WikiDiscuss

This is a *VERY* long mail, but I strongly suggest reading it. xod,
you in particular *need* to read it, as I wrote it for you.

On Thu, Aug 26, 2004 at 12:18:32PM -0400, xod wrote:
> John E Clifford wrote:
>
> >>I think it's more along the lines of trying to say "lidless
> >>bottle" or "seer that sees nothing" and ending up saying "camel
> >>or star". Not very helpful!
> >
> >If this is the problem — that contradictory negation opens too
> >many possibilities — then maybe you want merely contrary
> >negation, {na'e}, which requires that what is true is in the same
> >general area (although this is a matter of degree — what is true
> >in contradictory negation has also to be something that excludes
> >what is negated: "not green" can't mean "camel" unless camels
> >definitionally are not green).
>
> Hence lidless bottle = botpi fo na'ebo roda ?

Ideally, in Lojban, a lidless bottle is botpi fi zi'o

About this whole discussion in general:

The confusion here has been an unnecessary proliferation of "da".

We started with:

ta botpi fo no da

"This is a bottle with no lid".

Which is equivalent to:

ta botpi na ku fo su'o da

Which is equivalent to:

ta na botpi fo su'o da

"This is not a bottle that has at least one thing that is a
lid".

Because of the place structure of botpi, these two really are
equivalent; something that does not have a lid is *not* a botpi.

However, at some point someone (xod?) introduced the sentence:

da botpi fo no de

or something like that, now with two "da" variables. I'm pretty
sure that this was an error, that someone read "ta" as "da".
Regardless, This is a very different thing! It means:

"There exists at least one thing which is a bottle that has no
things to be its lid".

This sentence is equivalent to:

su'o da botpi na ku fo su'o de

Which is equivalent to:

su'o da na ku botpi fo su'o de

Which is equivalent to:

na ku ro da botpi fo su'o de

Which is equivalent to:

ro da na botpi fo su'o de

Which means:

"It is not the case that everything is a bottle with a lid."

My first draft of this mail had:

"It is not the case that for each thing that is a bottle, it has
a lid."

Which is *very* different thing indeed! This is actually a
conditional:

na ku ro da su'o de zo'u ga nai da botpi gi da botpi de

I carelessly (confused by the introduction of an extra "da"
variable) indicated in an earlier thread that {da botpi fo no de}
was, in fact, equivalent to:

da na botpi fo su'o de

Which is a very diffrenet thing! It means that:

"It is not the case that there exists a bottle with a lid."

So, my bad there.

Phew. Done with the predicate logic. As you can see, anything with
"no da" in it can (eventually) be converted to samething with "na"
in front of the selbri. This is a very basic feature of predicate
logic, but one I can try to expound on if people wish.

Now, we've been conflating in to the predicate logic issue a

• completely* seperate issue! Bad us.

The other issue is thruth.

A third issue is whether or not it makes any sense at all to talk
about a predicate in Lojban where one of the places cannot be
filled.

Truth first:

ro da na botpi fo su'o de

AKA

na ku ro da su'o de zo'u da botpi fo de

is definately true. Literally, "It is not the case that for each
thing X, there exists a Y such that X is a bottle with lid Y.", or,
"It is not the case that everything is a bottle with a lid.".

What's important to understand is that this is *NOT* equivalent
to "There exists a bottle with no lid", which is what

da botpi no de

• appears* to be saying. This is where most of the confusion has

been coming from. To say "There exists a bottle with no lid", you
need to say:

da poi botpi cu botpi no da

Those of us who speak Lojban regularily as a conversational language
without much regard to the logical formalism (and I'm thinking here
of me and xod in particular, although there are certainly others)
develop an intuiting that says "Anything in the first place of broda
is always a broda". This is simply not true with contradictory
negation, and "no da" hides a contradictory negation in itself.

{da botpi no de} actually says *nothing* about things that are
botpi (that is, things that can truthfully appear in the first place
of the botpi predicate). It says only that there exist things that
are *not* related by botpi (to a botpi x4, i.e. a bottle lid, in
particular, but that's a secondary issue).

Similarily, {mi patfu no da} is exactly equivalent to {mi na patfu
da}. Both of these things mean "I am a father to nothing", which is
the same as "I am not a father".

When a contradictory negation occurs, *nothing* is said about what
is *true*. {mi patfu no da} seems intuitively to be saying {mi
patfu}, but it is *NOT* saying that, and that's where the confusion
comes in. {mi patfu no da} is, as a contradictory negative
statment, saying *nothing*, when you get right down to it. I mean,
it says I'm not a father, but that's it, and that's all.

About the third issue, whether or not it makes any sense at all to
talk about a predicate in Lojban where one of the places cannot be
filled, we're all pretty clear: something without a lid cannot be
related to with the {botpi} predicate. Something without a child
cannot be related to with the {patfu} predicate. *Unless* a
negation is occuring. See
http://www.lojban.org/tiki//tiki-index.php?page=all+places+equally+important+gotcha

I think this exhastively (and exhaustingly) covers the current
confusion. Please let me know if I've missed anything.

-Robin