On Mon, Oct 1, 2012 at 2:16 AM, Mike S. <
maikxlx@gmail.com> wrote:
> On Sun, Sep 30, 2012 at 10:55 AM, Jorge Llambías <jjllambias@hidden.email>
> wrote:
>> If l- was the epsilon thingy, quantifiers would then be defined as:
>>
>> sa sma mlta = la mlta mlta
>> ra sma mlta = la na mlta mlta
>>
>> (The latter could be read as something like "that which is the closest
>> thing we have to being a non-cat is a cat", which means everything is
>> a cat.)
>
> It hadn't dawned on me that such a sentence might surface from formalizing
> "l-" as the epsilon operator, but I think I could tolerate anything more
> than having no formalization at all. A version of that sentence that we
> might more realistically encounter might be:
>
> ra sma sma = la na sma sma.
>
> What would your opinion of the truth value(s) of those sentences have
> been, before and after reading about epsilon calculus?
"ra sma sma" is obviously true.
As for "la na sma sma", since "l" presupposes a (single) referent for
"la Xa", and "sma" is true of anything, it has to be true as well.
This would seem to challenge the veridicality of l-, at least when
used with empty restrictions, which is fine with me.
There is, of course, for every F a least likely F such that, if it is an F, everything is an F. Likewise, a most likely F, such that if something is an F, this thing is. There is a funny but totally impractical proof system using these guys in place of the usual subproofs for universals and conditionals. Now, I never checked out whether the least likely F is also the most likely non-F, but that seems reasonable. However, if that is an F, there are no non-Fs and so any reference to non-Fs in the restriction would be incorrect, unless it is in a non-veridcal context. I don't think we want l to be non-veridical on top of its other problems. Of course, the least likely F does not refer to F in the restriction (there is none, or, if you prefer it is
sm), so the problem doesn't arise in standard logic. I think we ought to be either over about the "the least likely" or just drop the whole idea (which, as I said, is rather impractical).
co ma'a xrxe