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

[bob@MEGALITH.RATTLESNAKE.COM]

Chris Bogart said:

   My sense of English logic doesn't make a distinction between 'see'
   and 'like' for these sentences, so I can't comment.

Well, I am trying to get at the effects of this distinction as well as
the effect of {lo}.

Basically, I am saying both that {viska} and {nelci} behave
differently with arguments and also that that in some circumstances

    lo mlatu                 does not transform into   da poi mlatu
    some, one or more, cats                            x, such that x is a cat

as some people are presuming.

Put another way, we are *not* negating "I like one or more cats" as
Lee Crocker suggested.  We are negating a sentence with a different
meaning than "one or more" (albeit, in some circumstances "one or
more" is a good translation).

Clearly:

    .i naku zo'u mi viska lo mlatu
    It is false that I can see one or more cats  ==> I cannot see any cats.

There is no argument about this.
This is evidence of a context in which staightforward presumptions work.

But the issue at hand concerns a quite different case:

    It is false that I like some, one or more, cats
                =?=> I do not like any cats.

In this case, the phrase `some, one or more cats' is a gloss for

{lo}
    we have a procedure to discovering some number of real cats out of
    all those that are real, the number being at least one, but maybe
    more, and not necessarily all, with both the number and particular
    cats being left unspecified.


So the question is, does the phrase:

    It is false that I like some number of, not necessarily all, cats
                =?=> I do not like any cats.

I think the answer is clearly no.

This answer comes about because of a difference between `see' and
`like' that effects how logic works in the context of {lo}.

In the case of `see', {viska}, the seen entities, the x2, are
substitutable, such that a characteristic true of any one (such as
being seen) has consequences for all the others.

    .i naku zo'u mi viska lo mlatu
    It is false that I see some, one or more, cats

means: I do not see any

But in the case of `likes', {nelci}, the liked entities, the x2, are
independent, such that a characteristic true of one (such as being
liked) does not necessarily have consequences for all the others.

Besides revolving around the relationship between {viska} and {nelci}
and their arguments, this question revolves around the meaning of
{lo}.

I know there is a tendency to handle {lo} so sentences come out as
examples of textbook logic.

But as far as I can see, for

    .i naku zo'u mi nelci lo mlatu
    It is false that I like some, one or more, cats

to truthfully imply

    I do not like any cats.

the `veridicality operator' {lo} must each and every time identify
*all* things-which-really-are cats, not just some non-specific and
non-particular one or more of them.  Otherwise, I can like some and
non-like some.

This is quite different from the consequences of {lo} as a `veridicality
operator' when we are making utterances involving {viska}, `see'.
In this latter case, any thing-which-really-is a cat enables the
logic to work as in a text book example.  {lo} need only identify one
cat for one or more cats to be seen.


English translations of {lo}:

        at least one ...

        one or more ...

        one or more of all the things which really is or are ...

        at least one of all of those which really are ...

        some number, at least one, but perhaps more, of all real ...

        some, at least one ...

Chris Bogart goes on to say:

    ... all your translations of {lo} seem OK to me.  The problem is that
    they have different senses, to you, in English, but the same logical
    meaning in Lojban.  You're taking the glosses too seriously.

I agree with you in that I think all these translations of {lo} are
OK.  On the other hand, I understand some people to be saying that
only one of these glosses is OK, namely `at least one ...'.  That we
both agree is false.

In particular, I understand you to be saying that we both agree that
it is false to transform:

    lo mlatu                               da poi mlatu
    some, one or more, cats      =/=>      x, such that x is a cat
                                           Ex | cat(x)

Since this transformation is false, the logical conclusions that
depend on it are false.

Hence, I conclude that in utterances with {lo}, the logic is more
sensitive to context and more complex than a first look would suggest.

--

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