From jjllambias@hotmail.com Sat Mar 09 18:23:33 2002 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 10 Mar 2002 02:23:33 -0000 Received: (qmail 6397 invoked from network); 10 Mar 2002 02:18:38 -0000 Received: from unknown (216.115.97.167) by m5.grp.snv.yahoo.com with QMQP; 10 Mar 2002 02:18:38 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.151) by mta1.grp.snv.yahoo.com with SMTP; 10 Mar 2002 02:18:38 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Sat, 9 Mar 2002 18:18:38 -0800 Received: from 200.69.2.52 by lw8fd.law8.hotmail.msn.com with HTTP; Sun, 10 Mar 2002 02:18:37 GMT To: lojban@yahoogroups.com Bcc: Subject: More about quantifiers Date: Sun, 10 Mar 2002 02:18:37 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 10 Mar 2002 02:18:38.0188 (UTC) FILETIME=[E38242C0:01C1C7D9] From: "Jorge Llambias" X-Originating-IP: [200.69.2.52] X-Yahoo-Group-Post: member; u=6071566 X-Yahoo-Profile: jjllambias2000 X-Yahoo-Message-Num: 13593 In terms of sets (SP for the intersection, 0 is the empty set) we have: - + A SP=S [or S=0] SP=S and S/=0 E SP=0 [or S=0] SP=0 and S/=0 I SP/=0 or S=0 SP/=0 [and S/=0] O SP/=S or S=0 SP/=S [and S/=0] The square brackets show unnecessary conditions, as they are already implicit in the first part. The condition for non-import is "or S=0" = "or there is no S" = "if there is any S" and the condition for existential import is "and S/=0" = "and there is some S". To be perfectly clear in English we can say: A- All S are P, if there is any S A+ All S are P, and there is some S E- No S is P, if there is any S E+ No S is P, and there is some S I- Some S are P, if there is any S I+ Some S are P, and there is some S O- Not all S are P, if there is any S O+ Not all S are P, and there is some S Notice that in the set notation, the group that does not require the import condition is A-,E-,I+,O+. That condition is implicit already in the first part. Some people say that the same happens in English: A- All S are P E- No S is P I+ Some S are P O+ Not all S are P however this is controversial. Other people see A+ and E+ in the bare forms, and I think some see O- in the bare O form, but I'm not sure (if you see A+ in the bare A, it would make sense to see O- in the bare O). Now for the uncontroversial Lojban forms: The "simple" foursome: A- roda zo'u ganai da broda gi da brode E- noda zo'u ge da broda gi da brode I+ su'oda zo'u ge da broda gi da brode O+ me'iroda zo'u ganai da broda gi da brode (Maybe {me'iroda} is slightly controversial, but I think pc has not objected very strongly to it. Replace by {naku roda} or other equivalents if preferred.) And the "complicated" foursome: A+ ge da broda gi rode zo'u ganai de broda gi de brode E+ ge da broda gi noda zo'u ge de broda gi de brode I- ganai da broda gi su'oda zo'u ge de broda gi de brode O- ganai da broda gi me'iroda zo'u ganai de broda gi de brode We could write the import condition explicitly in the simple foursome too, but it would be an unnecessary complication, as it doesn't add anything. In any of this, we can use the following replacement rules and get equivalent forms: roda = noda naku = naku me'iroda = naku su'oda naku noda = roda naku = naku su'oda = naku me'iroda naku su'oda = me'iroda naku = naku noda = naku roda naku me'iroda = su'oda naku = naku roda = naku noda naku So far there should be no disagreement (I hope). Now comes the part where we disagree. I want {da poi broda} et al to stand for the four simple forms, thus: A- roda poi broda cu brode E- noda poi broda cu brode I+ [su'o]da poi broda cu brode O+ me'iroda poi broda cu brode The great advantage of this is that the transformation rules keep working just as before. So, for example {roda poi broda} is equivalent to {noda poi broda naku} and so on. The complicated forms as before get a more complicated form, just as in set terms and in explicit terms: A+ ge da broda gi rode poi broda cu brode E+ ge da broda gi node poi broda cu brode I- ganai da broda gi [su'o]de poi broda cu brode O- ganai da broda gi me'irode poi broda cu brode pc would use the simple forms for I- and O-, and to say I+ and O+ he would have to say: I+ ge da broda gi [su'o]de poi broda cu brode O+ ge da broda gi me'irode poi broda cu brode Notice that these last two also work for me, they just have unnecessary complications, just as my I- and O- work for pc as well, though they have unnecessary complications. Now we go to the even more reduced forms {ro broda} et al. In my system {Q broda} is just {Q da poi broda}, so we have the simple forms: A- ro broda cu brode E- no broda cu brode I+ su'o broda cu brode O+ me'iro broda cu brode Again, the big advantage of this is that the transformation rules keep working exactly as before. {ro broda} = {no broda naku} and so on. Again the complicated forms can be obtained as before: A+ ge da broda gi ro broda cu brode E+ ge da broda gi no broda cu brode I- ganai da broda gi su'o broda cu brode O- ganai da broda gi me'iro broda cu brode Now, pc does not make the identification of {ro broda} and {ro da poi broda}. Instead, he assigns the {Q broda} forms to the + cases, so we differ in {ro broda} and {no broda}, just as before we differed in {su'o da poi broda} and {me'iroda poi broda}. As a final quirk, Lojban has "inner quantifiers" that allow us in my system to use {ro lo su'o broda} for A+, and similarly for E+, so as a bonus I get: A+ ro lo su'o broda cu brode E+ no lo su'o broda cu brode There is no similar trick to force non-import, so I don't have equivalent short forms for I- and O- in terms of {su'o} and {me'iro}, but we can always get them in terms of the negations of the other two: I- naku no lo su'o broda cu brode O- naku ro lo su'o broda cu brode These last four forms should all work in pc's system as well. To summarize, the only conflicting forms are: ro broda cu brode no broda cu brode [su'o]da poi broda cu brode me'iroda poi broda cu brode which have different import in pc's system (Lojban's system if you wish) and mine. In my system the transformations: roda = noda naku = naku me'iroda = naku su'oda naku noda = roda naku = naku su'oda = naku me'iroda naku su'oda = me'iroda naku = naku noda = naku roda naku me'iroda = su'oda naku = naku roda = naku noda naku will work at all levels, {roda}, {roda poi broda} and {ro broda}. In pc's system they work at the basic level, but they have cross forms at the other levels, {roda poi broda} can only be transformed with {su'o broda} and so on. I find it much easier to work with my system (obviously) but there is nothing that you can do with one system and not in the other, they are just different notations for the same underlying logic. mu'o mi'e xorxes _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx