#ckule explanation about the uses of Lojban numbers

#ckule, 2018-02-10

[5:43 PM] la zeitypalydji.: well ok what about numbers
[5:43 PM] la zeitypalydji.: It was mentioned that "lo ci prenu" doesn't work at all, because it suggests there are only three dogs ever
[5:44 PM] Ilmen: Nah
[5:44 PM] Ilmen: lo ci prenu = the three persons
[5:44 PM] la zeitypalydji.: sorry
[5:44 PM] Ilmen: Those are all the three persons in our domain of discourse, but not necessarily in the whole universe
[5:44 PM] la zeitypalydji.: yeah I copied and pasted wrong got confused
[5:45 PM] la zeitypalydji.: Oh odd
[5:45 PM] Ilmen: For example, in English you can say "the key is on the table"
[5:45 PM] la zeitypalydji.: Yeah I understand the domain of discource
[5:45 PM] Ilmen: and that doesn't imply there's only one key and only one table in the world
[5:45 PM] la zeitypalydji.: I was the co-editor of Cantor's Attic for a while after all
[5:46 PM] la zeitypalydji.: A place of advanced mathematical logic
[5:47 PM] BOTkahai: simpson: I've seen that site. It's a cool site.
[5:47 PM] Ilmen: the key is on the table = lo pa ckiku cu cpana lo pa jubme
[5:47 PM] Ilmen: "the one key lies on the one table"
[5:47 PM] la zeitypalydji.: well if you look far back enough in the edits of that site you'll see that only two people were editing it, me and Julian
[5:48 PM] Ilmen: "pa/one" is added because by default the number (cardinality) is left to context
[5:49 PM] la zeitypalydji.: what is the exact logic of the numbers
[5:50 PM] Ilmen: numbers can appear in several distinct positions, each with different roles
[5:50 PM] Ilmen: let N be any number
[5:51 PM] Ilmen: li N (lo'o) = the number N  (to talk about an abstract number)
[5:51 PM] Ilmen: N can be followed by "mei" or "moi" to talk about cardinality or position in a sequence (N-th…)
[5:51 PM] Ilmen: ci moi = third
[5:52 PM] Ilmen: in [ N + SUMTI ], the number N is an "outer quantifier"
[5:52 PM] la zeitypalydji.: ok that's what I wanted
[5:52 PM] la zeitypalydji.: n + sumti
[5:52 PM] la zeitypalydji.: carry on
[5:52 PM] Ilmen: in [ lo N SELBRI ],  N is an "inner quantifier"
[5:53 PM] Ilmen: those are the main usages of numbers
[5:53 PM] Ilmen: An inner quantifier, as in "lo ci prenu", simply indicates the cardinality of the sumti, how many referents it has
[5:53 PM] Ilmen: "the three persons/people"
[5:53 PM] Ilmen: = the persons, who are 3 in number
[5:54 PM] la zeitypalydji.: ah ok
[5:54 PM] Ilmen: [N + sumti ] is a more complex beast
[5:55 PM] BOTkahai: simpson: Outer quantifiers perform a kind of selection. {ci mi} "three of us" {ci lo baknu} "three of the cows"
[5:55 PM] Ilmen: this is an "outer quantification", which corresonds to quantification in logics
[5:55 PM] la zeitypalydji.: well I'm fine with that
[5:55 PM] BOTkahai: simpson: Wait, how precise is this correspondence? Can {ro} be read "for all"? I didn't think so...
[5:56 PM] BOTkahai: jelca: i think solpa'i describes it here: https://solpahi.wordpress.com/2016/09/25/a-simpler-quantifier-logic/
[5:56 PM] Ilmen: N+SUMTI is actually a shorthand for "N da poi me SUMTI
[5:56 PM] Ilmen: = N things that are among SUMTI
[5:56 PM] BOTkahai: simpson: ua ki'e
[5:57 PM] Ilmen: "da" is a special pronoun used as a quantification variable
[5:57 PM] Ilmen: ci da prenu = three things are persons
[5:57 PM] Ilmen: It's about counting how many entities can satisfy a given property, a given place in an argument structure
[5:57 PM] Ilmen: You are considering the property "___ prenu"
[5:58 PM] Ilmen: and you're wondering "how many things have this property?"
[5:58 PM] Ilmen: if the answer is 3, then you get {ci da prenu}
[5:58 PM] Ilmen: no da prenu = no thing is a person
[5:58 PM] Ilmen: ro da prenu = everything is a person
[5:58 PM] Ilmen: mi viska ci da = I see three things
[5:59 PM] Ilmen: Then you can restrict the semantic scope of the quantification by adding "poi"
[5:59 PM] Ilmen: mi viska ci da poi mlatu = I see three things that are cats
[5:59 PM] Ilmen: and this can be shortened to
[5:59 PM] Ilmen: mi viska ci mlatu
[6:00 PM] Ilmen: "I see three cats"
[6:02 PM] Ilmen: When "N da" occurs somewhere, the quantifier N bounds the variable "da", which can be reused in the same sentence while keeping the same referent
[6:02 PM] Ilmen: so you can say
[6:02 PM] Ilmen: ci da viska da
[6:02 PM] Ilmen: = three things see themselve
[6:02 PM] Ilmen: the number of things which see themselve is 3
[6:03 PM] Ilmen: You can take the sentence "X sees X", and there's exactly three things which can be subtitute for this X resulting in a true proposition
[6:04 PM] Ilmen: *subtituted
[6:05 PM] Ilmen: If John, the cat and the dog are all the things that see themselves, then you can subtitute X with "John", or with "the cat", or "the dog", and all will yield a true sentence
[6:05 PM] Ilmen: but anything else will yield a false sentence
[6:06 PM] Ilmen: By default, number quantifiers are exact, but you can get inexact quantifiers with the appropriate cmavo's
[6:06 PM] Ilmen: .en su'o
[6:06 PM] BOTkahai: mensi: su'o = [PA4] digit/number: at least (some); no less than. | officialdata
[6:06 PM] Ilmen: su'o ci da mlatu = at least three things are cat
[6:07 PM] Ilmen: su'e ci da viska da = at most three things see themselves
[6:07 PM] Ilmen: ji'i vo da klama = approximately 4 things are going
[6:07 PM] Ilmen: etc etc
[6:08 PM] Ilmen: I hope that was helpful :smiley:
[6:08 PM] la zeitypalydji.: .ua
[6:08 PM] la zeitypalydji.: ki'e
[6:09 PM] la zeitypalydji.: so like "ci de mlatu pe mi" would mean "three things exactly are my cat" and thus "I have three cats"
[6:09 PM] Ilmen: Note also that quantifiers (e.g. number+da or number+sumti) have a rightward logical scope, they have scope over the other quantifiers, adverbs or connectives appearing on their right
[6:10 PM] Ilmen: ci da sipna na ku = three things are not sleeping
[6:10 PM] Ilmen: BUT
[6:10 PM] Ilmen: na ku ci da sipna = it's not the case that three things are sleeping
[6:11 PM] Ilmen: when "na ku" is moved before "ci da", it gets scope over the quantification, the quantification becomes negated
[6:11 PM] la zeitypalydji.: Yeah
[6:11 PM] Ilmen: when "ci da" precedes "na ku", the quantification scopes over the negation
[6:11 PM] la zeitypalydji.: instead of ci da na ku sipna  which I'm guess means "three things are not sleeping"
[6:11 PM] Ilmen: and therefore the meaning is different
[6:11 PM] Ilmen: yes
[6:12 PM] la zeitypalydji.: ok cool
[6:13 PM] Ilmen: Zeitypalydji: Quantification and logical scope are usually considered among the most difficult topics in Lojban's grammar
[6:13 PM] la zeitypalydji.: well actually I'm used to them
[6:14 PM] la zeitypalydji.: negating a universal gives an opposite existential and visa versa
[6:14 PM] Ilmen: yep
[6:14 PM] la zeitypalydji.: I'm pretty used to predicate logic, I'm just annoyed that a lot of sources for lojban try to tell the approximate english meaning rather than the logical meaning