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Mike S., On 28/09/2012 17:15:
On Fri, Sep 28, 2012 at 4:38 AM, And Rosta <and.rosta@hidden.emailObviously these are predicates getting given unary operator form for abbreviatory purposes. My first thought is there's no reason to privilege tense in this way. Better to have a more generalized system for creating operators from predicates. Or else have no operators.As a general observation, just formulas represent predicates. Non-formulas, including things that take exactly one formula as a complement, do not represent predicates. They represent functions from predicates to predicates. We already have a generalized system for creating operators from predicates; that's exactly what binary operators do. As far as the reason I created tense operators, they're just purely experimental while we work out how to handle worlds and situations. If there are more appropriate ways of handling tense (and there may well be) then I am sure that they will come out in the wash.
John E Clifford, On 28/09/2012 16:42:
If tenses are predicates of some sort, what do they range over and how is that fitted into the rest of the language? If your language talks explicitly about worlds, then, of course, tenses could be predicates over certain sets of worlds. But then every sentence involves placing the event described in some world or other (probably dropped in obvious cases, of course). Since shifting from world to world in this way creates a sort of intensional context, this throws most of language into an intensional mold (Montague would not find this undesirable, of course). On the whole, it seems easier to just take them as undefined operators (there may be matching predicates of course, since we allow events as objects) and deal with the problems witout the extra difficulties of worlds (same applies to alethic modalities).
I'm not sure if we're talking at cross-purposes. Mike's proposal has a semantic element (a range of relations between situations and the utterance time) and a syntactic element (a range of unary operators). The semantic element is unexceptionable. My comment pertains to the syntactic element. The syntactic apparatus of a loglang divides into the essential, without which the requisite meaning cannot be encoded, and the inessential, introduced for usability purposes such as brevity. Of the Xorban unary operators, all are inessential, apart from mV and fV. (fV doesn't have to be a unary operator, but if it weren't then some other device would have to be introduced, such as the fV argument marker that the current fV unary operator replaced.) What Xorban calls "simple-formulas" are essential. Given that the class of formula-stems is open, we may take it for granted that Xorban has formula-stems expressing tense relations. So the question is, which sorts of meanings warrant being encoded not only by formula-stems, essentially, but also by unary operators, inessentially? I see no reason at this stage to privilege tense relations for having these additional inessential encoding methods. Rather, I think we should either be backburnering inessential stuff, except where there's a very clear rationale for it (as in the case of the vV operator, for instance) or be introducing inessential devices that are meaning-neutral, such as a generalized way of converting a monadic formula into a unary operator. Mike says that binary operators are a generalized way of creating [unary] operators from predicates. E.g. "na bcdi" is "je jtfa fa bcdi". But that isn't abbreviatory. I had formerly suggested "jtfoi bcdi", where "oi" marks a simple-formula as taking as its complement another formula that binds the argument-place marked by "oi". That would be an inessential device for enhanced usability, which generalizes to all simple-formulas. As a result of this message, I've talked myself into proposing the resurrection of "oi", and the replacement of some of the existing unary operators by CC stem + oi. --And.