I'm not sure what you take as hackish about it. Simply allows quantifiers over predicate variables, which is all that is required. To be sure, it is does not seem to allow such quantifiers any place but prenex ('ko'a (cu) suo bu'a' don't seem to compute), but the embedded quantifiers are a main source of difficulty (pace xorxes) in reconstructing the logic of Lojban, so this may not be a flaw. What then is hackish? The pattern of real Logic is followed (less a mess of sub- and superscripts that are largely irrelevant to Lojban). Yes, Lojban is based on first order, but, then, so is second order and Lojban allows that extension (and, in principle, all the other orders on up).
As I said, part of the problem is to figure just what a predicate is in Lojban.
There are several candidates (sticking to unary predicates for simplicity): the things that have the property, the set of things that have the property, the characteristic function of that set, and the property, which may or may not be what a Montagovian would call a property. Three of these have clear expressions in Lojban, but the characteristic function does not really, but is the best candidate for the predicate in what follows in second order claims. There is talk of the lambda calculus but it is unimplemented, so far as I can see (and is second order).
From: Ian Johnson <blindbravado@gmail.com>
To:
lojban@googlegroups.com
Sent: Tue, July 26, 2011 9:24:10 AM
Subject: Re: [lojban] bu'a
Erm, poor phrasing; I meant that there is no easy way to get between those three things.
.u'u .i mu'o mi'e latros
On Tue, Jul 26, 2011 at 10:22 AM, Ian Johnson
<blindbravado@gmail.com> wrote:
Quantification over predicates was implemented in a horrifyingly hackish way. This alone is a problem, in my opinion. There is also, at least not in the main body of the language, an easy way to go from predicate-as-function (selbri) to predicate-as-concrete-object (typical sumti) to predicate-as-abstract-object.
Lojban is definitely based on FOPL, though, not SOPL, and not a bizarre hybrid of the two.
mu'o mi'e latros
On Sun, Jul 24, 2011 at 2:51 PM, John E. Clifford
<kali9putra@yahoo.com> wrote:
Lojban isn't clearly of one order or the other, since it treats sets and properties and the like on a par with tree and dogs. There is no particular problem in grammar or vocabulary to treating properties of predicates and quantification over them. There are some arguments about the correct way to express a predicate as an argument, but that seems to revolve around just what a predicate is in Lojban ontology. All the answers yield grammatical and intelligible results, though sometimes different ones. None of them seem particularly stilted, but I haven't seen enough cases to get a feel for that.
Sent from my iPad
I think bu'a/bu'e/bu'i would be much much much more useful if Lojban were a second order language, because then we could talk about the existence of predicates with desired properties in a non-stilted fashion. As a first order language, though, with second order mechanisms requiring stilted language, I don't think bu'a/bu'e/bu'i are especially useful.
mu'o mi'e latros
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