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

From: Edward Cherlin <[email-masked]>
Date: Tue, 05 Mar 2002 01:37:37 -0800

On Wednesday 27 February 2002 14:50, [email-masked] wrote:

> <Edward Cherlin:
> >The inverse of the logarithm function ku cu fancu domain-the-reals
> >range-the-positive-reals ma'o e^x
> >(where x is a bound variable representing the argument).
>
> That's the Cowan place structure, yes. One problem is that
> nobody quite knows how to put "ma'o e^x (where x is a
> bound variable representing the argument)" into Lojban.

I'm going to start from "li ma'o (te'o te'a xy)".
the-value the-operator (e to-the-power x)

> And if this is just a text then there is a second problem,
> because it is not the text but the meaning of that text
> that is of interest here.>
>
> This is not obvious, it depends upon what the purpose of the
> sentence is. Cherlin wants it to be a definition, and thus it is
> exactly text that is wanted, needed, possible.

Precisely not. x1 is a function, and x4 is a mekso expression turned 
into an "operator" by ma'o. Functions are defined by domain, range, 
and method of evaluation. They can be described in a variety of ways. 
They can have names, but this is not a requirement. Functions are not 
texts. They are mathematical objects.

The Book is entirely vague about expression syntax and operator 
semantics, and has nothing to say about binding argument variables, 
so there is more to do here. I'll have a go when I get some time free 
from the kind of work intended to bring in money. (We could use the 
Unlambda programming language model, in which the only primitives are 
the S and K combinators, ' for quoting, and some letters, and we 
never need variables or function names. You wouldn't like it, though.)

In the meantime, here is a workaround--use the same variable in x1 
and x4 of fancu.

le inverse de'o xy. ku cu fancu fo li ma'o (te'o te'a xy.)

What I need now is a word for "inverse function" that can be applied 
to an expression like de'o xy. I didn't find one in The Book. Also a 
precedence table.
-- 
Edward Cherlin
[email-masked]
Does your Web site work?