Date: Sat, 22 Feb 2014 00:02:51 -0800 (PST)
From: guskant <gusni.kantu@gmail.com>
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Subject: Re: [lojban] Individuals and xorlo
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Le samedi 22 f=C3=A9vrier 2014 07:16:34 UTC+9, xorxes a =C3=A9crit :
>
>
>
> On Fri, Feb 21, 2014 at 3:46 AM, guskant <gusni...@gmail.com <javascript:=
>
> > wrote:
>
>>
>> (D1-1) is not the same. (D1-1) says only that there is a largest referen=
t=20
>> of what is {me ko'a}.=20
>>
>
>
> Namely, ko'a themselves, right?
>
>

Yes.=20


=20
>
>> It is a tautology, and says nothing particular. The difference from=20
>> {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to be {su'o pa=
=20
>> mei}: once {ko'a} is fixed, the other thing that is {me ko'a} is not cal=
led=20
>> {su'o pa mei}. (D1-1) says nothing, but a kind of dummy to make (D1) (D2=
)=20
>> (D3) be meaningful also to non-individual.
>>
>
> Exactly. And "ro'oi da su'o mei" is also a statement that says nothing, i=
t=20
> can never be false. If "ro'oi da broda" is true, then the one-place=20
> predicate "broda" is tautological, and conversely, if the one-place=20
> predicate broda is tautological then "ro'oi da broda" is true. Your choic=
e=20
> D1-1 to define the tautological one-place predicate "su'o pa mei" is fine=
.=20
> Any other equivalent definition would=20
>


Because {su'o mei} is neither a sequence of logical elements, nor expanded=
=20
to a sequence of logical elements, a sentence including {su'o mei} itself=
=20
cannot be a logical axiom or the equivalent. I call a sentence "tautology"=
=20
only when it is expressed with a sequence of logical elements that is a=20
logical axiom or the equivalent.=20

When {ro'oi da su'o mei} is applied to (D1) (D2) for N=3D1, we obtain {ro'o=
i=20
da poi me ko'a ro'oi de poi me ko'a zo'u de me da}, which is a sequence of=
=20
logical elements, which is equivalent to the condition for ko'a being an=20
individual, and which is not a logical axiom or the equivalent.

It means that when we started with "ro'oi da su'o mei", it restricts the=20
usage of {su'o mei} to an individual or individuals. It defines the meaning=
=20
of {su'o mei}, and (D1) (D2) (D3) are therefore valid.

What I tried to do is to make (D1) (D2) (D3) valid with another meaning on=
=20
{su'o mei}, without using {ro'oi da su'o mei}, so that an expression with=
=20
{N mei} is available to non-individual referent.


=20

> have the same effect, for example:
>
> (D1-2) ko'a su'o pa mei :=3D ko'a me ko'a
>
> or my current favourite:
>
> (D1-3) Ko'a su'o pa mei :=3D su'oi da me ko'a
>
> I like it because it can be easily generalized to "no mei", "ro mei" and=
=20
> "me'i mei":
>
> (D4) ko'a no mei :=3D no'oi da me ko'a
> (D5) ko'a ro mei :=3D ro'oi da me ko'a
> (D6) ko'a me'i mei :=3D me'oi da me ko'a
>
> "no mei" is the contradictory predicate, nothing can satisfy it, but ther=
e=20
> may or may not be something that satisfies "ro mei".
>


Any of them are fine. (D1-1) is only a "one-shot" definition of a=20
particular ko'a in a particular universe of discourse defined by a speaker.=
=20
It is not for general use. Actually we don't need the part {su'oi da poi me=
=20
ko'a ku'o ro'oi de poi me ko'a zo'u de me da}. It says only that {ko'a} is=
=20
a plural constant. I am happy with only

(D1-7) ko'a su'o pa mei

as a "one-shot" definition instead of (D1-1). It defines a meaning of {su'o=
=20
pa mei} with a particular ko'a, and {su'o pa mei} is not necessarily=20
applied to other referents in the universe of discourse.

The form (D1-1) was given because I intended to use=20
(D1-1b) ko'e su'o pa mei :=3D {su'oi da poi me ko'e ku'o ro'oi de poi me ko=
'e=20
zo'u de me da ije da me de}
with minimal modification to (D1-1). It is a very trivial reason, and we=20
may discuss with (D1-7) instead of (D1-1).

(D1-1b) is also a "one-shot" definition by a speaker to be used on a=20
particular ko'a that is an individual. It is not for general use.


=20

> =20
>
>> When another condition {ije da me de} is added to (D1-1), (D1-1) is not =
a=20
>> tautology, and {ko'a} is an individual (not only {ko'a su'o pa mei} but=
=20
>> also {ko'a pa mei}, though): then the conditions are equivalent to {ro'o=
i=20
>> 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?=20
>
> If you change D1-1 to
>
> (D1-1b) ko'a su'o pa mei :=3D su'oi da poi me ko'a ku'o ro'oi de poi me k=
o'a=20
> zo'u de me da ije da me de
>
> then you no longer have a useful definition. Now "su'o pa mei" is no=20
> longer true of "mi jo'u do", for example, Why would you want to define=20
> "su'o pa mei" in a way that "mi jo'u do su'o pa mei" is false? I think yo=
ur=20
> new definition (D1-1b) is equivalent to my definition of "pa mei". =20
> =20
> And I don't see how that is equivalent to "ro'oi da su'o pa mei". "ro'oi=
=20
> da su'o pa mei" entails "mi jo'u do su'o pa mei", for example.
> =20
>
>> As long as talking about among theory, (D1-1)+{ije da me de} is not a=20
>> logical axiom or equivalent, though it is necessary for comforming to=20
>> mereology with atoms.
>>
>
> I have to disagree with that.  (D1-1)+{ije da me de} just doesn't work as=
=20
> a useful definition of "su'o pa mei".
>
>

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=20
particular ko'a that is an individual, and is not applied generally.=20
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 :=3D su'oi da poi me mi ku'o ro'oi de poi me mi zo'u=
=20
de me da ije da me de
Then {mi jo'u do} satisfies (D1) of N=3D2:
mi jo'u do su'o re mei

From (D1),=20
ganai ko'a su'o N mei gi ko'a su'o N-1 mei
is always true.

(proof:
da'i
ge ko'a su'o N mei gi naku ko'a su'o N-1 mei
iseni'ibo
ge 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=
=20
gi de na me da
gi naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u ge da su'o N-2=
=20
mei gi de na me da
iseni'ibo
ge su'oi da poi me ko'a ku'o su'oi de poi me ko'a ku'o su'oi di_1 poi me da=
=20
ku'o su'oi di_2 poi me da zo'u=20
ge ge di_1 su'o N-2 mei gi di_2 na me di_1 gi de na me da
gi ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u naku ge da su'o N-2=
=20
mei gi de na me da

ita'o=20
di_1 me da ijebo da me ko'a inaja di_1 me ko'a (A property of {me})
iseni'ibo
lo du'u=20
su'oi da poi me ko'a ku'o su'oi de poi me ko'a ku'o su'oi di_1 poi me da=20
zo'u ge di_1 su'o N-2 mei gi de na me da
cu natfe
lo du'u=20
ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u naku ge da su'o N-2 mei=
=20
gi de na me da

iseni'ibo=20
naku ge ko'a su'o N mei gi naku ko'a su'o N-1 mei
iseni'ibo
ganai ko'a su'o N mei gi ko'a su'o N-1 mei
uo
)

Therefore=20
mi jo'u do su'o pa mei
is also true.


=20

> =20
>
>>  (D1-1) ko'a su'o pa mei :=3D su'oi da poi me ko'a ku'o ro'oi de poi me=
=20
>>> ko'a zo'u de me da
>>> (D1) ko'a su'o N mei :=3D su'oi da poi me ko'a ku'o su'oi de poi me ko'=
a=20
>>> zo'u ge da su'o N-1 mei gi de na me da
>>> (D2) ko'a N mei  :=3D ko'a su'o N mei gi'e nai su'o N+1 mei=20
>>> (D3) lo PA broda :=3D 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=
=20
>> mei}.=20
>>
>
> (D1-1) entails "ro'oi da su'o pa mei", and conversely "ro'oi da su'o pa=
=20
> mei" requires "su'o pa mei" to be a tautological predicate. It doesn't=20
> require that the specific tautological form D1-1 be chosen to define it, =
of=20
> course, any other tautological one-place predicate will do just as well.
>


(D1-1) or (D1-7) requires that any referent _can be_ {su'o pa mei}, but a=
=20
speaker does not necessarily select all the referents to be {su'o pa mei}.=
=20
The speaker gives meaning to {su'o pa mei}. If the speaker finally does not=
=20
select all the referents to be {su'o pa mei}, the given meaning is=20
different from what is given by {ro'oi da su'o pa mei}.


=20

> =20
>
>> Do you agree that with just those definitions:
>>>
>>> ko'a pa mei
>>> =3D ko'a su'o pa mei gi'e nai su'o re mei
>>> =3D na ku ko'a su'o re mei
>>> =3D na ku su'oi da poi me ko'a su'oi de poi me ko'a zo'u ge da su'o pa =
mei=20
>>> gi de na me da
>>> =3D ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me d=
a
>>> =3D 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}.=20
>>
>
> If by that you mean that it requires D1-1, i.e. it requires that "su'o pa=
=20
> mei" is tautological, yes. Otherwise, I don't understand what you mean.=
=20
>


I meant the following part:
=3D 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=20
de na me da
=3D ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku  de me da

This derivation requires {ro'oi da su'o pa mei}.=20

When the meaning of {su'o pa mei} is given by (D1-1) or (D1-7),
ko'a su'o pa mei
is true because it is defined, but {su'o pa mei} is not defined to other=20
referents.
If ko'a is non-individual, that is to say, if a speaker regards {ro'oi da=
=20
poi me ko'a ku'o su'oi de poi me ko'a zo'u de me da ijenai da me de} is=20
true, {ro'oi da su'o pa mei} is false.


=20

> =20
>
>> As I discussed above, (D1-1) is a kind of dummy to say {ko'a su'o pa mei=
}=20
>> for a particular ko'a. With (D1-1), once ko'a is said to be {su'o pa mei=
},=20
>> {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?=
=20
>  "ro'oi da su'o pa mei" is independent of what values are assigned to=20
> "ko'a". It doesn't even mention ko'a.
> =20
>


When (D1-1) or (D1-7) is used, the speaker arbitrarily defines "ko'a su'o=
=20
pa mei" to a particular ko'a.=20
When (D1-1b) is used, the selection of ko'a is restricted to an individual.

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=
=20
da me de

That is, the speaker regards a half of {lo nanba} is also {me lo nanba}.=20
Even though there is no individual {lo nanba}, an expression {N mei} is=20
available with (D1-7) (D1) (D2) (D3).
The speaker arbitrarily fix a referent to be {lo pa nanba}. If another {lo=
=20
nanba xi re} is given, {lo pa nanba jo'u lo nanba xi re} is {lo re nanba}.


=20

>
> With a dummy defintion (D1-1), "PA mei" is not meaningless even for=20
>> non-individual.
>> Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a=20
>> property of {jo'u}, {B me B jo'u C} and {C me B jo'u C}. Then {B jo'u C=
=20
>> 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=20
>
> it can be shown that, for every natural N, "ro'oi da su'o N mei" and=20
> "no'oi da N mei", which is to say that for the anti-atomist all the numer=
ic=20
> predicates are trivial (either tautologies or contradictions).
>
>

When (AA) is true, "ro'oi da su'o N mei" is false, because it with (D1)=20
(D2) on N=3D1 results in "ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de=
=20
me da", and contradicts (AA).

As for "no'oi da N mei", (AA) says nothing. If the speaker select a=20
particular ko'a as {ko'a su'o pa mei}, "no'oi da N mei" is false; otherwise=
=20
no meaning is given to {N mei}.


=20

> For someone who holds the opposite position (the atomist):
>
> (A) su'oi da ro'oi de poi me da zo'u da me de=20
>
> then the numeric predicates are non-trivial: they are true of some things=
=20
> and false of other things (except for "su'o pa mei" which is still a=20
> tautology, and its negation "no mei" which is of course a contradiction).
>
> Perhaps by "non-individual" you mean someone who holds neither (A) nor=20
> (AA) as axioms, someone who doesn't know or doesn't care which one of (A)=
=20
> or (AA) is true. The that person (the atom-agnostic), the numeric=20
> predicates are also non-trivial, but if they ever assert that something=
=20
> satisfies "pa mei", or "re mei", or "ci mei", etc, then they are thereby=
=20
> commited to (A). They can still say things like "B jo'u C su'o re mei"=20
> without commiting to either (A) or (AA). Is that what you mean?
>


That is not what I meant.=20
I discussed only a particular ko'a, not all the referents in a universe of=
=20
discourse.
However, even (AA) holds with (D1-1) or (D1-7) (D1) (D2) (D3).


=20

>
> A non-atomist speaker must fix a referent of sumti to be {su'o pa mei}.=
=20
>> For enjoying atomicity, just add a condition {ije da me de} to (D1-1), t=
hen=20
>> it becomes clear that {ko'a} is an individual.=20
>>
>
> I think you are mistaken that you can add "ije da me de" to D1-1 in order=
=20
> to satisfy the atomist, Adding that breaks the definition of "su'o pa mei=
"=20
> for everyone.
>
>

It does not break (D1) (D2) (D2) because (D1-1b) is only a "one-shot"=20
definition for a particular ko'a that is an individual. {su'o pa mei} is=20
not defined to other sumti.


=20

> "ko'a su'o mei" is always true for all three, for the atomist, the=20
> anti-atomist, and the atom-agnostic.
>
> "ko'a pa mei" can be true or false for the atomist, depending on what=20
> "ko'a" refers to, it must be false for the anti-atomist, no matter what=
=20
> "ko'a"refers to, and can be false, but not true, for the atom-agnostic (I=
f=20
> it's true for them, then they've become atomists, if it's false, they can=
=20
> remain as atom-agnostics.)=20
>
>

It is meaningless to compare "ko'a su'o mei" for all three, because the=20
meaning of {su'o mei} is different between them. Atomist gives meaning to=
=20
{su'o pa mei} with your starting point {ro'oi da su'o pa mei}, or with=20
(D1-1b). Anti-atomist does with (D1-1) or (D1-7).


=20

> Starting with {ro'oi da su'o pa mei} is useful, but excludes=20
>> non-individual from expressions {lo PA broda}. (D1-1) makes (D1) (D2) (D=
3)=20
>> available also to non-individual.
>>
>
> If by PA you mean a natural number (it's better to use N in that case, fo=
r=20
> PA could stand for "su'o" for example), then "lo N broda" is useless for=
=20
> the anti-atomist. It cannot refer to anything for them, because starting=
=20
> from (AA) it can be shown that "... noi ke'a broda gi'e N mei" will be=20
> always false.
>

=20

As I discussed above, When (AA) holds, "ro'oi da su'o N mei" is false, and=
=20
an expression {N mei} is still available with (D1-1) or (D1-7) (D1) (D2)=20
(D3).


--=20
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<div dir=3D"ltr"><br><br>Le samedi 22 f=C3=A9vrier 2014 07:16:34 UTC+9, xor=
xes a =C3=A9crit&nbsp;:<blockquote class=3D"gmail_quote" style=3D"margin: 0=
;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div di=
r=3D"ltr"><br><div><br><div class=3D"gmail_quote">On Fri, Feb 21, 2014 at 3=
:46 AM, guskant <span dir=3D"ltr">&lt;<a href=3D"javascript:" target=3D"_bl=
ank" gdf-obfuscated-mailto=3D"ftf6xZ5B9NUJ" onmousedown=3D"this.href=3D'jav=
ascript:';return true;" onclick=3D"this.href=3D'javascript:';return true;">=
gusni...@gmail.com</a>&gt;</span> wrote:<br>


<blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-=
left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;p=
adding-left:1ex"><div dir=3D"ltr"><div><div><br></div></div><div>(D1-1) is =
not the same. (D1-1) says only that there is a largest referent of what is =
{me ko'a}. </div>


</div></blockquote><div><br></div><div><br></div><div>Namely, ko'a themselv=
es, right?</div><div><br></div></div></div></div></blockquote><div><br></di=
v><div><br></div><div>Yes.&nbsp;</div><div><br></div><div><br></div><blockq=
uote class=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;border-lef=
t: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div><div class=3D"g=
mail_quote"><div></div><div>&nbsp;</div><blockquote class=3D"gmail_quote" s=
tyle=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rg=
b(204,204,204);border-left-style:solid;padding-left:1ex">


<div dir=3D"ltr"><div>It is a tautology, and says nothing particular. The d=
ifference from {ro'oi da su'o pa mei} is that the speaker fixes {ko'a} to b=
e {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.</div>


</div></blockquote><div><br></div><div>Exactly. And "ro'oi da su'o mei" is =
also a statement that says nothing, it can never be false. If "ro'oi da bro=
da" is true, then the one-place predicate "broda" is tautological, and conv=
ersely, if the one-place predicate broda is tautological then "ro'oi da bro=
da" is true. Your choice D1-1 to define the tautological one-place predicat=
e "su'o pa mei" is fine. Any other equivalent definition would </div></div>=
</div></div></blockquote><div><br></div><div><br></div><div>Because {su'o m=
ei} is neither a sequence of logical elements, nor expanded to a sequence o=
f logical elements, a sentence including {su'o mei} itself cannot be a logi=
cal 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 th=
e equivalent.&nbsp;</div><div><br></div><div>When {ro'oi da su'o mei} is ap=
plied to (D1) (D2) for N=3D1, we obtain {ro'oi da poi me ko'a ro'oi de poi =
me ko'a zo'u de me da}, which is a sequence of logical elements, which is e=
quivalent to the condition for ko'a being an individual, and which is not a=
 logical axiom or the equivalent.</div><div><br></div><div>It means that wh=
en we started with "ro'oi da su'o mei", it restricts the usage of {su'o mei=
} to an individual or individuals. It defines the meaning of {su'o mei}, an=
d (D1) (D2) (D3) are therefore valid.</div><div><br></div><div>What I tried=
 to do is to make (D1) (D2) (D3) valid with another meaning on {su'o mei}, =
without using {ro'oi da su'o mei}, so that an expression with {N mei} is av=
ailable to non-individual referent.</div><div><br></div><div><br></div><div=
>&nbsp;</div><blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-le=
ft: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr">=
<div><div class=3D"gmail_quote"><div>have the same effect, for example:</di=
v>


<div><br></div><div>(D1-2) ko'a su'o pa mei :=3D ko'a me ko'a</div><div><br=
></div><div>or my current favourite:</div><div><br></div><div>(D1-3) Ko'a s=
u'o pa mei :=3D su'oi da me ko'a</div><div>


<br></div><div>I like it because it can be easily generalized to "no mei", =
"ro mei" and "me'i mei":</div><div><br></div><div>(D4) ko'a no mei :=3D no'=
oi da me ko'a</div><div>(D5) ko'a ro mei :=3D ro'oi da me ko'a<br>


</div><div>(D6) ko'a me'i mei :=3D me'oi da me ko'a</div><div><br></div><di=
v>"no mei" is the contradictory predicate, nothing can satisfy it, but ther=
e may or may not be something that satisfies "ro mei".</div></div></div></d=
iv></blockquote><div><br></div><div><br></div><div>Any of them are fine. (D=
1-1) is only a "one-shot" definition of a particular ko'a in a particular u=
niverse of discourse defined by a speaker. It is not for general use. Actua=
lly we don't need the part {su'oi da poi me ko'a ku'o ro'oi de poi me ko'a =
zo'u de me da}. It says only that {ko'a} is a plural constant. I am happy w=
ith only</div><div><br></div><div>(D1-7) ko'a su'o pa mei</div><div><br></d=
iv><div>as a "one-shot" definition instead of (D1-1). It defines a meaning =
of {su'o pa mei} with a particular ko'a, and {su'o pa mei} is not necessari=
ly applied to other referents in the universe of discourse.</div><div><br><=
/div><div>The form (D1-1) was given because I intended to use&nbsp;</div><d=
iv>(D1-1b) ko'e su'o pa mei :=3D {su'oi da poi me ko'e ku'o ro'oi de poi me=
 ko'e zo'u de me da ije da me de}</div><div>with minimal modification to (D=
1-1). It is a very trivial reason, and we may discuss with (D1-7)&nbsp;inst=
ead of (D1-1).</div><div><br></div><div>(D1-1b) is also a "one-shot" defini=
tion by a speaker to be used on a particular ko'a that is an individual. It=
 is not for general use.</div><div><br></div><div><br></div><div>&nbsp;</di=
v><blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;b=
order-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div><div c=
lass=3D"gmail_quote">


<div>&nbsp;</div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px =
0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-l=
eft-style:solid;padding-left:1ex"><div dir=3D"ltr"><div>When another condit=
ion {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}, tho=
ugh): then the conditions are equivalent to {ro'oi da su'o pa mei}, which m=
akes {ko'a su'o pa mei}&nbsp;always true.</div>


</div></blockquote><div><br></div><div>I don't follow that. What do you mea=
n by adding a condition to D1-1?&nbsp;</div><div><br></div><div>If you chan=
ge D1-1 to</div><div><br></div><div>(D1-1b) ko'a su'o pa mei :=3D 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</div>


<div><br></div><div>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=
". &nbsp;</div>


<div>&nbsp;</div><div>And I don't see how that is equivalent to "ro'oi da s=
u'o pa mei". "ro'oi da su'o pa mei" entails "mi jo'u do su'o pa mei", for e=
xample.</div><div>
&nbsp;</div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0=
.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-s=
tyle:solid;padding-left:1ex">

<div dir=3D"ltr"><div></div><div>As long as talking about among theory, (D1=
-1)+{ije da me de} is not a logical axiom or equivalent, though it is neces=
sary for comforming to mereology with atoms.</div></div></blockquote><div>


<br></div><div>I have to disagree with that. &nbsp;(D1-1)+{ije da me de} ju=
st doesn't work as a useful definition of "su'o pa mei".</div><div><br></di=
v></div></div></div></blockquote><div><br></div><div><br></div><div>Even wi=
th (D1-1b), "mi jo'u do su'o pa mei" is true.</div><div><br></div><div>(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.&nbsp;</div><div>It =
gives a meaning to {su'o pa mei} with a particular ko'a.</div><div><br></di=
v><div>For example, suppose a speaker applies (D1-1b) to {mi}:</div><div>(D=
1-1b) mi su'o pa mei :=3D su'oi da poi me mi ku'o ro'oi de poi me mi zo'u d=
e me da ije da me de</div><div>Then {mi jo'u do} satisfies&nbsp;(D1) of N=
=3D2:</div><div>mi jo'u do su'o re mei</div><div><br></div><div>From (D1),&=
nbsp;</div><div>ganai ko'a su'o N mei gi ko'a su'o N-1 mei</div><div>is alw=
ays true.</div><div><br></div><div>(proof:</div><div>da'i</div><div>ge ko'a=
 su'o N mei gi naku ko'a su'o N-1 mei</div><div>iseni'ibo</div><div>ge su'o=
i 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</div><div>gi naku su'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'=
u ge da su'o N-2 mei gi de na me da</div><div>iseni'ibo</div><div>ge su'oi =
da poi me ko'a ku'o su'oi de poi me ko'a ku'o su'oi di_1 poi me da ku'o su'=
oi di_2 poi me da zo'u&nbsp;</div><div>ge ge di_1 su'o N-2 mei gi di_2 na m=
e di_1 gi de na me da</div><div>gi ro'oi da poi me ko'a ku'o ro'oi de poi m=
e ko'a zo'u naku ge da su'o N-2 mei gi de na me da</div><div><br></div><div=
>ita'o&nbsp;</div><div>di_1 me da ijebo da me ko'a inaja di_1 me ko'a (A pr=
operty of {me})</div><div>iseni'ibo</div><div>lo du'u&nbsp;</div><div>su'oi=
 da poi me ko'a ku'o su'oi de poi me ko'a ku'o su'oi di_1 poi me da zo'u ge=
 di_1 su'o N-2 mei gi de na me da</div><div>cu natfe</div><div>lo du'u&nbsp=
;</div><div>ro'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u naku ge da =
su'o N-2 mei gi de na me da</div><div><br></div><div>iseni'ibo&nbsp;</div><=
div>naku ge ko'a su'o N mei gi naku ko'a su'o N-1 mei</div><div>iseni'ibo</=
div><div>ganai ko'a su'o N mei gi ko'a su'o N-1 mei</div><div>uo</div><div>=
)</div><div><br></div><div>Therefore&nbsp;</div><div>mi jo'u do su'o pa mei=
</div><div>is also true.</div><div><br></div><div><br></div><div>&nbsp;</di=
v><blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;b=
order-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div><div c=
lass=3D"gmail_quote"><div></div><div>&nbsp;</div><blockquote class=3D"gmail=
_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left=
-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">


<div dir=3D"ltr"><div><blockquote class=3D"gmail_quote" style=3D"margin:0px=
 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);bor=
der-left-style:solid;padding-left:1ex"><div dir=3D"ltr"><div><div class=3D"=
gmail_quote">


<blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-=
left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;p=
adding-left:1ex"><div dir=3D"ltr"><div></div></div></blockquote><div>(D1-1)=
 ko'a su'o pa mei :=3D su'oi da poi me ko'a ku'o ro'oi de poi me ko'a zo'u =
de me da<br>


</div><div><span style=3D"color:rgb(80,0,80);font-family:arial,sans-serif;f=
ont-size:13px">(D1) ko'a su'o N mei :=3D 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</span></div>


<div style=3D"color:rgb(80,0,80);font-family:arial,sans-serif;font-size:13p=
x">(D2) ko'a N mei &nbsp;:=3D ko'a su'o N mei gi'e nai su'o N+1 mei&nbsp;<b=
r></div><div style=3D"color:rgb(80,0,80);font-family:arial,sans-serif;font-=
size:13px">


(D3) lo PA broda :=3D zo'e noi ke'a PA mei gi'e broda</div></div></div></di=
v></blockquote><div><br></div></div><div>Yes, and please note that (D1-1) i=
s not equivatent to {ro'oi da su'o pa mei}.&nbsp;</div></div>


</blockquote><div><br></div><div>(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 tautologi=
cal predicate. It doesn't require that the specific tautological form D1-1 =
be chosen to define it, of course, any other tautological one-place predica=
te will do just as well.</div></div></div></div></blockquote><div><br></div=
><div><br></div><div>(D1-1) or (D1-7) requires that any referent _can be_ {=
su'o pa mei}, but a speaker does not necessarily select all the referents t=
o be {su'o pa mei}. The speaker gives meaning to {su'o pa mei}. If the spea=
ker finally does not select all the referents to be {su'o pa mei}, the give=
n meaning is different from what is given by {ro'oi da su'o pa mei}.</div><=
div><br></div><div><br></div><div>&nbsp;</div><blockquote class=3D"gmail_qu=
ote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padd=
ing-left: 1ex;"><div dir=3D"ltr"><div><div class=3D"gmail_quote">


<div>&nbsp;</div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px =
0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-l=
eft-style:solid;padding-left:1ex"><div dir=3D"ltr"><div><blockquote class=
=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;bo=
rder-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">


<div dir=3D"ltr"><div><div class=3D"gmail_quote"><div>Do you agree that wit=
h just those definitions:</div><div><br></div><div>ko'a pa mei</div><div>=
=3D ko'a su'o pa mei gi'e nai su'o re mei</div>
<div>=3D na ku ko'a su'o re mei</div><div>=3D 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</div><div>=3D ro'o=
i da poi me ko'a ro'oi de poi me ko'a na ku zo'u na ku &nbsp;de me da</div>


<div>=3D ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da</div></div=
></div></div></blockquote><div><br></div></div><div>The result requires {ro=
'oi da su'o pa mei}. </div></div>

</blockquote><div><br></div><div>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.&nbsp;</div></div></div></div></blockquote><div=
><br></div><div><br></div><div>I meant the following part:</div><div>=3D 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</div><div>=3D ro'oi da poi me ko'a ro'oi de poi me ko'a na ku zo'u=
 na ku &nbsp;de me da</div><div><br></div><div>This derivation requires {ro=
'oi da su'o pa mei}.&nbsp;</div><div><br></div><div>When the meaning of {su=
'o pa mei} is given by (D1-1) or (D1-7),</div><div>ko'a su'o pa mei</div><d=
iv>is true because it is defined, but {su'o pa mei} is not defined to other=
 referents.</div><div>If ko'a is non-individual, that is to say, if a speak=
er regards {ro'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u de me da ij=
enai da me de} is true, {ro'oi da su'o pa mei} is false.</div><div><br></di=
v><div><br></div><div>&nbsp;</div><blockquote class=3D"gmail_quote" style=
=3D"margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: =
1ex;"><div dir=3D"ltr"><div><div class=3D"gmail_quote"><div>&nbsp;</div><bl=
ockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-lef=
t-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padd=
ing-left:1ex">


<div dir=3D"ltr"><div>As I discussed above, (D1-1) is a kind of dummy to sa=
y {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 t=
he same result.</div>


</div></blockquote><div><br></div><div>How does giving a value to "ko'a" ma=
ke "ro'oi da su'o pa mei" not true? &nbsp;"ro'oi da su'o pa mei" is indepen=
dent of what values are assigned to "ko'a". It doesn't even mention ko'a.</=
div>


<div>&nbsp;</div></div></div></div></blockquote><div><br></div><div><br></d=
iv><div>When (D1-1) or (D1-7) is used, the speaker arbitrarily defines "ko'=
a su'o pa mei" to a particular ko'a.&nbsp;</div><div>When (D1-1b) is used, =
the selection of ko'a is restricted to an individual.</div><div><br></div><=
div>For example, suppose that a speaker regards {lo nanba} is non-individua=
l:</div><div>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</div><div><br></div><div>That is, the speaker regard=
s a half of {lo nanba} is also {me lo nanba}.&nbsp;</div><div>Even though t=
here is no individual {lo nanba}, an expression {N mei} is available with (=
D1-7) (D1) (D2) (D3).</div><div>The speaker arbitrarily fix a referent to b=
e {lo pa nanba}. If another {lo nanba xi re} is given, {lo pa nanba jo'u lo=
 nanba xi re} is {lo re nanba}.</div><div><br></div><div><br></div><div>&nb=
sp;</div><blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-left: =
0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div=
><div class=3D"gmail_quote"><div><br></div><blockquote class=3D"gmail_quote=
" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color=
:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div dir=3D"ltr=
"><div>With a dummy defintion (D1-1), "PA mei" is not meaningless even for =
non-individual.</div>


<div>Set {B su'o pa mei} according to (D1-1). Suppose {C na me B}. From a p=
roperty 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).</div></div></blockquote>


<div><br></div><div>For someone who holds the following as an axiom (the an=
ti-atomist):</div><div><br></div><div>(AA) no'oi da ro'oi de poi me da zo'u=
 da me de&nbsp;</div><div><br></div><div>it can be shown that, for every na=
tural N, "ro'oi da su'o N mei" and "no'oi da N mei", which is to say that f=
or the anti-atomist all the numeric predicates are trivial (either tautolog=
ies or contradictions).</div>
<div><br></div></div></div></div></blockquote><div><br></div><div><br></div=
><div>When (AA) is true, "ro'oi da su'o N mei" is false, because it with (D=
1) (D2) on N=3D1 results in "ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u=
 de me da", and contradicts (AA).</div><div><br></div><div>As for "no'oi da=
 N mei", (AA) says nothing. If the speaker select a particular ko'a as {ko'=
a su'o pa mei}, "no'oi da N mei" is false; otherwise no meaning is given to=
 {N mei}.</div><div><br></div><div><br></div><div>&nbsp;</div><blockquote c=
lass=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1px=
 #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div><div class=3D"gmail_q=
uote"><div></div><div>For someone who holds the opposite position (the atom=
ist):</div><div><br></div><div>(A) su'oi da ro'oi de poi me da zo'u da me d=
e&nbsp;<br></div><div><br></div><div>then the numeric predicates are non-tr=
ivial: 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).</div>
<div><br></div><div>Perhaps by "non-individual" you mean someone who holds =
neither (A) nor (AA) as axioms, someone who doesn't know or doesn't care wh=
ich one of (A) or (AA) is true. The that person (the atom-agnostic), the nu=
meric predicates are also non-trivial, but if they ever assert that somethi=
ng 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" wit=
hout commiting to either (A) or (AA). Is that what you mean?</div></div></d=
iv></div></blockquote><div><br></div><div><br></div><div>That is not what I=
 meant.&nbsp;</div><div>I discussed only a particular ko'a, not all the ref=
erents in a universe of discourse.</div><div>However, even (AA) holds with =
(D1-1) or (D1-7) (D1) (D2) (D3).</div><div><br></div><div><br></div><div>&n=
bsp;</div><blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-left:=
 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><di=
v><div class=3D"gmail_quote">
<div><br></div><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0p=
x 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-lef=
t-style:solid;padding-left:1ex"><div dir=3D"ltr"><div>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.&nbsp;</div>
</div></blockquote><div><br></div><div>I think you are mistaken that you ca=
n add "ije da me de" to D1-1 in order to satisfy the atomist, Adding that b=
reaks the definition of "su'o pa mei" for everyone.</div>
<div><br></div></div></div></div></blockquote><div><br></div><div><br></div=
><div>It does not break (D1) (D2) (D2) because (D1-1b) is only a "one-shot"=
 definition for a particular ko'a that is an individual. {su'o pa mei} is n=
ot defined to other sumti.</div><div><br></div><div><br></div><div>&nbsp;</=
div><blockquote class=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex=
;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir=3D"ltr"><div><div=
 class=3D"gmail_quote"><div></div><div>"ko'a su'o mei" is always true for a=
ll three, for the atomist, the anti-atomist, and the atom-agnostic.</div><d=
iv><br></div><div>"ko'a pa mei" can be true or false for the atomist, depen=
ding on what "ko'a" refers to, it must be false for the anti-atomist, no ma=
tter what "ko'a"refers to, and can be false, but not true, for the atom-agn=
ostic (If it's true for them, then they've become atomists, if it's false, =
they can remain as atom-agnostics.)&nbsp;</div>
<div><br></div></div></div></div></blockquote><div><br></div><div><br></div=
><div>It is meaningless to compare "ko'a su'o mei" for all three, because t=
he meaning of {su'o mei} is different between them. Atomist gives meaning t=
o {su'o pa mei} with your starting point {ro'oi da su'o pa mei}, or with (D=
1-1b). Anti-atomist does with (D1-1) or (D1-7).</div><div><br></div><div><b=
r></div><div>&nbsp;</div><blockquote class=3D"gmail_quote" style=3D"margin:=
 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div =
dir=3D"ltr"><div><div class=3D"gmail_quote"><div></div><blockquote class=3D=
"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;borde=
r-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><di=
v dir=3D"ltr"><div>Starting with {ro'oi da su'o pa mei} is useful, but excl=
udes non-individual from expressions {lo PA broda}. (D1-1) makes (D1) (D2) =
(D3) available also to non-individual.</div>
</div></blockquote>

<div><br></div><div>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 brod=
a" is useless for the anti-atomist. It cannot refer to anything for them, b=
ecause starting from (AA) it can be shown that "... noi ke'a broda gi'e N m=
ei" will be always false.</div></div></div></div></blockquote><div><br></di=
v><div>&nbsp;</div><div><br></div><div>As I discussed above, When (AA) hold=
s, "ro'oi da su'o N mei" is false, and an expression {N mei} is still avail=
able with (D1-1) or (D1-7) (D1) (D2) (D3).</div><div><br></div><div><br></d=
iv><div><br></div></div>

<p></p>

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