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John E Clifford, On 11/09/2012 03:45:
Well, a couple of examples: parallel predicates with intertwines strings of terms (Lojban can do this -- the rules are implicit, but never spelled out);
What's an example of this? I don't know what it is you're describing.
quantifiers whos scopes go beyond sentence boundaries (Lojban can do this, too, but muddles the process enormously). Of course, you say that no quantifier has scope beyond the end of the sentence to which it is prenex, but then the question is how are you going to patch up the cases in ordinary language when this happens.
The poor woodcutter sort of quantifier, I'm still pondering. I don't think either Jorge's response or a mere widest-scope existential is adequate, but I'm still thinking about it. The issues with the poor woodcutter case generalize to fractional quantifiers in general. E.g. "One in every three people has suffered from mental illness", and then that person, the one in every three, is projected into the UoD and can be referred to in later sentences. One existing possibility is to use dV, which is an afterthought method. A forethought method, which I have not hitherto proposed, but have been thinking about, might be to have a series of variables that carry on referring to that individual projected into the UoD.
And, of course, we have yet to see any attempts to deal with abstractions or other intensional situations.
Abstractions in the Lojban sense? I think if fV is defined to be an intensional situation, everything else can be based on that. But you're right, we haven't discussed it properly yet. Is there anything more you've thought of? I think the most constructive thing we can be doing is looking for gaps in what Xorban can do. --And.