>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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