BPFK Section: Logical Variables
pc:
> A> No, E is enough (it turns out in this case that this is also A, of
> course).
I'm sorry, but: "[E J: J among I] I among J" is not the same as
"I is an individual".
In fact "[E J: J among I] I among J" is true for any I. If I
are three individuals, then "[E J: J among I] I among J" is true.
On the other hand, "[A J: J among I] I among J" does mean that
"I is an individual".
> B> This does have to be A, otherwise this would be trivially true for any
> number greater than n.
"This" was:
(the other
numbers can be built on this inductively, given a defined "I is n in
number,"
"I is n+1 in number is just "EJ: J among I J is n in number & E K: K
among I and K not among J K is 1 in number").
What has to be A there? I think that's fine as it is.
> c> The original was
> "If da's were not singular, things like these would be false:
>
> pa da broda ijo ge su'o de broda gi ro di poi broda cu du de
> Exactly one thing1 is a broda iff some thing2 is a broda and
> every thing3 that is a broda is that thing2."
Right.
> So, assuming you are using "1x" in the usual way, not McKay's, what effect
> does these variable being plural have on the above.
It depends on which of the two universal quantifiers we take {ro}
to represent.
If {ro} is McKay's lambda, then {ge su'o de broda gi ro di
poi broda cu du de} just means {su'o da broda}.
If {ro} is the dual of {su'o}, (McKay's inverted A) then it
does work. But then how do we say "all students surround the
building"?
mu'o mi'e xorxes
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