Re: [ontolog-forum] Intensional relation

[Juan de Nadie <juandenavas@xxxxxxxxx>]

I agree, Matthew. 

And, particularly, I think that in this specific situation, the author (Guarino) tried to fit both requirements. He provide several examples that help in understanding the presented notions. I have previously understood the intuitive notions underlying the exposition. 

My troubles were related only to the mathematical formalization. And this occurred because I wanted to go into details (I hate to be defeated by math). But, with the aditional references to the notions of powerset and "n-th Cartesian power of a set", the formalization became clear.

I would like to thank all participants.

Best regards.

2013/1/3 William Frank <williamf.frank@xxxxxxxxx>

Surely, Leo's conclusion 



"One can use good English and formal definition together."

Is the only reasonable one.   What could really be argued about here? 

Me, I was accustomed to getting an intuitive explanation of a concept, **then** a formal exposition, and then an informal conclusion, and writing that way.  But I had a great teacher.

For example, on the current topic of intension, I have always though of intension as the rules for the use of an _expression_, while its extension being the set of phenomena to which it happens to apply.  So, I have thought to relate the two by saying that the meaning or intension of an _expression_ in a theory can be explicated (or modeled) as the equivelence class of all the extensions of the _expression_ in all the true interpretations (or models) of the theory.   When you take this approach,interesting properties of the space of models partitoned by the extensions of the terms in the theory might arise.  This model of the meaning of 'intension' might then seem to some to provide insight into the intuitive meaning of 'intension.'   From intution, to formal theory, back to insight.  Formal mathematics is critical part of this process.  And, without it, the arguments about the fine points of the English will be endless.

I do also agree with JS someone defines an intensional class in some elegant mathematical way, and does not explain how that relates to any wider interests, or spell out some of the notation, something is motivational suspect. 





--
William Frank

413/376-8167


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