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

In a message dated 2/15/2002 11:23:36 AM Central Standard Time, jjllambias@hotmail.com writes:

I see you won't explain what those functions with empty domains
are used for. In any case, I hope you accept the existence of
functions with non-empty domains which map every element of the
domain to a constant value.

I didn't know that was called for, but in the instant case, they are natural numbers.  And of course I accept normal functions, including constant-valued ones.  Function theory with only the empty domain cases would be remarkably boring, even by mathematics standards.

<<I the
Then your position is that a definition requires the mention
of the name? The use is not good enough for a definition?>

Definitions are, by definition, of words.  To be sure, there are exemplary definitions that talk about the things, but that is only a  convenience (or a mistake, depedning on how generous you are).  But you can't define a thing.

<<I the
"Let x=5" is sloppy, the Lojbanic version would be:
"Let 'x' be the name of a variable x, such that x = 5">

This wouldn't usually be a definition, rather than an instantiation, where 'x' is already specified in some functional way and here we are assigning it (not its name, so we use it name) a value.  I suppose that some computer people call that definition, too. For actually introducing 'x,'  the second is correcter.

<<I the
Are you really saying that? Or does the rule apply only
to the definition of functions?>

I think the sloppiness is mainly in definition, but it can creep in other places and occasionally wreak havoc.