Subject: Re: [lojban] pro-sumti question

From: [email-masked]
Date: Sat, 6 Jul 2002 16:15:53 EDT

In a message dated 7/6/2002 11:58:27 AM Central Daylight Time, 
[email-masked] writes:

> <I would have said overlapping was something things did well long
> before it could be metaphorically extended to sets!
> 
> Anyway, consider for example a wall covered with pictures.
> Each picture covers a certain area, but some of the pictures
> overlap, so the area covered by the mass of pictures is less
> than the sum of the areas covered by each picture.>
> 

An interesting problem in idees fixes: I was so wrapped up in the 
"overlapping" metaphor that I did not even think of literal overlapping. 
Thanks for the example.

<>What is emerging is the fairly clear evidence that masses
>are intensional, with all the horrors that that entails: two masses with
>exactly the same mebers may not be identical.

Could you give an example? In what would they differ?>

Presumably at least in essential properties and probably also in the relation 
between mass properties and individual properties (going to intensionals is a 
traditional way of putting off problems with extensional properties). 

<>And from that I think it
>follows as a possibility that two groups of people with the same properties
>individually may comprise two masses that have different properties.

Two groups of the same people? Like the reading club and the
hockey team, which happen to have the same members? But that
would be like saying that the teacher and Bob's mom, which
happen to be the same person, have different properties.>

Well, I was thinking of tow different groups of people doing the same things, 
rather than the same group of people doing different things, but it would 
surely work for them as well (see above). I would be like saying that the 
teacher and Bob's mom -- the same person -- has different propreties. And so 
they do: Bob's mom has necessarily had a child and the teacher has not, the 
teacher necessarily teaches, Bob's mom does not. "How is 'The Morning Star = 
The Evening Star', if true, different from 'The morning Star = the Morning 
Star?" except this is the other side of that coin.

<> That
>is, the relation between the properties of the members of a mass (including
>whether they are members of that mass) and the properties of the mass is an
>intensional one -- not generally reducible to any direct reading from fact 
>to
>fact without going through at least the intensionality of the definition of
>the mass. I'd sure like to find another way to do this.

I can't see how you could, but I'd love to see the details.>

Oh, I thought you were denying that mass definitions were intensional. I am 
merely hoping they are not but see no way to avoid it at the moment if the 
way of regularizing the mass notions that I have been playing with does not 
work.

<>{le panopamei} means "the mass I have in
>mind of 101 things." For this to make any sense at all, there has to be 
>more
>than one such mass, so that I can pick one to have in mind, and the only 
>way
>I can see to do that, short of intensionality (which I am trying to avoid, 
>if
>possible, remember) is to allow submasses to count.

There are infinitely many possible masses of 101 things that don't
involve intensionality, so I don't understand what you mean here.
You seem to be saying that somehow the 101 things get fixed first
and then {le} is used to select from masses of those things, but
that is not right. {le} selects from all posible 101-somes, and
there are plenty to choose from. {lo'i panopamei}, the set of all
101-somes, is a very large set. (And in any case the idea that
for {le broda} to make any sense there has to be more than one
broda is not right either.)>

Well, the first part is stretching, since we have always said "in context" 
for these examples and so we are here talking about those 101 ball, all white 
but the one green. So, which of the 2^101 submasses do I pick? And in any 
given case the critters will be picked (in some loose sense) by the context 
and then the massification done. And {le broda} only makes sense if there is 
other than 1 broda -- which there always is with {le} since it is 
non-veridical.

<><Well, I guess it is possible to set up a classification scheme[of how the
>properties of a mass are related to the properties of its members] but in 
>the
>end you need to examine the particular context before deciding in which 
>class
>a given property falls. It's not something you could put in a dictionary.>
>
>I would think it was a very important thing to put into a dictionary, even 
>if
>it had several clauses for different situations. Are you saying that there
>are no rules for relating a property of a mass to those of its members?

Intuitive general rules, yes. Steadfast rules, I doubt it.

>But
>many contrary cases have been cited -- and regularly are even in the
>semantically deficient Book.

Try to make explicit the rule for weights for example, which is
one of the clearest cases. We have something like:

ko'a grake ko'e ko'i
fo'a grake fo'e fo'i
ko'a joi fo'a grake le sumji be ko'e bei fo'e ko'i no'u fo'i

It's hard to give a general rule because somehow you have to specify
that ko'i has to be equal to fo'i, and you have to select the x2
place as the one that gets additioned. We can't say for a general
{broda} that it is in the same class as {grake} and leave it at
that, unless the place structures are very similar.>

Looks fine to me, except that part of the rule -- or part of the question -- 
has to specify the same standard in both members or we are back to an apples 
and oranges case. If all you mean by your objection is that things like what 
gets added (if anything specifiable by places structure) and so on, then, 
yes, every predicate probably has its own rules (place structures tend to be 
different), but that hardly seems a reason to say there are no rules. But it 
is a good reason to put those rules in the dictionary.