On Jul 26, 2011, at 14:35, Ian Johnson <blindbravado@gmail.com> wrote:

What is hackish about it is th= e syntax. In {ro bu'a zo'u da bu'a}, {ro bu'a} is syntactically a sumti, co= nsisting, presumably, of all x1's of whatever referent the {bu'a} ultimatel= y has (thinking classically; in intuitionistic logic, what I am saying is n= ot entirely sound), since that's what it means elsewhere. And yet then the = thing that is actually quantified over is a collection of predicates. It's = just an arbitrary decision plopped into the CLL, changing the type of a var= iable abruptly. My gripe about it is irrationally amplified by my irrationa= l mental attempts to statically type Lojban, but even putting that aside I'= d say it's a valid gripe, albeit irrelevant from a practical standpoint sin= ce predicate quantification has seen no use so far as far as I know, except= in my example here.

We're also missing second order predicates, or at least things that ser= ve as convenient required predicates in second order d= iscussions, in general. Saying something like "{mintu} is the opposite of {= drata}", even with {me'ei} (of selma'o LE, which converts selbri into abstr= act predicate sumti; I do NOT think quoted words are suitable as placeholde= rs for abstract predicates), becomes:

me'ei mintu cu dukti me'ei drata ....????
and I ultimately have no way o= f writing down the dukti3. (I would be pleased if you could, actually.) The= only precise way of saying this (yes, I admit the English is as imprecise = as a statement involving {dukti} with no dukti3, but I hope you can see the= precise meaning that I want to encapsulate) that I can see is first order = to its core:
ro da ro de ro di zo'u go da de di mintu gi da de di to'e drata

mu'o= mi'e latros
On Tue, Jul 26, 2011 at 11:58 AM= , John E Clifford <kali9putra@yahoo.com&g= t; wrote:

I'm not sure what you take as hack= ish about it. Simply allows quantifiers over predicate variables, whi= ch 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 c= ompute), 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.&= nbsp; What then is hackish? The pattern of real Logic is followed (le= ss a mess of sub- and superscripts that are largely irrelevant to Lojban).&= nbsp; Yes, Lojban is based on first order, but, then, so is second order an= d 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 i= n 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).

= From: Ian Johnson <blindbravado@gmail.com>
To: lojban@googlegroups.com
Sent: Tue, July 26, 2011 9:24:10 AMSubject: Re: [lojban] bu'a<= br>

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" href=3D"mailto:blindbravado@gmail.com" target=3D"_blank"= >blindbravado@gmail.com&g= t; wrote:

Quantification over predicates was implement= ed in a horrifyingly hackish way. This alone is a problem, in my opinion. T= here 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 (ty= pical 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 <ka= li9putra@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 wit= h tree and dogs. There is no particular problem in grammar or vocabul= ary to treating properties of predicates and quantification over them. &nbs= p;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 L= ojban ontology. All the answers yield grammatical and intelligible re= sults, though sometimes different ones. None of them seem particularl= y 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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