Le samedi 8 février 2014 09:28:10 UTC+9, xorxes a écrit :
On Fri, Feb 7, 2014 at 9:03 PM, guskant
<gusni...@gmail.com> wrote:
My problem is, for example, how {lo no broda} can be meaningful if {lo broda} implies {su'o da poi ke'a broda}.
To solve this problem, I need axioms for "plural constant".
"lo no broda" is not very meaningful, except perhaps as a joke or if you want to be whimsical or paradoxical.
As long as PA of {lo PA broda} is defined as zilkancu_2, {lo no broda} should be meaningful.
From that definition, I guess that PA should be a member of a countable set, a rational number.
There is no other information about this PA, then it is natural that {lo no broda} is meaningful.
Also from a practical point of view, it is better to give {lo no broda} some reasonable meaning:
- lo xo prenu cu jmaji gi'e jukpa gi'e citka
- no
Such a conversation is quite natural, and cannot be replaced by an outer quantifier in a simple way because it involves collectivity and distributivity. It should not be excluded from the language.
BTW, "lo broda cu brode" does not imply "su'o da poi broda cu brode", as you already pointed out, but it does imply "su'oi da poi broda cu brode". In other words "students are surrounding the building" does not necessarily imply that at least one student is surrounding the building, but it does imply that some student or students are surrounding the building.
Yes, such a description is indeed what I need on the page of gadri.
I guess finally one axiom related to plural constant C of Lojban:
- F(C) {inaja} there is X such that F(X),
where X is plural variable.
I became now aware of the reason why I was not aware of the fact that the constant of Lojban is not of classical predicate logic, nor of Thomas McKay, but plural constant.
I tried to understand the page of gadri based on plural logic, mainly of Thomas McKay.
I believe this principle was relevant, but undefined technical terms used in the gadri page are very misleading.
I supposed first that the term "individual" should be defined as follows:
"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
where RO DA is quantified plural variable.
This supposition was not bad.
However, I saw on the gadri page "An individual can be anything, including a group,..." Now I began to be misled.
I thought: "An individual can be a group, then it contradicts my first supposition."
(Now I know "a group" meant {lo gunma}, not "something in a domain of plural variable"; but I was not aware of it at that time.)
I abandoned my supposition, and supposed that the "individual" must be something another.
Then I saw "Any term without an explicit outer quantifier is a constant, i.e. not a quantified term. This means that it refers to one or more individuals..."
I have already abandoned my first correct supposition, and believed that this sentence meant a constant refers to one or more "something other than individual of plural logic". I did not conclude that it meant "plural constant", because Thomas McKay did not adopt it. I thought of the possibility of "plural constant", but I did not guess how a plural constant would be treated in logical axioms of Lojban, and finally abandoned the interpretation that it meant "plural constant".
To avoid such misleading, I now suggest adding the following information on the gadri page:
- definition of "individual", that is,
"SUMTI is individual" =ca'e {RO DA poi ke'a me SUMTI zo'u SUMTI me DA}
where RO DA is quantified plural variable. {ro'oi da} instead of {RO DA} may be better if you give a definition for it.
- "constant" of Lojban is not necessarily a singular constant, but a plural constant.
- logical axioms for plural constant.
Moreover, calling something in a domain of plural variable "one or more individuals" is misleading for me.
The term for "something in a domain of plural variable" should be first given; after that "individual" is defined using it. The concept "individual" is only a special case of "something in a domain of plural variable" as defined above. This is not my particular way of thinking, but general way of plural logic.
Something that is broda is not always "one or more individuals" defined above: when a universe of discourse is given, there is no need that {lo broda} in the universe of discourse is finally separated into individual pieces that are members of the universe of discourse. An _expression_ reasonable for me would be: say "{lo broda} is something that is {broda}" first, give a definition for "individual", and then "{lo broda} can be one or more individuals".
By the way, based on the fact that {lo broda} is plural constant, another problem occurs.
{lo broda} is defined as {zo'e}, and {zo'e} is defined as unspecific value.
When {lo broda} is a plural constant, it is a specific value, and contradicts the definition of {zo'e}.
My understanding is that {zo'e} is essentially a free variable, and a plural constant is implicitly substituted when a universe of discourse is given. If it is correct, such a description should be included on the gadri or zo'e page. If it is incorrect, some reasonable explanation is necessary.