In this article I will take a closer look at the quantifier logic
currently present in (post-xorlo) Lojban. I will identify logical
problems as well as practical disadvantages. Finally, I will offer a
solution that addresses both.
Not only is the current system both impractical and unintuitive, its
introduction also left behind one major logical flaw as Lojban made the
move from singular logic to plural logic.
Read on to find out what singular logic and plural logic are, how they
are related to xorlo, and why the current situation is not tenable.
https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/
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https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/
On 7 Oct 2016 13:09, "selpahi" <sel...@gmx.de> wrote:
> https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/
For me, this is Lojban's most valuable contribution to the world: the discovery of the practical necessity of plural logic. (It was xorxes's discovery, but wouldn't have happened without Lojban.)
I think a clearer example of the need for ru'o is "weighs 20 kg" -- ro'oi rock weighs 20kg must be false if there's more than one rock; ro'oi pa rock weighs 20kg gets the distrib reading; so ru'o rock weigh 20kg is needed for the collective or not-necessarily-distributive.
I do have one question, regarding the following:
"One last note about predicates not being defined clearly as distributive/non-distributive in xorlo; xorxes wanted lo to be absolutely non-committal with regards to distributivity, therefore, in his model, all predicates are left vague with regards to distributivity. In my proposed full plural logic, predicates are defined as distributive or non-distributive, so it is usually unnecessary to force distributivity via explicit universal quantification."
I take it that this is not held to be a necessary feature of full plural logic, but rather is held to be desirable so as to not have to force distributivity via quantification. And I take it also that by "predicates" you mean "argument places"? Each argument place is either distributive or collective? Would you not also want an "unspecified as regards distributivity"? And wouldn't this mean that where the xorxesian underspecification of distributivity would have one predicate with, say, three argument places, yours would have 2^3 or 3^3 predicates? This looks so untenable that I conclude I must be misunderstanding you.
--And.
On 9 Oct 2016 16:22, "selpahi" <sel...@gmx.de> wrote:
> (Getting rid of {so'e} entirely is possible, but I'm too lazy to type it out. The proportion is >0.5)
"Most" works for proportions of groups of infinite cardinality, but does ">0.5"? Better is ">0.5 of any typical group of". I remember that we discussed this 15--20 years ago, but do not remember any outcome.
--And.
What I really want is for the existential quantifier to become distinct from the "at least n" operator. In my preferred version of cekitauj (the cmavo swap dialects) the existential quantifier is spelled {su} and the "at least" operator is spelled {su'o}. This split is not possible in official Lojban, unfortunately, but it would keep the symmetry intact.
Would "no" become "no'oi" as well?
Yes, I believe it must and should.
{so'e jbopre cu banka'e lo .inglico} ("Most Lojbanists speak English") cannot be expanded like a normal numerically quantified statement:
? su'oi da poi jbopre gi'e so'e mei cu banka'e lo .inglico
"Some xx that are Lojbanists and most in number speak English." [1]
Quantifiers like {so'e}, {so'a}, ..., so-called proportional quantifiers, require there to be something they are proportional to. The number of broda in e.g. {so'e broda cu brode} is compared to the number of (all) broda that brode. "Out of all the Lojbanists, most of them speak English."
So I would say that
ru'o da poi jbopre zo'u so'e de poi menre da cu banka'e lo .inglico
"All [the] Lojbanists taken together are such that most of them speak English."
is a better (intermediate) expansion. (Getting rid of {so'e} entirely is possible, but I'm too lazy to type it out. The proportion is >0.5)
But {me'i} and {za'u} can be considered prefixes. I had thought {me'i PA da} would mean {su'oi da poi me'i PA mei}. A definition in terms of {ru'o} would also be possible, but I'm not sure that it would be better. It would mean allowing prefixes (like "<" and ">") to turn non-{ru'o} numerical quantifiers into {ru'o}-type quantifiers, and this requires a good justification.
On 08.10.2016 02:23, And Rosta wrote:
Each argument place is either
distributive or collective? Would you not also want an "unspecified as
regards distributivity"? And wouldn't this mean that where the xorxesian
underspecification of distributivity would have one predicate with, say,
three argument places, yours would have 2^3 or 3^3 predicates? This
looks so untenable that I conclude I must be misunderstanding you.
This would indeed be untenable, but I do not believe that you need every version of every predicate. For example, I believe that a distributive {citka} is enough. Very often, a non-distributive version is either not distinct from the distributive version, or includes some added meaning of "doing it together while possibly some of them only watch" (things like {kansi'u lo ka citka}). There is a lot more to be said here, but I'd rather first hear any additional points from you.
Unspecified distributivity in an argument place is a form of ambiguity at the definitional level of a predicate.
It makes it very difficult to ever answer "what does it mean to {broda}", because there are by definition multiple potentially non-overlapping answers.
(I cannot possibly count the hours that went into discussing {bevri lo pipno} over the years without ever getting to a conclusion. This sort of stuff is hard to sort out!)
There are other ways (for example, in the realm of pragmatics) to deal with vague distributivity, outside of the definition of argument places, and I prefer those ways.
On 9 Oct 2016 16:49, "selpahi" <sel...@gmx.de> wrote:
>
> On 08.10.2016 02:23, And Rosta wrote:
>>
>> Each argument place is either
>> distributive or collective? Would you not also want an "unspecified as
>> regards distributivity"? And wouldn't this mean that where the xorxesian
>> underspecification of distributivity would have one predicate with, say,
>> three argument places, yours would have 2^3 or 3^3 predicates? This
>> looks so untenable that I conclude I must be misunderstanding you.
>
>
> This would indeed be untenable, but I do not believe that you need every version of every predicate. For example, I believe that a distributive {citka} is enough. Very often, a non-distributive version is either not distinct from the distributive version, or includes some added meaning of "doing it together while possibly some of them only watch" (things like {kansi'u lo ka citka}). There is a lot more to be said here, but I'd rather first hear any additional points from you.
My view is the same as xorxes's (thanks to my long ago having been persuaded by his insights on this point, as on so many others). "The guests have eaten all the sausages" is not (fully) distributive and judgements of whether a given predicate, such as "eat all the sausages", can be fully collective, or fully distributive, or intermediate, are more a matter of pragmatics than of formal semasiology.
So I think the better way to handle this linguistically is to have ways to explicitly encode full collectivity ("plurality X but not necessarily any subplurality of X" = ru'o) and full distributivity ("every single X but not necessarily any plurality of them" = ro('oi) pa), without fretting about their truth-conditions with any given predicate.
--And.
On 10.10.2016 02:08, Jorge Llambías wrote:
Would "no" become "no'oi" as well?
Yes, I believe it must and should.
And singular "no" is then "no pa", right?
Yes, I would say so.
I think the expansion should be:
PA broda cu brode -> su'oi da poi PA mei lo broda cu brode
which I think would work for all the numeric quantifiers:
[da'a][su'o|su'e|me'i|za'u|ji'i] n; so'V; du'e, mo'a, rau; and also for
ru'o.
This seems to be pretty much the same as the {ru'o} expansion.
But I think it's only equivalent if you subscribe to {lo}'s maximality. (It wouldn't be the first expansion that presupposes maximality even though we never decided that {lo} must have maximality)
So, I take it, you do subscribe to maximality? (I do)
But {me'i} and {za'u} can be considered prefixes. I had thought
{me'i PA da} would mean {su'oi da poi me'i PA mei}. A definition in
terms of {ru'o} would also be possible, but I'm not sure that it
would be better. It would mean allowing prefixes (like "<" and ">")
to turn non-{ru'o} numerical quantifiers into {ru'o}-type
quantifiers, and this requires a good justification.
What do you mean by non-ru'o numerical quantifiers? su'oi, ro'oi, no'oi,
me'oi are non-ru'o, in the sense that they don't expand to a "su'oi da
poi PA mei" form. (I don't even know what "PA mei" would mean for them.)
Sorry if I wasn't clear. I meant "non-{ru'o}" in a {noi} way. All numerical quantifiers are of the non-{ru'o} type. Your prefixes turn them into {ru'o} types.
On 10.10.2016 02:36, Jorge Llambías wrote:
I don't believe a distributive "citka" is all that useful. I want to be
able to say "the children ate the whole cake" without having to
introduce any roundabouts.
Of course. But I believe that a distributive {citka} does not prohibit this.
Let us look at some of the many possible meanings of a simple quantified statement in English, say, "At least three people carried a chair":
1) At least three people are such that each of them carried a chair.
2) At least three people are such that each of them was involved in carrying a chair.
3) Some people that are at least three moved a piano together.
Would you say that all of these describe the same relationship or different relationships?
Or your "eating cake" example, would you say that each different reading is a different meaning of "eat"?
I mentioned above that there are other means by which intermediate distributivity can be achieved, and by which "the children ate the cake" is acceptable even with a distributive "eat".
One such approach is one that we use in other areas of Lojban (or any language) as well, and that is the idea of pragmatic slack. In certain contexts and situations, sentences that are false when taken literally can still be considered true at the level of detail that is currently relevant. We don't care if really every single one of the things ate cake, because it isn't relevant to our specific situation.
Similarly, we don't mind if someone says "I woke up at nine" when really they woke up a few minutes after nine. Nevertheless, the meaning of "wake up at nine" is not changed, nor is the meaning of "ate cake" changed.
(Lasersohn (1999) discusses this in great detail)
And additionally, when it is important, words like {kansi'u} exist (and I have proposed that a bunch of similar words could exist that express related forms of "doing something together", depending on the nature of the togetherness (e.g. just being in the same place as some of them eat, helping each other so that some of them eat, and so on). These are not necessarily roundabout, and you would only use them when you think it matters.
So all in all, you may say it doesn't matter which approach we use as long as you
> can say "the children took the chairs to the garden" when you don't know or don't care about how the action was distributed among children and chairs.
But it makes a difference to me, because in one case we throw our hands in the air about the meaning of a predicate, and in the other case we can decide what it means on a fundamental level.
For some places it's
reasonable that it be part of the definition of the predicate ("pavmei"
might be an example).
{pavmei} cannot be distributive. It is only true of things that are one in number. {[su'oi] re da pavmei} is false. If you meant its distributivity type must be non-distributive, then yes.
There are many predicates that only make sense non-distributively.
There are also many predicates that are fundamentally distributive, and where making them non-distributive only adds vagueness.
But it makes me wonder. Is it really such a crazy idea for Lojban to have different words for rather different kinds of carrying even though English only has one? Let's not forget that Lojban is also a way to experience new ways of thinking about situations. We split English words into multiple distinct brivla all the time, why shouldn't we here? It would be interesting.
On Monday, October 10, 2016 5:03:16 PM EDT Jorge Llambías wrote:
> On Mon, Oct 10, 2016 at 3:45 PM, selpahi <sel...@gmx.de> wrote:
> > On 10.10.2016 02:08, Jorge Llambías wrote:
> >> And singular "no" is then "no pa", right?
> >
> > Yes, I would say so.
>
> I don't know if it's a good idea to use the same word for the digit "0" and
> the (plural) quantifier "~E".
>
> It could be confusing that "no pa no" is "no ten" rather than "010".
"no pa" is equal to "pa". Do you mean "no boi pa"?