quantification and the meaning of ⟨ro⟩

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In October--November 2002 there was on Lojban List and then Jboske an intense and voluminous debate on the meaning of ro, particularly on the question of whether it has 'existential import'. The text below has been agreed on as representing the complete consensus that emerged from the discussion. (NB: pc resigned mid-way through the discussion, so he is not party to the final consensus.)

Quantification and the meaning of ro

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 (which is always exactly the same as ro (lo) 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 2 ).

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. It has not yet been determined which fractionals (if any) have existential import.

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. See Existential Import. (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 3 have exstential import and no and ro do not.

--And Rosta

  • Robin asks who agreed with the above. Essentially, the answer is Everyone. Everyone in the online lojban community had the opportunity to participate, and everyone had the chance to dissent with the above text. The main participants in the closing stages of debate were Adam, And, John, Jordan, Nick, xod, xorxes. Of these, I think Adam, Jordan, Nick and xorxes were all positively in favour, xod explicitly said he didn't have a problem with it, and John consented by not voicing dissent. --And Rosta
    • John did dissent: see [1]. I continue to dissent.
    • That message is from a much much earlier phase of the debate. Many many more arguments were subsequently raised and discussed pro and con importing ro. The clinching argument in favour of cardinal ro is that it makes ro mean the same thing in all environments. This means that the fractional meaning that you and I thought it had must in fact be expressed some other way. You didn't argue against those new arguments. Perhaps you were too busy & will raise counterarguments that mean the debate will have to be reopened. But at any rate, my view is that dissent is valid only if it keeps itself up to date and engages with all the arguments that favour the established position. --And Rosta
    • Umm, dissent is dissent. Whether you agree with the dissent's validity is a very seperate discussion. -- RobinLeePowell
    • And for the record, pc was adamantly opposed. As a tangent, sometimes there will just have to be majority and minority views; sometimes not everyone can be accommodated -- and that includes John. As a further tangent, the existential import of ro is a 'common sense' approach to 'all', while the non-existential is a more intellectualised approach. ("All Green members of the House of Representatives vote against plutonium mining" --- a statement it is convenient for logic to make true, even if it involves nu'o people.) In cases like these, where the language does not live or die on the ambiguity, there may will be some room for dissent and discrepancy of usage; but I think it fair to say that the majority either doesn't care, or would rather Lojban resemble legalistic English than naive English. Those who would denigrate this, remember that it is still a log-lan... -- nitcion
    • There is Valid Dissent (or Valid Opinion) and Invalid Dissent (or Invalid Opinion). (The problem with current political democracy is that it doesn't allow for this distinction.) Disagreements based on Valid Opinion will raise arguments and counterarguments and through a shared process of Reason will either converge on an agreed opinion or will reach a point of disagreement where each conflicting opinion is equally valid, given the arguments that have been raised. An Invalid Opinion is one that is put forward either without supporting arguments or without addressing counterarguments. John's current dissent is Invalid (not necessarily culpably so: it is very hard to keep up with debates when they number a couple of dozen messages a day). Likewise, pc, knowledgeable though he is, rarely supported his own position with compelling arguments or adequately addressed the counterarguments of his opponents. What really matters in these debates is that we end up with the most coherent position and know the reasons that support the position. The question of who is and isn't in favour, and the relevance of majority votes, matters only when we end up with two conflicting but equally valid positions. --And Rosta

The footnotes don't actually seem to work; I don't know why. Sorry. -- RobinLeePowell

  • Now they seem to work. -- Adam
    • Do not. Clicking on them takes you to the main page. -- RobinLeePowell

2: Everything in the universe is a da, sure, but not everything is a da ga broda gi brode, so I'm not sure what this comment means. -- RobinLeePowell

  • The point is that the ro of an unrestricted claim such as ro da ga broda gi brode also stands for however many das there are in the world, including no, if that should be the case. -- AdamRaizen
  • OK, that's pretty unclear from that comment. How about:
    • ro expresses the number that is the number of da in the universe that match the da ga broda gi brode restriction (remember, everything in the universe is a da if da is not restricted).

3: Why is me'i importing? Simply because "less than zero" makes no sense for discrete objects? -- RobinLeePowell