Re: [lojban] Individuals and xorlo

On Fri, Feb 21, 2014 at 3:46 AM, guskant <gusni.kantu@gmail.com> wrote:

(D1-1) is not the same. (D1-1) says only that there is a largest referent of what is {me ko'a}.

Namely, ko'a themselves, right?

It is a tautology, and says nothing particular. The difference from {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to be {su'o pa mei}: once {ko'a} is fixed, the other thing that is {me ko'a} is not called {su'o pa mei}. (D1-1) says nothing, but a kind of dummy to make (D1) (D2) (D3) be meaningful also to non-individual.

Exactly. And "ro'oi da su'o mei" is also a statement that says nothing, it can never be false. If "ro'oi da broda" is true, then the one-place predicate "broda" is tautological, and conversely, if the one-place predicate broda is tautological then "ro'oi da broda" is true. Your choice D1-1 to define the tautological one-place predicate "su'o pa mei" is fine. Any other equivalent definition would have the same effect, for example:

(D1-2) ko'a su'o pa mei := ko'a me ko'a

or my current favourite:

(D1-3) Ko'a su'o pa mei := su'oi da me ko'a

I like it because it can be easily generalized to "no mei", "ro mei" and "me'i mei":

(D4) ko'a no mei := no'oi da me ko'a

(D5) ko'a ro mei := ro'oi da me ko'a

(D6) ko'a me'i mei := me'oi da me ko'a

"no mei" is the contradictory predicate, nothing can satisfy it, but there may or may not be something that satisfies "ro mei".

When another condition {ije da me de} is added to (D1-1), (D1-1) is not a tautology, and {ko'a} is an individual (not only {ko'a su'o pa mei} but also {ko'a pa mei}, though): then the conditions are equivalent to {ro'oi da su'o pa mei}, which makes {ko'a su'o pa mei} always true.

I don't follow that. What do you mean by adding a condition to D1-1?

If you change D1-1 to

(D1-1b) 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 ije da me de

then you no longer have a useful definition. Now "su'o pa mei" is no longer true of "mi jo'u do", for example, Why would you want to define "su'o pa mei" in a way that "mi jo'u do su'o pa mei" is false? I think your new definition (D1-1b) is equivalent to my definition of "pa mei".

And I don't see how that is equivalent to "ro'oi da su'o pa mei". "ro'oi da su'o pa mei" entails "mi jo'u do su'o pa mei", for example.

As long as talking about among theory, (D1-1)+{ije da me de} is not a logical axiom or equivalent, though it is necessary for comforming to mereology with atoms.

I have to disagree with that. (D1-1)+{ije da me de} just doesn't work as a useful definition of "su'o pa mei".

(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

(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

Yes, and please note that (D1-1) is not equivatent to {ro'oi da su'o pa mei}.

(D1-1) entails "ro'oi da su'o pa mei", and conversely "ro'oi da su'o pa mei" requires "su'o pa mei" to be a tautological predicate. It doesn't require that the specific tautological form D1-1 be chosen to define it, of course, any other tautological one-place predicate will do just as well.

Do you agree that with just those definitions:

ko'a pa mei
= ko'a su'o pa mei gi'e nai su'o re mei

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

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

The result requires {ro'oi da su'o pa mei}.

If by that you mean that it requires D1-1, i.e. it requires that "su'o pa mei" is tautological, yes. Otherwise, I don't understand what you mean.

As I discussed above, (D1-1) is a kind of dummy to say {ko'a su'o pa mei} for a particular ko'a. With (D1-1), once ko'a is said to be {su'o pa mei}, {ro'oi da su'o pa mei} is not true, and we don't get the same result.

How does giving a value to "ko'a" make "ro'oi da su'o pa mei" not true? "ro'oi da su'o pa mei" is independent of what values are assigned to "ko'a". It doesn't even mention ko'a.

With a dummy defintion (D1-1), "PA mei" is not meaningless even for non-individual.

Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a property of {jo'u}, {B me B jo'u C} and {C me B jo'u C}. Then {B jo'u C su'o re mei} according to (D1).

For someone who holds the following as an axiom (the anti-atomist):

(AA) no'oi da ro'oi de poi me da zo'u da me de

it can be shown that, for every natural N, "ro'oi da su'o N mei" and "no'oi da N mei", which is to say that for the anti-atomist all the numeric predicates are trivial (either tautologies or contradictions).

For someone who holds the opposite position (the atomist):

(A) su'oi da ro'oi de poi me da zo'u da me de

then the numeric predicates are non-trivial: they are true of some things and false of other things (except for "su'o pa mei" which is still a tautology, and its negation "no mei" which is of course a contradiction).

Perhaps by "non-individual" you mean someone who holds neither (A) nor (AA) as axioms, someone who doesn't know or doesn't care which one of (A) or (AA) is true. The that person (the atom-agnostic), the numeric predicates are also non-trivial, but if they ever assert that something satisfies "pa mei", or "re mei", or "ci mei", etc, then they are thereby commited to (A). They can still say things like "B jo'u C su'o re mei" without commiting to either (A) or (AA). Is that what you mean?

A non-atomist speaker must fix a referent of sumti to be {su'o pa mei}. For enjoying atomicity, just add a condition {ije da me de} to (D1-1), then it becomes clear that {ko'a} is an individual.

I think you are mistaken that you can add "ije da me de" to D1-1 in order to satisfy the atomist, Adding that breaks the definition of "su'o pa mei" for everyone.

"ko'a su'o mei" is always true for all three, for the atomist, the anti-atomist, and the atom-agnostic.

"ko'a pa mei" can be true or false for the atomist, depending on what "ko'a" refers to, it must be false for the anti-atomist, no matter what "ko'a"refers to, and can be false, but not true, for the atom-agnostic (If it's true for them, then they've become atomists, if it's false, they can remain as atom-agnostics.)

Starting with {ro'oi da su'o pa mei} is useful, but excludes non-individual from expressions {lo PA broda}. (D1-1) makes (D1) (D2) (D3) available also to non-individual.

If by PA you mean a natural number (it's better to use N in that case, for PA could stand for "su'o" for example), then "lo N broda" is useless for the anti-atomist. It cannot refer to anything for them, because starting from (AA) it can be shown that "... noi ke'a broda gi'e N mei" will be always false.

mu'o mi'e xorxes