Just short responses to two points.
I think we have almost bottomed out here on differences that can be fruitfully
discussed further in anticipation of learning something.
(1) [PC] >> Is it possible that learning *some*
new things always requires creating new primitives? Possibly, but
that is the question that I have suggested can be investigated
To investigate that is the business of
cognitive psychology, not ontology engineering. I'm just not interested in this
question, and I don't think it is germane to this forum.
I strongly disagree, and feel
that the question of how many primitives are required to express the
meanings of an unlimited number of domain terms is one of the most basic
questions, beyond the definition of the basic logic, that can be asked
about how an ontology can be structured so as to achieve broad interoperability,
and I think it would be inherently interesting to anyone who deals in
representation of concepts. But ‘de gustibus non disputandum’
and if this is not a matter of interest to you, your opinion is noted, and there
is no point in discussing that further. It also has the very practical virtue
of providing a tactic that can focus collaborative construction of a common
foundation ontology on the minimum number of basic ontology elements that will
serve the purpose of translating among multiple ontologies. If you
don’t believe that there are such things as primitives, then I can see
this point as being questionable to you, but I feel strongly that the linguistic
evidence of the dictionary defining vocabularies is strongly suggestive of such
primitives, and if you don’t think that linguistic descriptions are
sufficiently related to ontological expressions, then again we just differ and
this is still a question that has to be resolved by experiment. If you
think it’s a waste of time, don’t participate.
(2) [PC] >> Well, knowledge is certainly open-ended,
but if new concepts (or terms labeling those concepts) are always composed from
some combination of pre-existing concepts
[PH] >> Again, what ARE you talking about? What is
this 'composed from some combination'? What kind of composition operations do
you have in mind here? How does these concept combinators relate to logical
ontologies? None of this makes sense to me.
time you (a) create an element in an ontology (type or relation) and (b) the
axioms expressing the intended meaning of that element (to a level of detail
sufficient for your intended purpose) contain only terms already pre-existing in
the ontology (no two or more newly created elements depend mutually one each other
for their axiomatic description); and (c) one asserts that the intended meaning
of that ontology element is adequately captured by the axioms, without appealing
to known instances of the type, or to a linguistic description that is
not also expressed by the axioms, then that type or relation is, in the sense I
am discussing, “expressed by” or “described by” or “specified
in terms of” the pre-existing ontology elements, i.e. it is not a “primitive”
in the sense I am using it for an ontology element. In the case of
relations, a proper description requires that every newly created relation have
some logical inference as part of its description. Relations that inherit
logical inferences from parent relations do not require additional inferences
This operation of ontological description does not, in my view,
require a “necessary and sufficient” definition in order to qualify
as “non-primitive” . It only has to express the intended
meaning axiomatically so that a person who understands the axioms can understand
the intended meaning without a textual gloss, and without pointing to instances
of a type or instances of usage of a relation – and the axiomatic specification
should be sufficiently detailed so that ambiguities that might occur to another
ontologist as being relevant to the same application are absent. This may
still leave, in some sense. some “primitive” component unspecified
logically (as with a natural kinds), but if the axiomatic description is sufficient
to distinguish each element from all the others, and is useful for the intended
purpose of the domain ontology, then it can be said, in the sense I am using,
to be “described by” or “specified by” or “expressed
by” a combination of pre-existing ontology elements – it is not a “primitive”
When you say “Those
various temporal theories can all be expressed in terms of three
concepts: time-point, time-interval and duration.” , what do you mean by
that? Is being “expressed in terms of” used only for
necessary and sufficient definitions?
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Saturday, January 10, 2009 7:39 PM
To: Patrick Cassidy
Cc: '[ontolog-forum] '
Subject: Re: [ontolog-forum] FW: Next steps in using ontologies as
On Jan 10, 2009, at 12:40 AM, Patrick Cassidy wrote:
... I confess it has been an assumption of mine that,
from the point of view of a “primitive” concept being indivisible
into smaller primitive concepts (crudely analogous to an atom, in its role as a
component of molecules), that a finite inventory of such primitive-atoms (if
such exists) would be unique.
Ignoring the finer to-and-fro points of the argument
for a moment, this seems to capture the basic place where we differ. You have a
central vision - I can't use a more precise term - of concepts being 'formed'
out of other concepts. by some process of combination, a kind of conceptual
chemistry; and then there must be a collection of elements, a kind of concept
periodic table. This analogy seems to drive a lot of your intuitions in this
debate. But I don't share this intuition, and indeed I can't make philosophical
sense of it: it seems to me to simply rest on a mistake, one that Fodor has
also critiqued very acutely. Concepts simply aren't made up of combinations of
other concepts in this way. They are all "atomic".
(Well, virtually all: all the 'natural kind' concepts, as opposed to artificial
combinations such as "French women between the ages of 25 and 50".)
Just look at a first-order theory: all the names in it are on
an equal footing; none are more 'primitive' than another, and they have no
internal conceptual structure which would permit their being decomposed into
something simpler or more elemental. The chemistry atom/molecule analogy is
just misleading. Peirce made the same mistake, and others since then (mostly
psychologists) have done so, but it seems to me that its long past time to bury
this idea of concepts having 'structure'. They don't divide into smaller
things, so they are all "primitive"; which is just another way of
saying that "primitive" isn't a useful notion here.
I have never seen this point raised, and it may be
significant, but right now I can’t think of any way a set of indivisible
primitives could be anything but unique.
But surely the time catalog is a clear case of this non-uniqueness.
I fail to understand how you cannot see this, it seems so obvious. What would
you reduce all of it to?
Limited imagination, perhaps.
Now I have noticed that there are mathematical
objects that have very non-intuitive properties, and perhaps a mathematician
can provide some examples of how a set of primitive concepts (not divisible
into component primitive concepts) might be able to be formulated in more than
one way. I am genuinely curious about this suggestion.
There are many, many ways to model space, for example, all
of them different and none of them reducible to the others.
(2) are primitives finite in number?
[PC] >> , though the modules can also have other ontology
elements in them. It is not clear to me that we can have a *stable*
set of modules to serve the purpose of interoperability unless we have some
confidence that all or most of the terms needed to express the meanings of
domain terms are there at the start.
[PH] > Seems clear to me that if we impose this condition
as a requirement, we have shot ourselves in the foot. And why should the set of
concepts be "stable" ? Isn't it more realistic to assume that new
concepts will always be being constructed, that knowledge is always open-ended?
Well, knowledge is certainly open-ended, but if new concepts
(or terms labeling those concepts) are always composed from some combination of
Again, what ARE you talking about? What is this 'composed
from some combination'? What kind of composition operations do you have in mind
here? How does these concept combinators relate to logical ontologies? None of
this makes sense to me.
, then the number of primitives need not increase as
knowledge increases. This may depend on what you mean by
‘knowledge’. With a set of basic concepts we can predict an
infinite number of things that *might* exist in the real world, but I
think of knowledge as knowing what actually does exist and what doesn’t.
Learning about the laws of physics (and chemistry and biology) that exist
in our real world allows us to know some of the things that can’t exist.
That’s knowledge, in my lexicon, but it doesn’t necessarily
require new primitives.
?? Really? So when you first learned about, say, the
distinction between temperature and heat (an example I recall especially
vividly from my own education), you already had all the necessary mental
apparatus to describe thermodynamics? The learning was just juggling the same
basic stock of ideas in a new way? It sure didn't feel like that to me: it felt
like learning something entirely new, something I had never previously thought.
Similarly the first time I came across the notion of entropy, it was a wholly
new idea, not reducible to anything previously known. I was able to use it to
understand things that had been previously mysterious. My inventory of mental
concepts had grown.
It continues to grow. Not long ago I learned the idea of
"duende", a word that cannot be translated into English.
it possible that learning *some* new things always requires creating new
primitives? Possibly, but that is the question that I have
suggested can be investigated
To investigate that is the business of cognitive psychology,
not ontology engineering. I'm just not interested in this question, and I don't
think it is germane to this forum.
by the process of creating a plausible set of ontology elements
based on primitives (as best we can discern them) and then seeing how quickly
that inventory in the FO must increase to allow the elements in each new
additional domain ontology to be expressed in terms of the primitive
set. If there is a finite set, then from the increase in required
primitives for each new block of domain concepts, it will be possible to assign
a probability that the total inventory will reach an asymptote at
infinity. The alternative is that no limit is indicated, and the number
of primitives behaves, say, like the number of prime numbers as the number of
integers increase. I do not know for sure which is more ‘realistic’,
but my suspicion lies with the finite number, based on evidence from linguistic
usage, such as the Longman defining vocabulary and the relatively small number
(2000 – 5000) in AMESLAN sign language dictionaries. There are
other suggestive kinds of evidence from language, but what needs to be
determined experimentally is whether the finite defining vocabularies in
languages are in fact analogous (at least on the point of the number of
primitives) to the task of creating ontology elements as combinations of other
Again: what do you mean here? What kind of combinations are
you talking about? How are they expressed?
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