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On Fri, Sep 7, 2012 at 12:18 AM, Mike S. <maikxlx@gmail.com> wrote: > On Thu, Sep 6, 2012 at 10:21 PM, Jorge Llambías <jjllambias@hidden.email> > wrote: >> On Thu, Sep 6, 2012 at 10:48 PM, Mike S. <maikxlx@gmail.com> wrote: >> > I tried something like that yesterday and it doesn't work formally: >> > >> > Assume def: li Ri Pi <=> jo si Ri Pi ri Ri Pi <=> jo ri Ri Pi si Ri Pi >> >> I think you need: li Ri Pi <=> je jo si Ri Pi ri Ri Pi jo si Pi Ri ri Pi >> Ri >> >> i.e. there's only one thing that Ri, and it's the only thing that Pi. > > That's a bit puzzling. Semantically, I don't see how "la mlta xkra" has > anything to do with a claim that the only thing black is a cat. Delete what I said there, it doesn't make that much sense. > Formally, I > don't see how that expansion can help demonstrate the curious "l-" identity > "na li Ri Pi <=> li Ri na Pi", an identity which appears to be a complete > nose-thumbing at FOL. (By the way, if *any* FOL expansion exists such that > that identity holds, I'd like to see it, whether it matches the semantics of > "l-" or not.) What happens is that l- invokes a universe of discourse where la Pa Ra <=> sa Pa Ra <=> ra Pa Ra, (a universe where Pa is satisfied by a single value, i.e. where "ra sma re sme ja na je Pa Pe dnlake" holds) and then, in that universe of discourse, you have: na li Pi Ri = na si Pi Ri = ri Pi na Ri = li Pi na Ri "na li Pi Ri" does not negate the presupposition. The presupposition is not a claim you make when using l-, it's something you use to build the universe of discourse. This also adresses the difference between "la Pa Ra" and "la Ra Pa". The former has a presupposition on P only, the latter on R only. That's why I think the first dependant of l- sets up the topic, i.e. what it is that you are making a claim about, rather than itself making any claims. If what you want is an equivalence between "li Pi Ri" and some expansion in terms or r/s that will hold in every universe of discourse, then I agree it can't be done, because l- requires a universe where Pi is only satisfied by one value (possibly a plural one). ma'a xrxe