|To:||"Patrick Cassidy" <pat@xxxxxxxxx>|
|From:||Pat Hayes <phayes@xxxxxxx>|
|Date:||Thu, 20 Mar 2008 15:16:39 -0500|
At 3:02 PM -0400 3/20/08, Patrick Cassidy wrote:
PatH gave some interesting additional detail about his formalization of 3D/4D inconsistency:
[PC] >. In the axiomatization above PatH says that (C at t) = c for all times t;
> . . .
[PH] > Those two senses ARE the contradiction between 3D and 4D.
[PC] >> Thus the subtle problem in the first set of axioms is that (x at t) was
So, it appears that PatH agrees that the syntactic structure (x at t) which has one meaning in his 3D formalization, and a different meaning in the 4D formalization, will cause an apparent contradiction when one attempts to use it in one sense in a grammar where it has a different sense.
Not sure about the 'agrees'; this is what Ive been trying to tell you since the beginning of this conversation. Except that the contradiction isn't 'apparent', and speaking strictly there is no 'grammar' involved: all of these are axioms written in a single logical language.
It is inappropriate to call the misuse of a term a ?logical contradiction¹. It¹s just an error in using the language.
No. In 4D, it is definitely not an error to time-slice me. In 3D, assuming I am a continuant, it is. (Or, if its not an error, it gives rise to a contradiction, as we have now all seen.) Two different frameworks giving two different ontologies, both written in the same language. Of course one can translate between them, and of course they are both describing, in a sense, the same objective reality. Nevertheless, they are as they stand different and incompatible (or inconsistent), yet written in the same logical language and even to a large extent using the same signatures. For example, it would be perfectly appropriate to have a single name 'PatHayes' denoting me in both ontologies. But if we simply unified them, we would need to have two names denoting two different PatHayeses.
The question I am addressing is not whether the grammars of 3D and 4D are identical, but whether there is a translation between them that preserves the intended meanings of the terms that are used. This is tested by first trying to find a *translation* of the terms (or phrases) from one grammar into the corresponding terms (if any) in the other grammar.
Ah, but this is a new idea in this thread. Yes, there is a translation of one ontology into the other. This has been known for a while. (Actually, strictly the 4D can express things that are impossible in the 3D, so the translation is not always possible in one direction.) But we began with a discussion of the claim that there was a single ontology that everyone would find satisfactory.
If an accurate translation can be found, I consider the two terms to be logically consistent (though requiring translation).
Then you really should express yourself more carefully. Obviously, being logically consistent, and being logically consistent after a translation, are not the same notion.
A single ontology that contains *both* perspectives
I don't think this can exist, in any useful sense. If it does, then it will be no more than a kind of overlay of one on the other, requiring the ontology to distinguish between things like me (3D) vs my lifetime (4D), which abandons completely one of the main reasons for using the 4D framework in the first place.
would have to choose one of the meanings for that syntactic structure, and use a different syntactic structure for the other meaning.
So there needs to be two of everything. Two PatHayeses, two PatCassidys, etc.. Yes, indeed, this can be done: what it amounts to in practice is abandoning the 4D approach and using the 3D one, since the needless obfustication of being obliged to make all these arbitrary classifications into continuants vs occurrents is what motivates the 4D ontological approach in the first place.
This isn¹t a change of meaning for the concept represented by the terms, just a change of representational formalism in which to express those concepts. That is not a logical incompatibility.
Sure it is, if both have to be represented in a single logic, and we wish to retain the full expressive power of both of them. It is an inherent assumption of the 4D approach that there is only one, single entity with a given 4D envelope. The denial of this is seen as a necessary truth in the 3D ontology. It is hard to find a more direct and unequivocal logical clash between assumptions. If you put them together directly, what keeps the two 'halves' separated adequately? Loose talk of 'grammars' needs to be fleshed out with more detail: the only grammar that I can see as being relevant here is the EBNF of CLIF.
I am not at all clear why PH considers the misuse of a term as demonstrating inconsistency.
In one framework it is not misuse: it is normal use, required in order to perform ordinary inferences. The ontology would be incomplete without it. But in the other framework, it is either illegal or produces inconsistencies.
If I tried to use ³rouge² in an English sentence, and intended it to mean the attribute ³red², of course it would generate nonsense. I would have to translate it first (from the French), even if it looked like an English word. In the demo by PatH he uses terms without translation.
But Im not translating between languages. All of the axioms are written in the same logical language (CLIF). What is needed is to translate between ontologies. And we need to translate between them because if we simply unite them into a single ontology (ie. simply conjoin them without translation), the result is logically inconsistent. Which was my point all along, and which you have until now adamantly denied.
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