Re: [lojban] Individuals and xorlo

On Sat, Feb 22, 2014 at 5:02 AM, guskant <gusni.kantu@gmail.com> wrote:

Because {su'o mei} is neither a sequence of logical elements, nor expanded to a sequence of logical elements, a sentence including {su'o mei} itself cannot be a logical axiom or the equivalent. I call a sentence "tautology" only when it is expressed with a sequence of logical elements that is a logical axiom or the equivalent.

But we _are_ defining "su'o mei" (as well as all the other "su'o N mei" and "N mei") as logical elements! That's the whole point of what we're doing, isn't it? Why would you want to give "su'o mei" different meanings in differnet contexts?

"su'o mei" is just the tautological predicate. It has nothing to do with whether or not there are individuals. It is true of anything at all.

Any of them are fine. (D1-1) is only a "one-shot" definition of a particular ko'a in a particular universe of discourse defined by a speaker. It is not for general use.

But what does D1 even mean if you only know what "su'o mei" means when applied to a particular ko'a? According to D1

ko'a su'o re mei := su'o da poi me ko'a su'o de poi me ko'a zo'u ge da su'o mei gi nai de me da

How is that a complete definition of "ko'a su'o re mei", when there is an undefined term on the right hand side?

In all my definitions "ko'a" was intended as a place holder. They otherwise don't make sense as definitions of the predicates.

Even with (D1-1b), "mi jo'u do su'o pa mei" is true.

(D1-1b) is also a "one-shot" definition defined by a speaker on a particular ko'a that is an individual, and is not applied generally.

It gives a meaning to {su'o pa mei} with a particular ko'a.

For example, suppose a speaker applies (D1-1b) to {mi}:
(D1-1b) mi su'o pa mei := su'oi da poi me mi ku'o ro'oi de poi me mi zo'u de me da ije da me de

Then {mi jo'u do} satisfies (D1) of N=2:
mi jo'u do su'o re mei

From (D1),
ganai ko'a su'o N mei gi ko'a su'o N-1 mei
is always true.

(proof:

I didn't check your proof in detail, but it seems to me you must be be relying on D1-1, not just on D1. Otherwise both "su'o N mei" and "su'o N-1 mei" are undefined. With D1-1b in effect, the statement is false. From "mi jo'u do su'o re mei" we cannot conclude "mi jo'u do su'o pa mei" if "D1-1b" applies to "mi jo'u do".

Therefore

mi jo'u do su'o pa mei
is also true.

As long as D1-1b applies only to "mi", and D1-1 applies to "mi jo'u do", yes. But why would you use different definitions of "su'o mei" in the same context?

For example, suppose that a speaker regards {lo nanba} is non-individual:

ro'oi da poi me lo nanba ku'o su'oi de poi me lo nanba zo'u de me da ijenai da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}.

Yes.

Even though there is no individual {lo nanba}, an _expression_ {N mei} is available with (D1-7) (D1) (D2) (D3).

No:

"lo nanba cu su'o pa mei" is true

"lo nanba cu su'o re mei" is true

"lo nanba cu su'o ci mei" is true

and so on, but:

"lo nanba cu pa mei"

= "lo nanba cu su'o pa mei gi'e nai su'o re mei" is false

"lo nanba cu re mei"

= "lo nanba cu su'o re mei gi'e nai su'o ci mei" is false

and so on. "lo nanba cu su'o N mei" is true for all N, while "lo nanba cu N mei" is false for all (finite) N.

The speaker arbitrarily fix a referent to be {lo pa nanba}. If another {lo nanba xi re} is given, {lo pa nanba jo'u lo nanba xi re} is {lo re nanba}.

If "lo pa nanba" satisfies D1-1 and D1 and it also satisfies "ro'oi da poi me lo pa nanba ku'o su'oi de poi me lo pa nanba zo'u de me da ijenai da me de", then it cannot satisfy D2.

mu'o mi'e xorxes