`at least one ' vrs `one or more'

[bob@MEGALITH.RATTLESNAKE.COM]

On 3 Nov 1997, Lee Crocker wrote

    {mi na nelci lo mlatu}, for example, says exactly the right thing:
    I don't like some cats.

Jorge Llambias responded by saying:

    No, it says that you don't like any cats. ...  Remember that {na}
    is a bridi negator, it negates the whole bridi: "It is not the
    case that there is at least one cat that I like."

Which is right?  Should the Lojban be translated as:

  1. It is false that I like one or more cats.

     which can be read as Lee suggests, that
     `I don't like one or more cats.'
or

  2. It is false that I like at least one cat.

     which can be read as Jorge suggests, that
     `I don't like any cats.'

_The Complete Lojban Language_ suggests both.
Chapter 6.2 translates {lo} as:

    one-or-more-of-all-the-things-which-really are

At the same time, Chapter 6.7 translates {lo} as:

    at least one of all of those which really are

In every day English `one or more' means the same as `at least one'.
But consider the differing translations that Lee and Jorge provided.


Let's step through the translations in detail:

    Jorge is right to say that:         mi na nelci lo mlatu

    can be transformed into:            naku zo'u mi nelci lo mlatu

This is described in Chapter 16 of _The Complete Lojban Language_.
{naku zo'u} can be translated as `It is not the case that' (or as `It
is false that').

Using
    the cmavo list of 06/01/93, 00968,
    the gismu list of 26 September 1994,
    and Chapter 6 of _The Complete Lojban Language_.

we get these definitions

    mi
           me/we the speaker(s)/author(s); the speaker and perhaps
           others for whom the speaker speaks

    nelci
           is fond of/likes/has a taste for x2 (object/state)

    mlatu
           is a cat/[puss/pussy/kitten] [feline animal] of species/breed x2

    lo
        at least one of all of those which really are
        one or more of all the things which really are


It is conventional to ignore whether {mi} refers to I singular or we
plural and to use the present tense for tenses that are not specified
in time, contour, or place.

So we can transform

    mi na nelci lo mlatu
to
    naku zo'u mi nelci lo mlatu

and translate this as

   1. It is false that I like at least one or all of those
      which really are cats.

or else as

   2. It is false that I like one or more of all those which really
      are cats.


Jorge interprets the Lojban utterance as:

   1a. It is not the case that there is at least one cat that I like.

which I think can be fairly restated similar to my translation 1 as

   1a. It is not the case that I like at least one cat.

Lee interprets the Lojban utterance as:

   2a. I don't like some cats.

which I think can be fairly restated similar to my translation 2 as

   2b. It is not the case that I like one or more cats.

We can also phrase this more like Jorge's first translation:

   2c. It is not the case that there are one or more cats that I like.

The translations end up with quite different meanings:

    Jorge does not like even one cat.  He does not like *any* cats
    Lee does not like some cats.

Yet, out of context, one would think that

    at least one
    one or more

mean the same!  But if they meant the same, the following would mean
the same:

    1.  It is not the case that there is at least one cat that I like.
    2.  It is not the case that there are one or more cats that I like.

Yet the first sentence suggests I don't like any cats at all while the
second suggests that I don't like some cats but like others.

The English phrase `at least one' suggests the reference is with
respect to all the members of a set; but the phrase `one or more'
lacks that implication.  Hence the difference in meaning.

So what does

    naku zo'u mi nelci lo mlatu

mean?

As far as I can see, the best way to answer this question is to
examine the Lojban grammar.  In this utterance, {lo} binds tighter to
{mlatu} than to anything else.

Using the old parser, the utterance parses like this:

    ({<na ku> zo'u} {mi <nelci [(lo mlatu KU) VAU]>})

The original form looks like this:

    (mi {<na nelci> <[lo mlatu KU] VAU>})


This means we should think of {lo mlatu} as a phrase somewhat on its
own; and the English translation of {lo mlatu} should also stand
alone.

Hence, the proper English parse is

    It is not the case that there is {at least one cat} that I like.

When you read the English like this you see that {at least one cat}
does *not* require that there be no other cats.  It only requires that
there be at least one cat you do not like.  There can be some cats you
*do* like.

Consequently, Lee Crocker's translation is better.  He `does not like
some cats.'

And the best gloss for {lo} is:

    one or more of all those which really is or are

--

    Robert J. Chassell               bob@rattlesnake.com
    25 Rattlesnake Mountain Road     bob@ai.mit.edu
    Stockbridge, MA 01262-0693 USA   (413) 298-4725