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John Cowan, On 03/10/2012 19:38:
And Rosta scripsit:Mike S., On 01/10/2012 18:19:Binding a variable to nothing, particularly when the restriction says nothing as in "sa bbbe ...", is unsettling, though "sa bbba ccce" is probably not so terrible as to be worth the trouble of fixing.It's as easy to prohibit it as to allow it.Prohibiting it, however, means that certain reasoning steps permitted by ordinary FOPL cannot be represented in Xorban without ungrammaticality. In particular, given a well-formed formula of predicate logic, it is always possible to prefix it by a quantifier binding any variable, whether or not that variable is free in the formula. IMHO, what is possible in FOPL should be possible in Xorban.
I accept that what is possible in FOPL should be possible in Xorban, but not that given a well-formed formula of predicate logic, it is always possible to prefix it by a quantifier binding any variable, whether or not that variable is free in the formula. However, we may mean different things by FOPL, especially in the context of loglanging. I understand it to be the minimal syntax of propositional meaning. I expect others understand it to be a fairly standardized combinatorics of symbols supplemented by a body of interpretation rules. These different understandings may well give different answers in edge cases such as the one under discussion. --And.