Le vendredi 21 février 2014 10:51:11 UTC+9, xorxes a écrit :
On Thu, Feb 20, 2014 at 10:01 PM, guskant
<gusni...@gmail.com> wrote:
Le vendredi 21 février 2014 06:43:48 UTC+9, xorxes a écrit :
On Thu, Feb 20, 2014 at 1:50 AM, guskant
<gusni...@gmail.com> wrote:
For precise definitions on {PA mei}, we need therefore an explicit definition of {ko'a su'o pa mei} besides (D1).
That's why I started by saying "ro'oi da su'o pa mei", which is to say that "su'o pa mei" is a tautological predicate, always true of anything
Yes, and in order to say "ro'oi da su'o pa mei", an axiom that is not an logical axiom should be given. That's why an explicit definition for {ko'a su'o pa mei} is necessary especially for the case that ko'a is an individual.
No, I'm defining "su'o pa mei" as the tautological predicate, a predicate true of anything. I'm doing exactly the same thing you do with D1-1
(D1-1) is not the same. (D1-1) says only that there is a largest referent of what is {me ko'a}. 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.
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.
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.
You are right under the condition that "ro'oi da su'o pa mei" is true. However, it is a non-logical axiom or the equivalent. I discussed that (D1) (D2) (D3) without any non-logical axioms are meaningful even in the case that ko'a is non-individual in the point that they give an order of cardinality.
Definitions D1 are not a valid set of definitions without a starting point. "su'o re mei" is undefined if "su'o pa mei" is not defined first, and then "su'o ci mei" is also undefined, and so on.
That is the reason why I added (D1-1), a dummy definition for {ko'a su'o pa mei}, so that (D1) is meaningful without {ro'oi da su'o pa mei}.
I mean "pa mei" by "one-some". As I mentioned above, In order to say {pa mei} is an individual, a non-logical part {ije da me de} is necessary to be added to (D1-1). This addition is equivalent to a non-logical axiom "ro'oi da su'o pa mei", but explicitly mentions the condition for ko'a being an individual. Because (D1) (D2) (D3) give only an order of cardinality, they alone can be used both cases of individuals and non-individual. Starting with a non-logical axiom "ro'oi da su'o pa mei" is available only to the case that ko'a is an individual or individuals, but (D1) (D2) (D3) themselves are more generally available without non-logical axioms.
I'm sorry, I don't follow you now. Are these the definitions we are discussing:
(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}.
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}. 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.
which is pretty much what an individual is. If there are no individuals in the world, "ko'a pa mei" is false, because whatever ko'a refers to, it won't satisfy that anything Y among it will be among anything X among it. Only individuals satisfy that. I'm not sure what you say has to be added. In a world without individuals, "pa mei" is false of everything (and so are all of the "N mei" with finite N) , and in such a world not just "su'o pa mei", but every "su'o N mei" are tautologies. In such a world all these numeric predicates are pretty useless. That's why by using any of these predicates we invoke a world with individuals. That doesn't mean we can't have a universe of discourse without individuals, it just means that in such a universe of discourse we won't be using the numeric predicates, because they all reduce to tautologies and contradictions.
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).
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.
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.