Re: Eggs and hens



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From: Joaquin Miller (jm-miller-at@sbcglobal.net)
Date: Wed 21 Apr 2004 - 20:44:49 BST


>Right, but you have to commonly agree on the semantic of the basic axioms. 
>Then it starts to work...

That's right.

If we agree that means: commonly agree on the intended interpretation of 
the elements of the specification.

There will be the basic axioms, primitives, terms defined using the 
primitives, and so on.  The axioms can be purely formal and the primitives 
undefined, but we need an interpretation to put them to work.

...... Example, if needed ......

We might have primitives, object, action, and __ participates in __, and 
the basic axiom, at least one object participates in every action.

We then need to provide to users an explication or demonstration of how to 
use those three primitives, before that axiom is of any use.

Either we do that using ordinary language, or we do it as Wittgenstein's 
brick layers did, help the users figure out what to say or do next, rather 
than decipher the meaning of what is said.  Without a definition, we can 
teach an interpretation that shows how to use 'brick' and 'slab' or 
'object,' 'action,' and '__ participates in __.'

What is impossible it to define all of 'object,' 'action,' and '__ 
participates in __' while avoiding circularity.

I'm sure this is all common knowledge, and i apologize for repeating the 
obvious.  This is essential for a clear and clean understanding of how the 
MOF language can be useful.

>>Friends:
>>
>>One can avoid stepping on eggs and being tripped up by hens if one uses 
>>the axiomatic method to specify poultry.
>>
>>The 3C UML 2 submission shows how this is done for a modeling 
>>language.  The other advantages of the axiomatic method won't fit here.
>>
>>Cordially,
>>
>>Joaquin
>>
>>http://www.omg.org/cgi-bin/doc?ad/02-09-15.pdf
>>or
>>http://www.omg.org/cgi-bin/doc?ad/02-09-15.mif
>>
>>.................
>>
>>Sure, axioms need to be expressed in some language.  But that's 
>>unavoidable, and the most general case has been much discussed.
>>Wittgenstein is a good author on that, and Tarski on the axiomatic 
>>method.  Bunge says it in few words:  it is not possible to define 
>>everything while avoiding circularity.  The axiomatic method does the 
>>job: it does not attempt to define everything.
>>
>>Having defined a formal system using the axiomatic method, what remains 
>>is to express how that system and the parts of that system are intended 
>>to be used.  Then we have a practical system.

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