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* Wednesday, 2012-09-12 at 16:26 -0400 - Mike S. <maikxlx@gmail.com>:
> It was time for a new post on the blog.
>
> _Operator “l-” and FOL_:
> http://xorban.wordpress.com/2012/09/12/operator-l-and-fol/
>
> That's more or less where *I* stand at the moment. Feedback appreciated.
> A "myopic singularization" M is a function that for every formula
> F with respect to a variable V free within F yields a formula MV
> F expressing some predicate guaranteed to be true for exactly one
> entity in the universe of discourse.
So this is similar to And's description, but less "destructive". For
example, it isn't immediately incompatible with
la mlta [births two kittens] .
The following looks like an error, though:
> One other thing to note about the M function is that the following
> transformations are valid:
>
> o sV[2] R MV[1] P <=> MV[1] sV[2] R P
>
> where V[1] is different from V[2] and V[1] does not occur free in R.
That's surely false for (some) natural interpretations of M. For
example, taking R to be trivial and P(x,y) to be "x=y", and making the
reasonable-seeming assumption that if we apply M to a unary formula with
singleton extension the result has the same singleton extension, then
left hand side is:
Ey. Mx. x=y <=> Ey. x=y
whose extension is the entire domain; but the right hand side
Mx. Ey. x=y
has singleton extension.
Or do you intend to demand some uniformity, such that Mx. F(x,y) is
constant with y? That would make your commutation rule feasible, but
doesn't seem to fit the "singularisation" idea very well.
Martin
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