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

From: "Jorge Llambias" <[email-masked]>
Date: Tue, 05 Mar 2002 22:39:28

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)

This is virgin ground we're breaking here.

{li} requires an operand to follow, so you can't just use an
operator. You could do something like {li ma'o te'o te'a xy te'u tu'o}
(this beasts get ugly real fast), cancelling the argument place of
your operator. I gather {xy} somehow opens the place up again at
a different level. Is that how {ma'o} is supposed to work? I never
quite understood how an operand gets transformed into an operator.
And all this assumes that xy does not have a previously assigned
value, I suppose.

>x1 is a function, and x4 is a mekso expression turned
>into an "operator" by ma'o.

This is not how Cowan had it though. He just quoted the expression
with {me'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.

This is one way the inverse of the logarithm function can
be described, not using the predicate {fancu}:

ro xy poi namcu zo'u li te'o te'a xy mapti xy le dugri fatne
For every number x, the number e^x corresponds to x by the
logarithm inverse.

{le dugri fatne} is probably not the best description, but that's
not our main issue here.

The domain is explicit though not referred to directly. The
range could be made equally explicit by commenting that
{li te'o te'a xy} belongs to it. The rule is used but not
referred to.

I'm not confident though that I can quantify {xy} outside of
MEX and then use it inside. They seem to be parallel universes,
and I don't know whether communication between them is allowed.

>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.

Yes, a lot.

>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.

No such thing in sight. But if you had such a word, would it
be true that {le inverse de'o xy du li ma'o te'o te'a xy te'u tu'o}?

mu'o mi'e xorxes

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