Re: `at least one ' vrs `one or more'

[Chris Bogart <cbogart@QUETZAL.COM>]

And Rosta <a.rosta@uclan.ac.uk> writes:

   Can I suggest that discussions about scope of negation,
   etc., use some sort of logical notation instead of
   ordinary English?

This is fine, but does not help answer the question, which English
translation of

    mi na nelci lo mlatu

is better?

It would help answer the question -- translate the Lojban into logic, =
then the logic into idiomatic English, instead of glossing the Lojban =
into English and attempting to manipulate English logically.  The latter =
leads to pitfalls, into which I think you've fallen.  Specifically here:

>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.
>
>   [parser text omitted]
>
>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.

This "proper English parse" is not really idiomatic English, and your =
sense about what it means is wrong -- not that it's a bad interpretation =
of English as such, but that this weird style of English is =
traditionally used as a way of pronouncing the equations of formal =
logic, and your interpretation of the underlying logic to this sentence =
is wrong.

You've grouped {at least one cat} together, as the parser does in =
Lojban, and indicated that it should "stand alone" somewhat.  The =
logical equivalent of that "standing alone" idea is outermost =
quantification -- the thing that goes furthest to the left before {zo'u} =
in Lojban.  Formal logic communicates the concept by sentence ordering, =
not by how closely grouped a construct is.  The same ordering is used in =
English when glossing formal logic:  thus the meaning you were thinking =
of here would be expressed as:

     For at least one cat,    it is not the case that             I like =
it
     da poi mlatu                naku                          zo'u    =
mi nelci da
     Ex | (cat(x))                 ~                                     =
    Likes(I,x)

Whereas what the pseudo English sentence really says is:

     It is not the case that     for at least one cat              I =
like it
     naku                             da poi mlatu             zo'u    =
mi nelci da
     ~                                  Ex | cat(x)                      =
    Likes(i,x)

Take the question "Is there at least one cat that I like?".  The first =
statement says to negate the last three words ("that I like"  --> "that =
I don't like"), then answer the question.  The second says to answer the =
question, then change yes to no or no to yes.  The results are very =
different.

You have to have the logical distinction straight before you can =
translate to English, and the second step isn't particularly relevant to =
the Lojban list (as if Dvorak, APL, and Ham radio were :-)   )  which is =
why And suggested dispensing with the latter.

This question of the order of quantification is interesting to me =
because it's a tricky mind-bending exercise in English, but =
straightforward in Lojban or in formal logic.  To me it seems like =
evidence of the truth of *some* generous interpretation of the sapir =
whorf hypothesis -- knowing a logical language allows you to grasp =
something that is very hard to explain in English.

PS this may be an overly basic review but I figured someone on this list =
may not have seen it before, so it wouldn't be bytes wasted

Chris