Re: [lojban] About plural 'ro'

[Jorge Llambías <jjllambias@gmail.com>]

On Wed, Apr 21, 2010 at 4:31 PM, John E Clifford <kali9putra@yahoo.com> wrote:
> From: Jorge Llambías <jjllambias@gmail.com>
>>
>> Right, the corresponding inference when you have a singular quantifier
>> 'Ax' and a plural term 'a' is:
>>
>> "AxFx, therefore if a is one, Fa"
>
> [[[Where did the "if a is one come from?  It is not anywhere in the formula above.

That's why it's the *corresponding* inference. The inference rule you
gave was for singular quantifier to singular term, or for plural
quantifier to plural term. It is obvious why you need to add the "if a
is one" when going from singular quantifier to plural term, isn't it?

> And, of course, it won't help in the reverse case, even if it does here.  But it doesn't of course, because a ios not one but plural ex hypothesi]]]

What is the reverse case? Existential generalization? The
corresponding rule would be:

 "Fa, therefore if a is one, ExFx"

If the reverse case was from plural quantifier to singular term, then
neither rule need modification:

 "AxFx, therefore Fa"

 "Fa, therefore ExFx"

both work with singular 'a' and plural 'Ax' or 'Ex'.


>  Suppose a piano (or something) ways a ton and a half.  Then, "all the people who carried the whatever will be rewarded" is going to be either either vacuously false or vacuously true, even though the piano got carried (if we are going by singulars) or either nobody gets a reward or everybody gets several (if we go by plurals).  Since both plural reference of at least the latter sort and plural quantification (which follows) seems
>  useful, some trick is needed.  And one that can be reliably and consistently used,]]]

      ro lo prenu poi bevri lo co'e cu ba se cnemu
      = ro da poi me lo prenu poi bevri lo co'e zo'u da ba se cnemu
      "Each of (the people who carried the whatever) will be rewarded."
      "For each x, such that x is one of (the people who carried the
whatever): x will be rewarded."

(Reward for each participant in the carrying.)

      ro lo prenu ku poi bevri lo co'e cu ba se cnemu
      = ro da poi me lo prenu zi'e poi bevri lo co'e zo'u da ba se cecmu
      "Each of (the people) who carried the whatever will be rewarded."
      "For each x, such that x is one of (the people) and x carried
the whatever: x will be rewarded."

(Only Superman gets reward.)

Neither of those two, however, involve plural quantification. Using
"roro" as the plural quantifier:

      roro lo prenu poi bevri lo co'e cu ba se cnemu
      roro da poi me lo prenu poi bevri lo co'e zo'u da ba se cnemu
      "Any one or more of (the people who carried the whatever) will
be rewarded."
      "For any X, such that X is one or more of (the people who
carried the whatever): X will be rewarded."

(Lots of rewards for anybody involved.)

      roro lo prenu ku poi bevri lo co'e cu ba se cnemu
      roro da poi me lo prenu zi'e poi bevri lo co'e zo'u da ba se cecmu
      "Any one or more of (the people) who carried the whatever will
be rewarded."
      "For any X, such that X is one or more of (the people) and X
carried the whatever: X will be rewarded."

(Any teams that carried it gets reward.)

mu'o mi'e xorxes

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