach you, but I seem not to be doing a very good job.
First, being a universal is like being true; there is no easy marker,
so that we can point, e.g. to pieces of language and say: these
represent universals, those do not. There are some linguistic clues
(universals are likely not referred to by means of disjunctive
noun-phrases, for example), but the only effective way to discover
what the universals are in reality is to do science, to see what
terms are used indispensably in the formulation of scientific laws.
Nowadays, some of this science is done with the help of ontology
building. All of it is, like all science, tentative and provisional;
but also (I hope we are all sensible enough to believe) getting
better with time.
Biologists engaged in collecting and reasoning with phenotype
descriptions use terms like 'furry' to describe phenotypes. This
leads me to hypothesize that 'furriness' designates a universal. (We
have lots of instances; the term is used, at least, in scientific
descriptions.)
Does 'furry animal' represent a universal? I believe not. But
fortunately we do not need to worry about this, since we have the two
universals, furriness and animal, and we can build ontologies by
using cross-products without having to commit ourselves to the
existence of the furry animal universal in their asserted hierarchies.
>>(Properties alone do not capture what is general, since we have
>>properties like 'is identical to Patrick Hayes')
>
>Generality is expressed using quantifiers.
not all by themselves, it isn't
>But there is no distinction
>in kind between a property which is true for large swathes of reality
>and one which it true only very locally. They are both properties, but
>differ in extent.
See my remarks on what you call 'kinds' in earlier email.
BS
The reason is probably because I have long since decided that the
distinction between universal and not universal, or if you prefer, the
category of 'universal', is ultimately meaningless. I say,
ultimately, because of course it - the distinction - may be reasonably
clear in a given context of use. But I do not believe that it is a
sensible distinction to insist upon in any ontology that is likely to
be extended or to interact with other ontologies (as the status of
'universal' is likely to change with context), and also that it has no
ultimate meaning (because what counts as 'universal' is going to
change as science changes, or even within specialized subdisciplines)
and also that it has no real utility (since to count something as not
universal says nothing about it other than that it can admit
exceptions, which is true of virtually all properties that have ever
been conceptualized by any thinker.) It seems to me that you in fact
agree with this, in essence. Your own judgements about universality
seem to often be ad-hoc, guarded or provisional.
> First, being a universal is like being true; there is no easy marker,
> so that we can point, e.g. to pieces of language and say: these
> represent universals, those do not. There are some linguistic clues
> (universals are likely not referred to by means of disjunctive
> noun-phrases, for example), but the only effective way to discover
> what the universals are in reality is to do science, to see what
> terms are used indispensably in the formulation of scientific laws.
Quite. But surely the lesson of science is that the only real
universals are to be found in particle physics, and even those are
under constant review and hostage to theoretical advances which are
universally acknowledged to be incomplete.
> Nowadays, some of this science is done with the help of ontology
> building. All of it is, like all science, tentative and provisional;
> but also (I hope we are all sensible enough to believe) getting
> better with time.
>
> Biologists engaged in collecting and reasoning with phenotype
> descriptions use terms like 'furry' to describe phenotypes. This
> leads me to hypothesize that 'furriness' designates a universal. (We
> have lots of instances; the term is used, at least, in scientific
> descriptions.)
>
> Does 'furry animal' represent a universal? I believe not. But
> fortunately we do not need to worry about this, since we have the two
> universals, furriness and animal, and we can build ontologies by
> using cross-products without having to commit ourselves to the
> existence of the furry animal universal in their asserted hierarchies.
We do not have to commit to it AT ALL. We can simply write ontologies
in logic, completely ignoring this question of what counts as a
universal. As I write axioms I never seem to have to ask myself, but
is this a universal?? The question simply does not arise. So let us
ignore it. We have enough problems already, without inventing
unanswerable questions for ourselves to answer.
Pat
>
>>> (Properties alone do not capture what is general, since we have
>>> properties like 'is identical to Patrick Hayes')
>>
>> Generality is expressed using quantifiers.
>
> not all by themselves, it isn't
>
>> But there is no distinction
>> in kind between a property which is true for large swathes of reality
>> and one which it true only very locally. They are both properties,
>> but
>> differ in extent.
>
> See my remarks on what you call 'kinds' in earlier email.
>
> BS
>
> --
> informatio...@googlegroups.com
> To change settings, visit
> http://groups.google.com/group/information-ontology
>
------------------------------------------------------------
This is why we should never buy a laptop, since the laptops they will
be selling next month will be better and cheaper.
>
>and also that it has no real utility (since to count something as not
>universal says nothing about it other than that it can admit
>exceptions, which is true of virtually all properties that have ever
>been conceptualized by any thinker.)
I believe that we are beginning to understand how to deal with this,
in biology at least, through the ideas on canonicity introduced by Rosse
http://www.ncbi.nlm.nih.gov/pubmed/14759820
and drawing on the idea, already present in Aristotle, that
universals (natural kinds) always have borderline instances.
But note that the crucial distinction is not that between universals
and ad hoc classes, but that between universals and instances.
>It seems to me that you in fact
>agree with this, in essence. Your own judgements about universality
>seem to often be ad-hoc, guarded or provisional.
>
> > First, being a universal is like being true; there is no easy marker,
> > so that we can point, e.g. to pieces of language and say: these
> > represent universals, those do not. There are some linguistic clues
> > (universals are likely not referred to by means of disjunctive
> > noun-phrases, for example), but the only effective way to discover
> > what the universals are in reality is to do science, to see what
> > terms are used indispensably in the formulation of scientific laws.
>
>Quite. But surely the lesson of science is that the only real
>universals are to be found in particle physics,
sounds like the no true Scotsman fallacy:
Teacher: All Scotsmen enjoy haggis.
Student: My uncle is a Scotsman, and he doesn't like haggis!
Teacher: Well, all true Scotsmen like haggis.
> and even those are
>under constant review and hostage to theoretical advances which are
>universally acknowledged to be incomplete.
Let me repeat, for the 9th and last time, that I am aware that
science is subject to correction, and that those ontologies which are
parts of science will therefore also be subject to correction.
> > Nowadays, some of this science is done with the help of ontology
> > building. All of it is, like all science, tentative and provisional;
> > but also (I hope we are all sensible enough to believe) getting
> > better with time.
> >
> > Biologists engaged in collecting and reasoning with phenotype
> > descriptions use terms like 'furry' to describe phenotypes. This
> > leads me to hypothesize that 'furriness' designates a universal. (We
> > have lots of instances; the term is used, at least, in scientific
> > descriptions.)
> >
> > Does 'furry animal' represent a universal? I believe not. But
> > fortunately we do not need to worry about this, since we have the two
> > universals, furriness and animal, and we can build ontologies by
> > using cross-products without having to commit ourselves to the
> > existence of the furry animal universal in their asserted hierarchies.
>
>We do not have to commit to it AT ALL. We can simply write ontologies
>in logic, completely ignoring this question of what counts as a
>universal.
When people attempt to build ontologies following this rule, they
often make errors some of which could be avoided if they are taught
to avoid confusing universals and instances.
http://www.bioontology.org/top-10-errors
is just a sampling from lists of thousands of such errors which I can
supply you with if you insist.
> As I write axioms I never seem to have to ask myself, but
>is this a universal?? The question simply does not arise. So let us
>ignore it. We have enough problems already, without inventing
>unanswerable questions for ourselves to answer.
You really should get out more, and discover how hard it is for those
who were not trained in philosophy to avoid use-mention confusions,
is-a overloading, confusing knowledge with the thing known, confusing
information with the object that it is information about, and all the
other things which generate crappy ontologies, some of them happily
imposed e.g. by the Federal Government on US hospitals.
http://ontology.buffalo.edu/hl7/doublestandards.pdf
BS
But laptops, unlike pointless distinctions, are useful.
>> and also that it has no real utility (since to count something as not
>> universal says nothing about it other than that it can admit
>> exceptions, which is true of virtually all properties that have ever
>> been conceptualized by any thinker.)
>
> I believe that we are beginning to understand how to deal with this,
> in biology at least, through the ideas on canonicity introduced by
> Rosse
> http://www.ncbi.nlm.nih.gov/pubmed/14759820
> and drawing on the idea, already present in Aristotle, that
> universals (natural kinds)
Whoa. A universal is a natural kind? That seems like a new/different
idea. I thought universals were supposed to be *universal*. Natural
kinds are a much messier notion (and probably more useful.) Whether
something is a natural kind isn't really of central importance for
reasoning, for example, but it can avoid pointlessly looking for a
definition.
> always have borderline instances.
> But note that the crucial distinction is not that between universals
> and ad hoc classes, but that between universals and instances.
No, thats is the set/member distinction, which applies both to
properties that are universals and those that are not.
>> It seems to me that you in fact
>> agree with this, in essence. Your own judgements about universality
>> seem to often be ad-hoc, guarded or provisional.
>>
>>> First, being a universal is like being true; there is no easy
>>> marker,
>>> so that we can point, e.g. to pieces of language and say: these
>>> represent universals, those do not. There are some linguistic clues
>>> (universals are likely not referred to by means of disjunctive
>>> noun-phrases, for example), but the only effective way to discover
>>> what the universals are in reality is to do science, to see what
>>> terms are used indispensably in the formulation of scientific laws.
>>
>> Quite. But surely the lesson of science is that the only real
>> universals are to be found in particle physics,
>
> sounds like the no true Scotsman fallacy:
>
> Teacher: All Scotsmen enjoy haggis.
> Student: My uncle is a Scotsman, and he doesn't like haggis!
> Teacher: Well, all true Scotsmen like haggis.
>
>> and even those are
>> under constant review and hostage to theoretical advances which are
>> universally acknowledged to be incomplete.
>
> Let me repeat, for the 9th and last time, that I am aware that
> science is subject to correction, and that those ontologies which are
> parts of science will therefore also be subject to correction.
I know, but you also insist upon ignoring the engineering consequences
of this for ontology construction. If you know that something is going
to change, or is going to be different in the next ontology over (the
one built for the other subdiscipline), and if its not particularly
useful or important in any case, why insist on giving it such
importance and a name like "universal" ?
>
>>> Nowadays, some of this science is done with the help of ontology
>>> building. All of it is, like all science, tentative and provisional;
>>> but also (I hope we are all sensible enough to believe) getting
>>> better with time.
>>>
>>> Biologists engaged in collecting and reasoning with phenotype
>>> descriptions use terms like 'furry' to describe phenotypes. This
>>> leads me to hypothesize that 'furriness' designates a universal. (We
>>> have lots of instances; the term is used, at least, in scientific
>>> descriptions.)
>>>
>>> Does 'furry animal' represent a universal? I believe not. But
>>> fortunately we do not need to worry about this, since we have the
>>> two
>>> universals, furriness and animal, and we can build ontologies by
>>> using cross-products without having to commit ourselves to the
>>> existence of the furry animal universal in their asserted
>>> hierarchies.
>>
>> We do not have to commit to it AT ALL. We can simply write ontologies
>> in logic, completely ignoring this question of what counts as a
>> universal.
>
> When people attempt to build ontologies following this rule, they
> often make errors some of which could be avoided if they are taught
> to avoid confusing universals and instances.
I grant you that people make errors. I am far less convinced that
teaching them to avoid confusing warbles with blongles is going to
help them avoid errors.
> http://www.bioontology.org/top-10-errors
> is just a sampling from lists of thousands of such errors which I can
> supply you with if you insist.
>
>> As I write axioms I never seem to have to ask myself, but
>> is this a universal?? The question simply does not arise. So let us
>> ignore it. We have enough problems already, without inventing
>> unanswerable questions for ourselves to answer.
>
> You really should get out more, and discover how hard it is for those
> who were not trained in philosophy to avoid use-mention confusions,
> is-a overloading, confusing knowledge with the thing known, confusing
> information with the object that it is information about, and all the
> other things which generate crappy ontologies, some of them happily
> imposed e.g. by the Federal Government on US hospitals.
I do get out quite a lot, and the moral I draw from all this is that
philosophers should make less noise and be more humble. Have you
noticed that in spite of all these deplorable philosophical errors,
the world actually manages to carry on quite well in getting its
business done? That the ubiquity of use/mention confusions in language
since time immemorial (I noticed a humdinger recently while listening
to the Messiah: "and his name shall be called, wonderful counselor,
the everlasting father, the prince of peace.") does not, in fact, seem
to greatly matter. People do not confuse the word for the world, in
spite of the way that they talk. Nor do they confuse objects with
thoughts, etc.. How is it that apparently foolish errors like these
don't cause the fabric of societal communication to rend apart? There
is a moral here for our own professional work, and its not that a few
enlightened souls should take on the task of teaching the rest of the
planet how to Think Proper.
But apart from this larger issue, and even if we were to accept that
getting ontologies damn-silly-error-free is a good goal to attempt,
its not at all clear how adopting this particular meaningless
distinction (between universal and mere property) is going to help
avoid making use/mention confusions. They seem on the face of it to
have nothing to do with one another.
Pat
I invite you to compare the current version of the Gene Ontology,
above all its structure and definitions, with the way it was before I
became involved (when it contained nice definitions such as hemolysis
=def. the causes of hemolysis). The Gene Ontology itself is
demonstrably useful. The Gene Ontology Consortium demonstrably finds
what I do useful.
> >> and also that it has no real utility (since to count something as not
> >> universal says nothing about it other than that it can admit
> >> exceptions, which is true of virtually all properties that have ever
> >> been conceptualized by any thinker.)
> >
> > I believe that we are beginning to understand how to deal with this,
> > in biology at least, through the ideas on canonicity introduced by
> > Rosse
> > http://www.ncbi.nlm.nih.gov/pubmed/14759820
> > and drawing on the idea, already present in Aristotle, that
> > universals (natural kinds)
>
>Whoa. A universal is a natural kind?
as I explained earlier in this interchange, e.g. on Dec. 18. And
again, one reason for using 'universal' rather than 'type', 'kind',
'sort', etc., is that, because it is so ugly, it has not become
associated with a detritus of alien meanings.
>That seems like a new/different
>idea. I thought universals were supposed to be *universal*. Natural
>kinds are a much messier notion (and probably more useful.) Whether
>something is a natural kind isn't really of central importance for
>reasoning, for example, but it can avoid pointlessly looking for a
>definition.
>
> > always have borderline instances.
> > But note that the crucial distinction is not that between universals
> > and ad hoc classes, but that between universals and instances.
>
>No, thats is the set/member distinction, which applies both to
>properties that are universals and those that are not.
You still, I'm afraid, don't get it.
In the 'natural kind' idiom you seem to prefer, there is something of
a logically different sort being said when we assert
[1] Fido is an instance of the natural kind dog
and
[2] Fido is a member of the set {Fido, 3, the planet Jupiter}
And again (since we have been round this circle at least once
already), if we say
[3] Fido is a member of the set of dogs
then what we are saying is really
[4] Fido is a member of the set defined by the fact that all its
members are instances of the natural kind dog
and so we cannot understand [4] unless we already understand [1].
Not at all. I take these consequences very seriously, as my ontology
engineering colleagues will attest.
>If you know that something is going
>to change, or is going to be different in the next ontology over (the
>one built for the other subdiscipline), and if its not particularly
>useful or important in any case, why insist on giving it such
>importance and a name like "universal" ?
The exquisite pleasures gained by irritating you by using this name
are, as they say, priceless.
It did and it does. The full strategy is a work in progress, and we
are learning all the time about how to do it, but it is having
demonstrable positive effects already -- and no one has been able to
work out a competing strategy which has equivalent positive effects.
> > http://www.bioontology.org/top-10-errors
> > is just a sampling from lists of thousands of such errors which I can
> > supply you with if you insist.
> >
> >> As I write axioms I never seem to have to ask myself, but
> >> is this a universal?? The question simply does not arise. So let us
> >> ignore it. We have enough problems already, without inventing
> >> unanswerable questions for ourselves to answer.
> >
> > You really should get out more, and discover how hard it is for those
> > who were not trained in philosophy to avoid use-mention confusions,
> > is-a overloading, confusing knowledge with the thing known, confusing
> > information with the object that it is information about, and all the
> > other things which generate crappy ontologies, some of them happily
> > imposed e.g. by the Federal Government on US hospitals.
>
>I do get out quite a lot, and the moral I draw from all this is that
>philosophers should make less noise and be more humble.
I agree.
>Have you
>noticed that in spite of all these deplorable philosophical errors,
>the world actually manages to carry on quite well in getting its
>business done? That the ubiquity of use/mention confusions in language
>since time immemorial (I noticed a humdinger recently while listening
>to the Messiah: "and his name shall be called, wonderful counselor,
>the everlasting father, the prince of peace.") does not, in fact, seem
>to greatly matter.
http://www.syleum.com/2009/03/17/healthcare-data-model/
> People do not confuse the word for the world, in
>spite of the way that they talk.
Computers, unfortunately, do. The members of many healthcare
standards bodies (etc.) do. The authors of W3C standards documents do.
> Nor do they confuse objects with
>thoughts, etc.. How is it that apparently foolish errors like these
>don't cause the fabric of societal communication to rend apart?
An example (it would be funnier if the HL7 organization (represented
here by Dan) were not involved in keeping us alive when we get to hospital):
http://hl7-watch.blogspot.com/2006/02/is-there-difference-between-person-and.html
I can give you the names, off-line, of leading healthcare IT
professionals who have been tearing their hair out for years because
of the incoherence of the HL7 standard along precisely the dimensions
you, whistling Haendel, see no problems with.
>There
>is a moral here for our own professional work, and its not that a few
>enlightened souls should take on the task of teaching the rest of the
>planet how to Think Proper.
Again, there is a significant well-authenticated demand for people
who can take on this task.
>But apart from this larger issue, and even if we were to accept that
>getting ontologies damn-silly-error-free is a good goal to attempt,
>its not at all clear how adopting this particular meaningless
>distinction (between universal and mere property) is going to help
>avoid making use/mention confusions. They seem on the face of it to
>have nothing to do with one another.
The confusion of property with predicate is one example of the
use-mention confusion.
I have argued earlier in this interchange that, to get clear about
the relations between predicates and properties we need to become
clear about the fact that not all predicates correspond to
properties. The reason is analogous to the reason why [1] and [2]
above are logically distinct sorts of assertions. You get one clear,
there is hope that you can get the other clear.
BS
....
>>>
>>> This is why we should never buy a laptop, since the laptops they
>>> will
>>> be selling next month will be better and cheaper.
>>
>> But laptops, unlike pointless distinctions, are useful.
>
> I invite you to compare the current version of the Gene Ontology,
> above all its structure and definitions, with the way it was before I
> became involved (when it contained nice definitions such as hemolysis
> =def. the causes of hemolysis). The Gene Ontology itself is
> demonstrably useful. The Gene Ontology Consortium demonstrably finds
> what I do useful.
Im sure you do many useful things, Barry. But I was referring to the
notion of Universal, not to you.
Well, Im afraid I still disagree. These are not different in their
*logic*. They differ, perhaps, in that the sets in question differ.
But even this is very hard to make into a *logical* distinction. In
both cases, the logic (in the exact sense of the set of correct
entailments from the assertion) sanctions exactly the same kinds of
entailments. The logic does not care about what 'kind' of set - or, if
you prefer, what kind of predication - it is, only that it is a
predication.
> And again (since we have been round this circle at least once
> already), if we say
>
> [3] Fido is a member of the set of dogs
>
> then what we are saying is really
>
> [4] Fido is a member of the set defined by the fact that all its
> members are instances of the natural kind dog
True. But one can say this about any set, membership in which can be
otherwise characterized linguistically. X is a member of the set {x:
P(x) } just when P(X).
>
> and so we cannot understand [4] unless we already understand [1].
Not at all. They are just two ways of saying the same thing. Neither
of them has epistemic priority over the other. True, the 'set' way of
talking may be less natural to someone without a mathematical
background; but then I have never argued that we should be talking of
sets explicitly. I prefer the simple FO style of predication, using
CLIF notation: (Dog Fido), (Silly Fido) , where someone has, for some
crazy reason, asserted that
(forall (x)(iff (Silly x)(or (= x Fido)(= x 3)(= x Jupiter)) ))
Silly is, of course, silly; but once it has been introduced into the
lexicon, (Silly Fido) is perfectly meaningful and has the same
relation to Silly (and to Fido) that (Dog Fido) has to Dog (and Fido).
Pat
PS I will not pursue the rest of this exchange, as it is getting way
too ad hominem to be useful. You may have the last word.