Re: A Logical Model for Lists as Relations
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Fri, 12 May 2006 18:57:27 GMT
Message-ID: <rU49g.6857$A26.173334_at_ursa-nb00s0.nbnet.nb.ca>
>>Mikito Harakiri wrote:
>>
>>>Kuratowski and Quine' constructions are not definitions. The ordered
>>>pair definition is
>>>
>>> (x,y) = (a,b) if and only if x=a and y=b.
>>
>>You are confused. That's not a definition but rather a property an
>>ordered pair should satisfy. True, there are alternative definitions
>>of the ordered pair, but what's important is that the condition should
>>hold. Besides, when you write (a,b) = (c,d), what exactly do you
>>mean ? What *are* (a,b) and (c,d) ? The Kuratowsky (or anybody else's
>>pair) tells you what it is in terms of sets.
Date: Fri, 12 May 2006 18:57:27 GMT
Message-ID: <rU49g.6857$A26.173334_at_ursa-nb00s0.nbnet.nb.ca>
Mikito Harakiri wrote:
> vc wrote: >
>>Mikito Harakiri wrote:
>>
>>>Kuratowski and Quine' constructions are not definitions. The ordered
>>>pair definition is
>>>
>>> (x,y) = (a,b) if and only if x=a and y=b.
>>
>>You are confused. That's not a definition but rather a property an
>>ordered pair should satisfy. True, there are alternative definitions
>>of the ordered pair, but what's important is that the condition should
>>hold. Besides, when you write (a,b) = (c,d), what exactly do you
>>mean ? What *are* (a,b) and (c,d) ? The Kuratowsky (or anybody else's
>>pair) tells you what it is in terms of sets.
> > > Don't we introduce new symbols together with properties they must > satisfy? When we are saying that group is a set of elements which > satisfy some axioms, do we have to tell what those elements "are" in > terms of set?
You already have. "A set of elements which satisfy some axioms" tells what they "are" in terms of set.
[snip] Received on Fri May 12 2006 - 20:57:27 CEST