Le samedi 22 février 2014 07:16:34 UTC+9, xorxes a écrit :
On Fri, Feb 21, 2014 at 3:46 AM, guskant
<gusni...@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?
Yes.
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
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.
When {ro'oi da su'o mei} is applied to (D1) (D2) for N=1, 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 equivalent to the condition for ko'a being an 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 usage of {su'o mei} to an individual or individuals. It defines the meaning 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 {su'o mei}, without using {ro'oi da su'o mei}, so that an _expression_ with {N mei} is available to non-individual referent.
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".
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. Actually 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 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 pa mei} with a particular ko'a, and {su'o pa mei} is not necessarily applied to other referents in the universe of discourse.
The form (D1-1) was given because I intended to use
(D1-1b) ko'e su'o pa mei := {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}
with minimal modification to (D1-1). It is a very trivial reason, and we 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 particular ko'a that is an individual. It is not for general use.
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".
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:
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 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 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 ku'o su'oi di_2 poi me da zo'u
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 mei gi de na me da
ita'o
di_1 me da ijebo da me ko'a inaja di_1 me ko'a (A property of {me})
iseni'ibo
lo du'u
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
cu natfe
lo du'u
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
iseni'ibo
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
mi jo'u do su'o pa mei
is also true.
(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.
(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 to be {su'o pa mei}. The speaker gives meaning to {su'o pa mei}. If the speaker finally does not select all the referents to be {su'o pa mei}, the given meaning is different from what is given by {ro'oi da su'o pa mei}.
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.
I meant the following part:
= 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
This derivation requires {ro'oi da su'o pa mei}.
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 referents.
If ko'a is non-individual, that is to say, if a speaker regards {ro'oi da poi me ko'a ku'o su'oi de poi me ko'a zo'u de me da ijenai da me de} is true, {ro'oi da su'o pa mei} is false.
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.
When (D1-1) or (D1-7) is used, the speaker arbitrarily defines "ko'a su'o pa mei" to a particular ko'a.
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 da me de
That is, the speaker regards a half of {lo nanba} is also {me lo nanba}.
Even though there is no individual {lo nanba}, an _expression_ {N mei} is available with (D1-7) (D1) (D2) (D3).
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}.
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).
When (AA) is true, "ro'oi da su'o N mei" is false, because it with (D1) (D2) on N=1 results in "ro'oi da poi me ko'a ro'oi de poi me ko'a zo'u de me da", and contradicts (AA).
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}.
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?
That is not what I meant.
I discussed only a particular ko'a, not all the referents in a universe of discourse.
However, even (AA) holds with (D1-1) or (D1-7) (D1) (D2) (D3).
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.
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 not defined to other sumti.
"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.)
It is meaningless to compare "ko'a su'o mei" for all three, because the meaning of {su'o mei} is different between them. Atomist gives meaning to {su'o pa mei} with your starting point {ro'oi da su'o pa mei}, or with (D1-1b). Anti-atomist does with (D1-1) or (D1-7).
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.
As I discussed above, When (AA) holds, "ro'oi da su'o N mei" is false, and an _expression_ {N mei} is still available with (D1-1) or (D1-7) (D1) (D2) (D3).