Re: [lojban] Individuals and xorlo

On Thu, Feb 20, 2014 at 1:50 AM, guskant <gusni.kantu@gmail.com> wrote:

I don't yet understand how the definitions on {PA mei} could suggest implicit atomicity.

The definitions on the topic are:

(D1) ko'a su'o N mei := su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-1 mei gi de na me da

(D2) ko'a N mei := ko'a su'o N mei gi'e nai su'o N+1 mei
(D3) lo PA broda := zo'e noi ke'a PA mei gi'e broda

For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).

That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything.

Once {ko'a su'o pa mei} is defined in some way, (D2) and (D3) are valid for an integer N>=1. (D2) is expanded as follows:

[...]
Then {ko'a N mei} implies also
ro'oi de poi me ko'a zo'u de me ko'a

"ro'oi de poi me ko'a zo'u de me ko'a" is true independently of whether "ko'a N mei" is true or not. It's just a case of the general "ro'oi de poi broda zo'u de broda".

When N=1,

ko'a pa mei
= ge ko'a su'o pa mei
gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u

ganai da su'o pa mei
gi de me da

Yes, and since "su'o pa mei" is a tautology, that reduces to:

ko'a pa mei

= ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

which says that "ko'a" is an individual. (Which is to be expected, what else would a one-some be if not an individual?)

In every derivation from (D1) and (D2), {ko'a} may have {ko'e} such that {ko'e me ko'a ijenai ko'a me ko'e}.

I don't think that can happen if "ko'a pa mei" is true.

As a reasonable definition for {ko'a su'o pa mei}, I would suggest as follows:

(D1-1) ko'a su'o pa mei := su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u de me da

Since that is also a tautology ("ko'a" itself will instantiate "su'oi da poi me ko'a"), it works, but it's more complicated that it needs to be. We can just as well define it as:

ko'a su'o pa mei := ko'a me ko'a

or:

ko'a su'o pa mei := ko'a du ko'a

or any other tautology. Or just state that "su'o pa mei" is the tautological predicate.

(D1-1) says nothing related the number one, but it reflects a property of one-some of non-individual: any non-individual sumti can be one-some. Once non-individual B such that {B me ko'a} is fixed as one-some {B pa mei}, and if C such that {C me ko'a} satisfies conditions (D1) and (D2), C is counted to be an integer, and it is meaningful: at least, an order of cardinality is given to the pair of B and C.

If by "one-some" you mean "pa mei", then only indiciduals can satisfy it. If you mean "su'o pa mei", then yes, anything satisfies it, it's a tautology. Or am I missing something?

It may be off topic, but if there were a definition for inner fractional quantifier
{lo piPA broda} =ca'e {zo'e noi ke'a piPA si'e be lo pa broda}
then the language would be richer; this definition would be avaiable both atomist and non-atomist.

Actually, an outer fractional quantifier {piPA sumti} =ca'e {lo piPA si'e be pa me sumti} is available to atomists only.

I assume "lo piPA broda" will have some such meaning , but it's a different system. And it relies on a previous definition of "si'e", which we don't have from basics like the ones we're discussing here for "mei".

mu'o mi'e xorxes