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Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: Christopher Menzel <cmenzel@xxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 14 Feb 2007 11:38:16 -0600
Message-id: <p06230902c1f8f80a78ea@[10.100.0.26]>
>On Feb 13, 2007, at 4:38 PM, Pat Hayes wrote:
>>>  On Feb 13, 2007, at 2:18 PM, Pat Hayes wrote:
>>>>   ...For example, adding the power to make
>>>>   definitions to IKL would make the entire logic paradoxical, and
>>>>   re-create the Russell paradox in CL.
>>>
>>>  Pat, I agree strongly with your general point, but I think what you
>>>  say here is not true about CL and moreover reflects an incorrect
>>>  concept of definitions (which puzzles me because I know you know what
>>>  a good definition of "definition" is!).  What you say above seems to
>>>  identify "the power to make definitions" with the ability to call
>>>  things into existence ex nihilo.  But that is *exactly* what one
>>>  cannot do in giving a definition.  A critical condition on a genuine
>>>  definition is that it be *non-creative*: A definition (within a
>>>  theory) cannot entail the existence of anything that was not already
>>>  entailed by the theory.  Hence, any purported definition in IKL of a
>>>  Russell set (property, class, type, whatever), or any other
>>>  paradoxical entity, would be illegitimate, for the same reason that
>>>  the Russell set {x | x not in x} is illegitimate in ZF set theory.
>>>  You can't prove the existence of a set of all non-self-membered sets
>>>  in ZF, hence, you can't legitimately introduce the name "{x | x not
>>>  in x}", as it violates the non-creative condition on definitions.
>>>  Same for CL.
>>
>>  I wont argue with what you are saying, but you are here using a
>  > very sophisticated notion of what a "definition" is. I don't think 
>>  this notion (which is informed by a century of post-Russellian 
>>  thought about how to deal with paradoxes) is what people usually
>  > mean by "definition". You are, to use a philosophical semi-joke 
>>  term, assuming that all definitions come pre-Quined; but that is 
>>  not how they are usually understood.
>
>I won't dispute your point about what people usually mean by 
>"definition", but your claim that it is "informed by a century is 
>post-Russellian thought about how to deal with paradoxes" is not 
>historically accurate.  Russell sent his fateful letter to Frege 
>informing him of the paradox in the Grundgesetze der Arithmetik in
>1902; Padoa published his first paper on the theory of definitions 
>(which included a notion of non-creativity) in 1901.    (01)

Ah, I stand corrected. Thanks. I am amazed that 
it was possible to even think of these ideas that 
early.    (02)

Pat    (03)


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