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Nick:
> The bits of substance that I've been talking about (anything from "the
> top quarter of" to {pi ro}) are, I would claim, extensionally defined
> notions of substances
>
> And wants vei mo'e tu'o lo namcu ve'o lo broda to be the substance
>
> My god, that's ugly,and I have no idea what it means at all. Sorry,
> I'll need to come back to it
Think of a quantifier as a fraction: N out of all the D things that
are P. For some P, there is only ever one conceivable fraction.
Because we can't conceive of any other fraction, we can't say
what it is. So I suggest that it is Mr Number.
> And's main contention is that talk of the substance makes nonsensical
> any outer quantifier
Redundant rather than nonsensical. "Mr-number lo Mr-number broda"
makes sense, I think.
> We have two ways to non-quantify things in Lojban already. Both
> intensional: Prototype and Kind
>
> And, give me some representative statements about substance that are
> not about bits of substance, and we'll see if they're not all Kinds or
> Prototypes
Well, the outer quantifier for Kinds and Prototypes would be Mr Number.
Kinds include numbers and sets and du'u too, so they're not novel
to Lojban.
I'm not sure if I can give you a statement about non-kind Substance that
you cannot recast as a statement either about Bits of substance or about
Mr Broda or about the Collective of all Bits of Substance. But pretty
much any English sentence with an unquantified mass noun or proper noun
would count as an example of conceptualizing something as Substance.
Furthermore "instantiates Mr Stuff" is probably Substance.
> Water is a liquid: Prototype
> I like Water: Kind (or Intension, anyway.)
Or Substance. You like Mr Xodium, but you can like either Mr Water
or Water-stuff (that which instantiates Mr Water).
> Water got into my boots: Bit of substance (pisu'o djacu)
That last one is just Substance in English. It's no different from
"Nick got into my boots".
> Link said something about substance as distinct from bits of substance
> too, in his paper --- where he did something like my ontology, but in
> the other direction and much more cogently: he started with atoms, then
> the goo of them, then the goo-join and the collective-join of them, and
> built up a universe. And I think what he said was they were all nominal
> masses (= kinds, I think.) But I'll check tomorrow
>
> Aside:
>
> I think And is still wrong about it being impossible to count bits of
> substance: you *can* count them, if the ve memzilfendi is constrained
> (Eastern Hemisphere vs Western Hemisphere water --- cut by the
> Greenwich Meridian.)
These are Individual of Bit of Water. They have cardinality su'eci'ino
-- in this case, the cardinality is 2.
> Just as you can count real numbers if you consider
> only the natural ones -- or a mapping of natural to real ones. So
> countable bits of substance exist as a subset of all bits of substance,
> and are analogous to Natural being a subset of Real numbers. Writing
> down natural numbers and saying you're counting real numbers is no less
> true than picking out bisections and trisections of space and saying
> you're counting spaces. Of course you are. And there will be spaces you
> miss, just as there will be real numbers you miss
I have been saying from the outset that you can count numbers.
I don't know what point you're making in saying, in effect, that
some bits of substance can be individuals. In introducing the term
"Bit of" I started off by saying "arbitrarily defined bit of".
Every bit of substance is individuable, if only by its haecceity.
The fact that something can be viwed either as a bit of substance
or as an individual is something we had already established, I
thought. So a table can either be seen as an individual table
or as a bit of table-stuff.
--And.