I'm not sure what you take as hackish about it. Simply a= llows quantifiers over predicate variables, which is all that is required.&= nbsp; To be sure, it is does not seem to allow such quantifiers any place b= ut prenex ('ko'a (cu) suo bu'a' don't seem to compute), but the embedded qu= antifiers are a main source of difficulty (pace xorxes) in reconstructing t= he logic of Lojban, so this may not be a flaw. What then is hackish?&= nbsp; The pattern of real Logic is followed (less a mess of sub- and supers= cripts that are largely irrelevant to Lojban). Yes, Lojban is based o= n first order, but, then, so is second order and Lojban allows that extensi= on (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 proper= ty, 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 seco= nd order claims. There is talk of the lambda calculus but it is unimplement= ed, so far as I can see (and is second order).

<= font size=3D"2" face=3D"Tahoma">

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 <<= a rel=3D"nofollow" ymailto=3D"mailto:blindbravado@gmail.com" target=3D"_bla= nk" href=3D"mailto:blindbravado@gmail.com">blindbravado@gmail.com> wrote:

Quantification over predicates was implemen= ted 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 t= o go from predicate-as-function (selbri) to predicate-as-concrete-object (t= ypical 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 2= 4, 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 wi= th tree and dogs. There is no particular problem in grammar or vocabu= lary to treating properties of predicates and quantification over them. &nb= sp;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 r= esults, though sometimes different ones. None of them seem particular= ly stilted, but I haven't seen enough cases to get a feel for that.

Sent from my iPad

On Jul 24, 20= 11, at 14:13, Ian Johnson <b= lindbravado@gmail.com> wrote:

=
I think bu'a/bu'e/bu'i would be much much much more useful if Lojban w= ere 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 stilte= d language, I don't think bu'a/bu'e/bu'i are especially useful.

mu'o mi'e latros

On Sun, Jul 24, 2011 at 12:01 PM, tijlan <jbotijlan@gmail.com> wrote:

What is your view on the bu'a series= ? Potentially useful? Totally
pointless? I've never used it myself, but = I could be missing some
important aspect of Lojban as a logical language.

mu'o mi'e tijlan
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