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Date:         Wed, 25 Aug 1993 13:38:42 +0100
Reply-To: Colin Fine <C.J.Fine@BRADFORD.AC.UK>
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From: Colin Fine <C.J.Fine@BRADFORD.AC.UK>
Subject:      Re: TECH: nec (Was: QUERY: quantifier scope & cumk
To: Erik Rauch <rauch>
Status: O
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X-From-Space-Date: Wed Aug 25 14:38:42 1993
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Iain answers john and me:

+++++++++++++>
> "nibli" is closer to the sentence operator Nec, which
> in Quine takes a quoted sentence, than to the standard modal operator nec.

Don't you both mean {sarcu}?
>++++++++++++++

No I don't think so.  'sarcu' is about contingent necessity,
nibli about logical necessity. I'm not sure that either is
completely appropriate (each has another argument) but
I am sure that we are talking about logical rather than
contingent necessity.

nibli nib     ni'i necessitate                               x1 logically necess
 itates/entails/implies
action/event/state x2 under rules/logic system x3

sarcu         sa'u necessary                                 x1 is necessary/req
 uired for continuing state/process
x2 under conditions x3; (cf. nitcu)

+++++++++++++>
I'm not familiar with the particular system(s) you're referring to,
and I may be misunderstanding what you're saying, but surely it *is*
possible to reason about the argument of nec - you just have to be
careful to apply the appropriate rules.
>+++++++++++++

Of course it is.  But the rules are not just a couple of extra
rules of inference. Look what's going on in John's example:


>         nec 5 < 9
>         9 = the number of planets
>         nec 5 < the number of planets

It's substitution of equal terms that has broken down - as far as
I can remember you have to go into intensions and extensions to
fix this. (Your example works because 'nec' makes the intension
a constant function).

Colin