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On Oct 28, 11:21 pm, "LauLuna" <laureanol...@xxxxxxxx> wrote:
> I thank you both Abo and Srinivasan for your responses.
>
> But none of you tell why D is ill-formed; you just go to the
> contradiction in the result. Note that Priest would not be convinced by
> this kind of argumentation.
The purported definition is not really a definition -- it assumes that
the natural numbers are pre-defined. Since we already have prior
knowledge that there is no natural number n such that n=n+1, the
purported definition is little more than an assertion of a
contradiction.
>
> Srinivasan says he doesn't accept a definition containing 'this
> definition'. But 'the last letter in the written form of this
> definition' looks like an admissible definition of the letter 'n' or at
> least an expression unambiguously identifying it.
>
When "the natural number" or "this definition" is written, it is
understood that a unique natural number/definition must be specified
constructively -- inability to do this even in principle renders the
sentence meaningless.
> It seems obvious that we should reject D on the grounds of circularity.
> Perhaps what is not admissible is that D contains not just 'this
> definition' but 'defined by this definition' , and this renders evident
> that D means to be built upon itself, so to say.
Yes. And if the definition really makes sense, we can also remove "this
definition" from the sentence -- so it is not required at all and
should be banned as self-referential.
Regards, RS
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