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Re: [lojban] Individuals and xorlo




On Tue, Feb 18, 2014 at 10:13 AM, guskant <gusni.kantu@gmail.com> wrote:

Le mardi 18 février 2014 07:41:04 UTC+9, xorxes a écrit :

lo PA broda := zo'e noi ke'a PA mei gi'e broda


I prefer that definition to the current one because the system of counting is clearer than {zilkancu}, though atomicity is still not required for {PA mei}.

Atomicity is not strictly required for the definition, but it's kind of implicit. If atomicity is false, then "su'o N mei" is always true. They are just a series of tautological predicates. And "N mei" is always false for any finite N, a series of contradictory predicates. So we _can_ define "PA mei" in the absence of atomicity, but actually using those predicates for anything meaningful requires atomicity. In the absence of atoms, anything at all satisfies su'o N mei and consequently nothing at all satisfies N mei.

If we really need atomicity for {lo PA broda}, we could add a condition of individual for {lo pa broda}:
{lo pa broda} =ca'e {zo'e noi ro'oi da poi ke'a xi pa me ke'a xi re zo'u ke'a xi re me da gi'e broda}

However, I think atomicity is not necessary for a definition of inner quantifier. 

I agree it's not necessary for the definition, but the use of a finite inner quantifier presupposes individuals.

mu'o mi'e xorxes

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