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I've attempted a write-up of where we've ended up. It's (temporarily) at http://nuzban.wiw.org/wiki/index.php?On%20the%20meaning%20of%20%22ro%20broda%20cu%20brode%22 But the text from there is repeated below. I'd like it that if we agree that it represents the consensus (with any necessary revisions), then the url can be sent to Lojban list so that people can see that we do get things settled. I haven't attempted an exposition of the 'quantificational square' -- that's a job for xorxes and Jordan and Adam, maybe on a separate page that could be linked to. ---And. '''Two types of quantification.''' Quantifiers come in two sorts, which we can tentatively label __'cardinals'__ and __'fractionals'__. The numbers ''pa, re, ci...'', "1, 2, 3...", are examples of cardinals. ''So'e'', "most", is an example of a fractional. Fractionals may either involve taking a fraction of the extension of a set, as in "one third of all lojbanists", or they may be formulated as 'frequencies', as in "one in (every) three lojbanists", "one per three lojbanists". The frequency variety of fractionals is suitable for fractionally quantifying over sets with infinite size. '''The meaning of ''ro''.''' What does ''ro'' mean in ''lo ro broda''? Well, if there are 7 broda, then ''lo ro broda'' is equivalent to ''lo ze broda''. If there are a hundred broda, then it is equivalent to ''lo pa no no broda''. ''Ro'', then, expressed a cardinal number. In ''lo ro broda'', ''ro'' expresses the cardinal number that is the cardinality of ''lo'i broda''. In ''ro (lo) broda'', ''ro'' again expresses the number that is the cardinality of ''lo'i broda'', but here the number is functioning as a cardinal quantifier, so ''ro lo ze broda'' = ''ze (lo ze) broda'', ''ro lo pa no no broda'' = ''pa no no (lo pa no no) broda''. The same goes for ''ro da poi broda''. In the case of unrestricted quantification, as in ''ro da ga broda gi brode'', ''ro'' expresses the number that is the number of da in the universe (-- everything in the universe is a da). '''Ways of saying "all".''' Sometimes we might want to express "all" by means of a fractional quantifier -- "all (of the) lojbanists", "1 in every 1 lojbanist", "100% of lojbanists". However that would be done in Lojban, it is not done by plain unadorned ''ro''. '''Existential import of ''ro''.''' The issue that led to the discussion that led to this record was the question of whether ''ro broda cu brode'' can be true when there are no broda. It turns out that ''ro broda cu brode'' can be true when there are no broda''. This is easy to see. If the cardinality of ''lo'i broda'' is 0, then ''ro broda'' = ''no broda''. Plainly, ''no broda cu brode'' is true when there are no broda. '''The principal quantiers.''' There are four principal cardinal quantifiers: ''no'', "0"; ''su'o (pa)'', "at least one"; ''me'i (ro)'', "less than ro"; ''ro''. The details of these are discussed elsewhere. [[WHERE?] (NB It has not yet been fully established that plain ''me'i'' is equivalent to ''me'i ro'', or that ''me'i'' is the best choice to express one of the four principal cardinal quantifiers.) By deduction, ''su'o'' and ''me'i'' have exstential import and ''no'' and ''ro'' do not. '''Existential import of fractionals.''' Fractionals involve a slightly modified notion of existential import: for example, "99% of lojbanists are broda" or "99 in (every) hundred lojbanists are broda" are meaningful only if there are at least a hundred lojbanists. So the crucial issue here is not whether the sentence is true when there are no lojbanists, but whether the sentence is true when there are fewer than 100 lojbanists. Given this generalized notion of importingness, it turns out that sometimes we want fractionals to be importing, and sometimes we don't. For example, we probably want "half my messages to Lojban list this month have been garbage" to (importingly) mean "I have written at least 2 messages ti Lojban list this month, and 1 in 2 of them have been garbage". On the other hand, we probably want "half my message to Lojban list each month are garbage" to (nonimportingly) mean "For each month, either I write fewer than 2 messages to LL or I write at least 2 messages to LL and 1 in 2 of them are garbage"; that way, the statement holds true even though there are some months when I don't write as many as 2 messages to Lojban list. Of course, the statement would be rather daft if I have never written as many as 2 messages in a single month. It is probably best to see fractionals as basically nonimporting, the oddity of saying "half my messages to LL this month have been garbage" when I've not written 2 or more messages to LL is due to its extreme uninformativeness, analogously to saying "every brother of mine has emigrated" when I have no brothers.