English, like most languages, I suspect, has problems defining the scope of its quantifiers. This is the reason for a week in the middle o0f a formal logic course about how to translate the the various English (or whatever) quantifier expressions. Lojban, in trying to be a more "natural" language has inherited this problem. The main problem for English seems to be the universal quantifiers "each, every, any and all". For the purposes of ordinay logic, most of the differences here can be dealt with by determining the scope of the quantifier represented, the most complex rule being "'any' in the scope of a negation or in the antecedent of a conditional is a particular if its scope is limited to that part, but a universal over the larger sentence if the scope goes outside that part". This is followed by
some practice exercises including, usually, "If any boy comes, the girls will be happy" ("If there is an x such x is a boy and x comes then the girls will be happy") and "I any boy comes, all the girls will dance with him ("For all x, if x is a boy and x comes the all the girls will dance with x") (the ambiguity of "all the girls' is in the next exercise).
The world and language tends to go beyond logic, however, so that this limited advice does not help much. The scope of quantifiers may well be beyond sentence boundaries: the second example above might well continue "He will be wined and dined. He may even get lucky a couple of times." and so on. Or there may be no obvious scope: "Get me a gun!" "Which one?" "Any one; just get me a goddam
gun!". Here we might well read the "a" as "any" and note that commands are another of those strange places where "any" follows its usual rule, though here the scope is harder to determine and the results are less certain. Straightforwardly, we have "!there is an x, x is a gun and you get me x", but he move with negations and conditionals of moving the quantifier out as a universal does not seem to work: "For every gun x, ! you get me x" seems like a lot more orders than occurred. But maybe the surface is misleading here: a question is logically the disjunctive set of its answers; maybe a command is the disjunctive set of its obediences. Thus, "you get me gun a" is a proper member of the command, and, hence, so is "For some gun x, you got me x", and als all the corresponding sentences about guns b, c, .... But again, not "For all guns x, you get me x", since that exceeds the order. We need to move beyond the set of
obediences to the rule which built the set, rule into near worlds (as much like this one as possible except for the defining characteristic) "If you were to get me gun a, then the order would be obeyed" and so on, which can now be summarized as either "If you were to get me some gun, the order would be obeyed." or "For all guns x, if you were to get me x, the order would be obeyed." (Whether the rules also requires "If the order were to be obeyed, you would have got me some gun" -- but not the particular cases nor the external universal -- is for another discussion.) In Lojban terms, {da'i}, even when invisible, creates one of special places for "any". But as a practical matter, "any" is just a particular quantifier, until the obviously extended scope (the real one, not the superficial) forces it up a level (or more) as a universal.
From: la gleki <gleki.is.my.name@gmail.com>
To: lojban@googlegroups.com
Sent: Friday, August 24, 2012 9:15 AM
Subject: Re: [lojban] "Any" and {ro}
On Friday, August 24, 2012 4:42:37 PM UTC+4, la .lindar. wrote:
CLEARLY we must invent a new gismu for this!I propose {bleni} because "Blah!" for how you react to this suggestion, and then it also sounds like "any".
On a more serious note, I think a clear-cut PA would be very handy.
- Give me an apple?
- Which one? There are several in this basket.
- Any. I want to eat.
I think logic can't define the difference between "one of..." and "any". There for {xe'e} in PA would be strange.
What are your objections against {su'a}?
{da} - some apple in the basket.
{da su'a} - any apple in the basket.
{da su'anai} - some specific apple in the basket (e.g. the yellow one).
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