[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: [lojban] About plural 'ro'

----- Original Message ----

From: Jorge Llambías <jjllambias@gmail.com>
To: lojban@googlegroups.com
Sent: Wed, April 21, 2010 4:37:30 PM
Subject: Re: [lojban] About plural 'ro'

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?

[[[[It's a universal quantifier, it applies to all instances.  Is Fa not an instance?  If not, how is "instance" defined?

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

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

[[[[ No.  And not just because there is no "a is one" involved, though that , too.  I meant, if A is a plural quantifier and a a singular term.]]]]

"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'.

[[[[If so, just what do "singular' and "plural" mean here. This, I know, is Lojban, where no word can be trusted to mean what it ordinarily means, but this seems a clear case even here.]]]


>  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 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) seem
>  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.)

[[[[Yes, there are any number of other sentences which can be worked up to take care of various problems, but let's stick to the one at hand, since we have no way of deciding which alternative to use as correct. In Lojban, iirc, it would be something like 'ro da poi bevri lo co'e cu ba se cnemu' (I admit I am trusting you for vocab here), where I leave the nature of 'ro' open.  Suppose there are five strongmen, no one or two of which can lift the whatsis and any three of which can.  And all the groups that can, do.  And the reward is a hundred bucks.  How much do you have to pay out?  The obvously correct answer is $500.  No interpretation of 'ro' presented gives that answer (they range from $0 to $1600)  I should add that the shift from "carries the whatsis" to "is a member of a bunch that carries the whatsis" seems particularly illegitimate, since we are trying to work up to questions about what quantifiers mean applied to terms by figuring out what
 they mean in their natural habitat -- and of course, carrying a pianno is very different from being in a group, even if the group is carrying a piano.  (And, as a terminological point, 'roro'; is obviously the singular quantifier, since it takes the plural and breaks it down again.)]]]]

mu'o mi'e xorxes

-- 
You received this message because you are subscribed to the Google Groups "lojban" group.
To post to this group, send email to lojban@googlegroups.com.
To unsubscribe from this group, send email to lojban+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/lojban?hl=en.


      

-- 
You received this message because you are subscribed to the Google Groups "lojban" group.
To post to this group, send email to lojban@googlegroups.com.
To unsubscribe from this group, send email to lojban+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/lojban?hl=en.