Dear PatH,
<snip>
I don't think so, mia culpa for trying to be too cute. I'll
try again. Types are sets, OK. Why not just call them 'sets', then? I suspect
the reason is that while all types are sets, not all sets are types. Some sets
are, other sets are just damn silly sets. FOr example, the set of all
triangular pieces of 3-space might be a type, but the set of all African lions
over three years old, my aunt, the number 14 and the sodium atoms contained at this
moment in my left pinkie's fingernail, might not be a type. The point being
that a set really can be a set of anything, assembled for no rational reason at
all; but (I suspect) you don't want to be this liberal with what counts as a
type (?). If I'm right, what criterion distinguishes the sets which are types
from the other, sillier, sets? If I'm wrong, why not just say "set"
instead of "type" everywhere?
[MW] I’m pretty certain any set is allowed, otherwise the
powertype stuff doesn’t make a lot of sense.
If you want to discuss this
sort of stuff, you’re better engaging with Matthew and Chris, who’ve
actually bothered to go and read books on logic and philosophy.
4) Never thought about it, but I
can’t see why not. The bigger question is why on earth would you ?
Oh, because it is often handy. In RDFS for example the class
of all classes is a class. (What else would it be?) The reason for asking was
to probe into your underlying logic, to tell you the truth.
[MW] Well as you know I take the class of all classes as a
class, but I’m not sure where Chris P stands.
5) Purple is a type, it’s
extent is all things that are purple.
So colors are sets of things with that color, do I have that
right? Including all parts of things that are purple, I presume? This
does work, though the best account of color is that its a property of a surface
rather than of an object.
Being square is membership of
the type “square things”.
So is membership in a type a kind of thing, or
individual?
[MW] It’s a type of couple (see the ontology fragment
below).
? I fail to follow this. A couple of what? (Do you mean, a
set of 2-tuples? If so, I'm cool with that answer,
[MW] Yes.
but I'd like to be able to treat that set as an individual
(my sense), ie be able to talk about it standing in relations and having
properties.)
[MW] Yes. It is a thing (again you only need to read what is
below) and so can stand in a tuple.
, though you may also wish to
define other things like birth, which would be a type of individual, my
son’s birth is an individual – it had spatio temporal extent, and
had as it’s parts, a temporal state of his mother, a temporal state of
him, a temporal state of the birthing suite, a temporal state of the midwife,
and a highly stressed temporal state of me.
Yup, this all makes sense. I think when it comes to concrete spatiotemporal
entities we will be in almost complete agreement, though Im less of a strict
extensionalist (your sense) than you all are.
A death mask is obviously an
individual (it has an extent). There is a temporal extent of it when it was
touching a corpse’s face (haven’t we all ?).
Yes, but what I wanted to know about was the shape of
the mask. Is the shape an individual?
[MW] Depends a bit on what you think the shape actually is. If
you think it is the physical surface of the mask, then it is an individual (our
sense). If you mean the geometric shape – an abstraction of the physical
surface, it is a class (of all things with that shape).
Moby Dick, even 2nd edition of Moby Dick is a type.
OK, so the work is the set of its physical copies or
editions. So when Melville was sitting writing, what he was writing was a set,
none of whose elements existed at that time? Hmm. Seems kind of
implausible to me.
[MW] No, he was writing the first copy.
The copy of Moby Dick on my
bookshelf is an individual. An e-mail is a type,
An email is a set? That just seems plain flat wrong. You
can't send sets from place to place using network transfer protocols.
[MW] Again, depends what you are talking about, the common
content (we’ve been here before) or the physical sign.
the rendition of it on my
screen is an individual. I think all this is based on Strawson’s
utterance work, but you’d have to ask Chris about that…me no do
philosophy. Me engineer.
I think the points you raise are very interesting arguments, and
I’m glad someone’s thinking about stuff like that. If I ever decide
to do an ontology about Sherlock Holmes investigating quantum uncertainty of
death masks whilst simultaneously conjecturing about sets which contain
themselves, you’ll be the first person I call….just don’t
expect a call any time soon.
Every question had a direct root in a practical issue,
believe it or not. I'm surprised you havn't come across most of them
already.
[MW] And there are more, like what sort of thing is The President
of the United States?
Regards
Matthew
West
Information Junction
Tel: +44 560 302 3685
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On Feb 10, 2009, at 3:53 PM, Ian
Bailey wrote:
Does anybody read past the first
sentence before firing off responses to the
exploder ?
As I said earlier, this is the IDEAS *foundation*. I did ask what your
understanding of "foundation" was in a previous posting...I guess I
got my
response, albeit not quite in the manner I expected.
Under the foundation, we have common patterns for agent, process, etc.
As for syntax...I seem to recall getting a severe beasting from Pat for
suggesting RDF is just a syntax (it is).
I helped define and RDF, and I wrote
the semantics specification document, which is normative. RDF is not just a
syntax. Repetition of a mistake does not stop it being a mistake. By repeating
it, you are just making yourself look sillier.
The IDEAS categories are
extensional, therefore tightly coupled to the real world.
? I fail to see the connection
here. Set theory is extensional. Group theory is extensional.
I can choose to
represent them in RDFS if I wish, 'cos it's a syntax.
You can indeed, but not for that
reason.
In the previous mail,
I represented them as a tree of text...which is also a syntax. I could also
barcode them on my backside, 'cos that's a syntax (in fact I have, but
that's a private matter). Because we bothered to record our criteria for
identity of the IDEAS categories, we can be confident of what they are.
Because we know what they are, we don't give a monkey's what we use to
represent them. I realise this a quite a long way down the mail, so you
won't be reading it, but here goes again:
INDIVIDUALS have spatio-temporal extent (i.e. you can kick them, or could
kick them in the past / future)
TYPES are identified by their members - which could be individuals, types or
tuples
TUPLES are identified by their ends
OK, I've read all the way down.
Now, let me respond. First, OK y'all have described your system quite tightly
and thoroughly, which is good. But you are also stuck in a cul-de-sac,
apparently paying no attention to the rest of the world, which is not good. You
don't understand RDF and RDFS, which maybe isn't itself very important but I
fear may be only a symptom of a deeper malaise. You mis-use established
terminology ("individual" here being the worst culprit: that isn't
what everyone else means by "individual". For example, the number
three is an individual, but not one of yours.) Just generally, you appear to
not know about basics like the distinction between syntax and semantics, what
'extensional' means, the difference between actual and possible, and so on.
Look, I'm not meaning to criticize or pull rank here, just letting you know
that there is a big ontological world out there, and before suggesting that
your brand-new minor variation on a theme by Aristotle is the final answer to
the world's problems, it might be a good idea to try reading a little more
about what others have done. You aren't the first people to invent a formalized
system for representing general knowledge, and you ought to at least know a
little bit about what was already done. After all, suggesting any ontology as a possible general ontology standard amounts to making a VERY large
philosophical claim, one that most professional philosophers or ontologists
would hesitate to even approach. At the very least, it surely behooves one to
know just a little about the field in which one is making such grand
suggestions. Like knowing what some of the long words mean, and being able, or
maybe willing, to actually read and understand the specifications of the
notations one is bandying about.
Here's a few questions for y'all.
(1) Is Sherlock Holmes an
individual? One might say he is located in a possible space-time, but not in the actual one.
Do you want to say that? If so, how are the many possible but non-actual
space-times related to one another, if at all? If not, what do you want to say
about S.H. ?
(2) How much extent is required?
Is the event of a quantum being emitted by a sodium atom's moving from a higher
to lower energetic state an Individual? (How does one kick that?) Are things
like vortices in a fluid, waves on the ocean, burstings into flame, explosions
all Individuals? (How does one kick them?) Is an acceleration an Individual?
(Say my truck goes from zero to 30 in about a minute when I set off to work
tomorrow. Is that acceleration an Individual? How does one kick it?)
(3) You say a type is identified by its members, which I take to mean
that if it has the same members, its the same type. That sounds like saying
that a type is a set. Is a type a set, in fact? If not, how do they differ from
sets? If they are, are all sets types? If not, what distinguishes the type-type
sets from the non-type-type sets?
(4) You say that a type can be a
member of a type (which is good, and not un-extensional.) Can a type be a
member of itself? More generally, can there be circles of type-membership, so
that A is a type of B is a type of C is a type of A ? If not, why not?
(5) Into which basic ontic
category would you put the following: the number three; the color purple; the
property of being square; the relation between people of being the natural mother of ;
the shape of a face (in the sense in which a death mask has the same shape as the face it is a casting of); the
Krebs cycle in cellular biology; Moby
Dick, the novel by Melville
(not any particular imprint or edition of it, but the work itself); a website
(c.f. the current W3C debates over the notion of an "information
resource"); an email message; the sentences in that same email message; a
substance (such as clay or air: not any particular piece of it, but the stuff
itself); a time-interval? I realize this is a longish list, but since you
have your identity criteria so well defined, you ought to be able to rattle
them off pretty quickly.
like the underlying formalism of
an ontology. I would add
immediately that this isnt a clear
boundary, but your list
here doesn't seem to be about the
world being described so
much as about the apparatus you
propose to use to describe it.
The following classification is closer to a description of the
permissible syntactic categories:
-Thing
-Individual
-Type
-Powertype
-TupleTyple
-IndividualType
-Name
-NameType
-tuple (thing, thing, thing, ...etc.)
-couple (thing, thing)
-superSubtype (type, type)
-typeInstance (type, thing)
-powertypeInstance (powertype,
type)
-nameTypeInstance (nametype,
name)
-namedBy (thing, name)
-triple (thing, thing, thing)
-quadruple (thing, thing, thing, thing)
-quintuple (thing, thing, thing, thing, thing)
Common Logic, for example, is called a logic rather
than an ontology. But it is possible to define a dialect
of CL that uses the labels above to name the syntactic
features of CL.
- A thing is anything named by a CL name.
- A type is a monadic relation that is used as a
restriction on a quantified name.
But as Pat said, the boundary isn't clear. You could say that
your system does make the following "ontological commitment":
- If there exists a thing x and a thing y, then there exists
a couple consisting of x and y.
In CLIF, that statement could be written as the following axiom:
(forall (x y) (exists (z) (= z (couple x y))))
However, this level of commitment is far below what you would
get from adopting any first-order logic plus some obvious
mathematical theories that can be axiomatized in FOL: sets,
functions, relations, integers, real numbers, etc.
But that is still very far from giving us an ontology that can
represent all the stuff of science, engineering, business, etc.
John
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