Re: [lojban] Re: [jboske] RE: Anything but tautologies

[Edward Cherlin <edward.cherlin.sy.67@aya.yale.edu>]

On Monday 18 February 2002 17:32, pycyn@aol.com wrote:
> In a message dated 2/18/2002 5:29:05 PM Central Standard Time,
>
> jjllambias@hotmail.com writes:
> > We seem to have at least four different interpretations of
> > x1 and x4 of fancu:

The refgrammar gives the impression that all of this must have been 
worked out at least once, and the current discussion gives the 
impression that nobody can remember what was decided.  *<%-b

> > xod: x1 is a name and x4 is the function
> > cowan: x1 is the function and x4 is an expression (a text)
> > lojbab: x1 is the function and x4 is something like li f(x)=x*2,
> >         which is not very clear what it is because equations
> >         are not numbers.
> > pc: x1=x4 both are the function, with the proviso that good style
> >     requires to use a more helpful description in x4.

Lewis Carroll: We have to specify the function, the name of the 
function, what the function is called, what the _name_ of the 
function is called, and what the function _is_, and similarly for the 
domain and range, so we're short a dozen places.

ed: x1 is a function, and x4 is an expression for evaluating it, 
marked with ma'o to turn it into an operator (i.e., a function, but 
in this case without the domain and range specified). 
le fancu zo'e zo'e ma'o vei li xy te'a li re ve'hu

so everybody is partly right and partly wrong. Both x1 and x4 are 
functions, but of different kinds, and it is frequently appropriate 
to have a named function for x1 and a transformed expression in x4.

Part of the problem is that there is no generally-accepted method for 
defining functions accurately in mathematics, in part because there 
are numerous kinds of functions that behave differently. Lambda 
calculus omits mention of domain and range, which are taken as the 
set of natural numbers in the original theory, while Lojban omits 
mention of arguments, which is fine if they are always drawn from x, 
y, and z in that order, or if all of the argument variables appear in 
the function expression.

Another part of the problem is that we are all quite vague on the use 
vs. mention distinctions, and none of us understands the Foundations 
of Mathematics well enough to give useful definitions. Actually, 
nobody understands FM that well, so it's OK if we improvise some. FM 
is a Work in Progress with its own set of rwars, which we would do 
well *not* to emulate. I can get My Brother the Math Professor to 
recite chapter and verse if anybody doubts this.
 
> > I much prefer pc's version over any of the others, although even
> > better for me would be to drop x4 altoghether.
>
> Why, thanks; I needed a pleasant surprise.
> So, leave off fancu4 and put it in, when needed (as often) in
> subordinate clauses.

I don't think that will be necessary.
-- 
Edward Cherlin
"You can call me by name, pronouncing it "Veert", or by value, 
pronouncing it "Worth"--Niklaus Wirth