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Re: [engelang] intensions & extensions (Xorban)



On Sat, Sep 15, 2012 at 6:58 PM, Jorge Llambías <jjllambias@hidden.email> wrote:
 

On Sat, Sep 15, 2012 at 6:25 PM, Mike S. <maikxlx@gmail.com> wrote:
>
> I think the rules in summary are:
>
> hW B R P => B R hW P
> hW N F => N hW F
> hW J F1 F2 => J hW F1 hW F2
> BV RV P[hW]V => BV hW RV PV (definition of P)

ha re mlte xkre => re mlte ha xkre
A is a world in which every cat is black => For every cat, A is a
world in which it is black

It's clear that the domain of the quantifier for the first formula
contains only the cats in A. Can the domain of the quantifier for the
second formula include cats that are not in A? If it can, the
implication doesn't seem right.

"re mlte ha xkre" means what you say, but it is not a correct transformation of "ha re mlte xkre".  V in xkrV would be defined extensionally, so it means xkr[h^]V, which means "V is black and exists in the worlds in which it is black" i.e. the black thing and the state of being black have to occur in the same world, which sounds a little weird, but seems to work.  So

sa sma ha re mlte xkre
=> sa sma ha re mlte xkr[h^]e
=> sa sma re mlte ha xkr[h^]e
=> sa sma re mlte ha xkr[ha]e
=> sa sma re ha mlte ha xkre
"There is some A such that for all E, if E is a cat in world A, then E is black in world A".
"In some possible world, every cat [in that world] is black."

In that world, all the cats that exist are black and actual ones.  Here's an intensionally defined predicate for comparison, ignoring "o'e":

sa sma ha re mlte pxro'eke
=> sa sma ha re mlte pxro'ek[lo smo ho]e
=> sa sma ha re lo smo ho mlte pxro'eke
=> sa sma re lo smo ho mlte ha pxro'eke
"There is some A such that for all E, if there is some O such that E is a cat in world O, then E is depicted in world A."
"In some possible world, every [seemingly imaginable] cat is depicted."

Not all of the depicted cats would necessarily be actual cats in that weird but comprehensible possible world.