From @uga.cc.uga.edu:lojban@cuvmb.bitnet Sun Jul 02 19:10:50 1995 Received: from stryx.demon.co.uk by stryx.demon.co.uk with SMTP id AA3709 ; Sun, 02 Jul 95 19:10:46 BST Received: from punt3.demon.co.uk by stryx.demon.co.uk with SMTP id AA3706 ; Sun, 02 Jul 95 19:10:36 BST Received: from punt3.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Fri, 30 Jun 95 23:46:16 GMT Received: from uga.cc.uga.edu by punt3.demon.co.uk id aa21818; 1 Jul 95 0:45 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 2730; Fri, 30 Jun 95 19:43:49 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 5461; Fri, 30 Jun 1995 19:42:54 -0400 Date: Fri, 30 Jun 1995 16:42:27 -0700 Reply-To: Gerald Koenig Sender: Lojban list From: Gerald Koenig Subject: Re: pc answers To: lojban@cuvmb.cc.columbia.edu Message-ID: <9507010046.aa21818@punt3.demon.co.uk> Status: R Jorge has convinced me that his translation of: ci remna ku so gerku zo'u ra pencu ri, as: For each of exactly three humans, there are 9 dogs that the human touches. ( Not necessarily the same ones for each human. ) is quite correct using the existing lojban grammar rules. This is the case where there are up to 27 dogs. My predicate calculus formula: E^!3(x) (remna (x) E^!9(y)(gerku(y) & pencu(x,y))) declares that there are exactly 3 humans and exactly 9 dogs, for the scope of the entire sentence. How to say it in lojban? I get: ro lo ci remna ku ro lo ci gerku zo'u ra pencu ri These sentences don't have to be in topic-comment form. They give the desired two distinct interpretions of , a 9 dog and a 27 dog interpretation. 1. ro lo ci nanmu cu pencu ro lo ci gerku, (9 dogs) and 2. ci lo nanmu cu pencu ci lo gerku, (27 dogs) which is the same as ci nanmu cu pencu ci gerku, by the quirk in the grammar. An interesting point to me is that merely by exchanging ci and lo in front of a gismu we are changing the underlying number explication from the standard predicate calculus formulation to the lojban system of selection from a larger set defined by the predicate. Or at least that is my assumption. I assume that in the case of an exact numerical claim with exactly N objects in the universe of discourse, there is no call to make a selection from a larger set defined by the predicate. To select N objects from N objects seems nonsensical to me. Perhaps the FOL (first order logic) system of making numerical claims has been abandoned altogether. In that case there may be no particular relationship between lojban and logic, it is simply a new language with other interesting features. It was believed prior to about 1900 that there were no problems with the intuitive idea that there is a set defined by every predicate asserting a property, such as gerku(x). This assumption led to Russell's paradox and the need for new foundations of set theory on an axiomatic basis. Sooner or later I would guess that we will have to deal with problems arising from this same assumption, which is built into the lojban number grammar. >From the sumti paper: ______________________________________________________________ Using exact numbers as inner quantifiers in lo-series descriptions is dangerous, because you are stating that exactly that many things exist which really fit the description. So examples like 7.7) [su'o] lo ci gerku cu blabi [some-of] those-which-really-are three dogs are-white are semantically anomalous; Example 7.7 claims that some dog (or dogs) is white, but also that there are just three dogs in the universe! Nevertheless, inner quantifiers are permitted on "lo" descriptors for consistency's sake, and may occasionally be useful. 8. Indefinite Descriptions By a quirk of Lojban syntax, it is possible to omit the descriptor "lo" from a description like that of Example 7.5; namely, one which has an explicit outer quantifier but no explicit inner quantifier. The following example: 8.1) ci gerku [ku] cu blabi Three dogs are white. is exactly equivalent in meaning to Example 7.5. Even though the descriptor is not present, the elidable terminator "ku" may still be used. ___________________________ djer