Le dimanche 9 février 2014 22:12:31 UTC+9, xorxes a écrit :
On Sun, Feb 9, 2014 at 8:05 AM, guskant
<gusni...@gmail.com> wrote:
Why don't you define
{lo no broda} =ca'e {zi'o noi ke'a broda}
only for the case that PA=no?
Under the condition that there is no official plural quantifier in Lojban, the inclusion of {lo no broda} is necessary for keeping the expressiveness of Lojban equal to that of plural quantification.
If "zi'o" did what you wanted, then official Lojban would already have that expressiveness, wouldn't it?
But "zi'o" doesn't work for what you want. "zi'o sruri lo dinju" is true when some students are surrounding the building. "zi'o" doesn't say that nothing satisfies the predicate. "zi'o" changes the predicate to a new predicate that doesn't have that place. It's hard to describe what exactly the new predicate resulting from "zi'o poi tadni cu sruri" means, but it does not mean "x2 is not surrounded by students".
I see. However, under the conditions that:
- {lo broda} is defined as a plural constant, and
- a logical axiom for a plural constant C is given as
F(C) {inaja} there is X such that F(X),
{lo no broda} is now excluded from the language.
In order to take it back and to give a reasonable meaning for it, we need an additional definition applied only to {lo no broda}.
How do you think the following suggestion?
{lo no broda} =ca'e {naku lo broda}
only for the case that PA=no.
{naku lo broda} should be actually {naku lo su'oi broda} with a plural quantifier {su'oi} that you once proposed, but it is not necessary to mention it in the definition if the innner quantifiers are in general an implicit _expression_ of plural quantifiers.
I would call {lo broda} "Something that is/are broda": I think it's enough for the most general value that is "something in a domain of plural variable", and no other description on the sumti is sufficient to describe the most general plural constant.
Using technical terms without definition is source of misleading.
One problem with using "something" is that it looks very much like a quantifier. Another problem for me (perhaps not so much for others) is that being a singular word, it seems to be talking about one thing. You sort of get around that a bit with the plural verb, "something that are broda", but that is ungrammatical English. You say "the most general value", but the whole point of plural logic is that a variable takes _values_, not _a value_.
Those problems are caused by the English language, and then I would better abandon using "something".
I would suggest instead:
{lo broda} =ca'e "what is/are broda"
With this definition, it seems that the problems you remarked on will be avoided.
Based on this simple definition, we can define "individual", "sumti that satisfies a selbri collectively" and "a set", then the readers will understand the whole aspect of gadri.
If by "a set" you mean, for example, "lo selcmi", then it is an individual as well. Everything is an individual in this context, there is nothing that is not an individual.
Of course a set is an individual. Once the terms "individual" and "set" are defined, it will be easy to explain that {lo selcmi} is one or more individuals:
{lo selcmi} is a set or sets.
a set is an individual: when {lo selcmi} refers to one set,
RO DA poi ke'a me lo selcmi zo'u lo selcmi me DA
If definition of terms are not given, "a set is an individual" cannot be explained.
I'm not sure if it is permitted to edit the BPFK page of green line, but if you don't mind, I will try to modify the description of gadri page so that everyone will understand gadri correctly.
The page doesn't appear to be locked, but I don't think it's a good idea to edit it. It's better if you create a new page with your take on things.
OK, I will not touch the gadri page.