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 pre-existing concepts
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.
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.
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 ontology elements.
Again: what do you mean here? What kind of combinations are you talking about? How are they expressed?
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