Message-Id: <199411080334.AA18322@nfs2.digex.net> From: Gerald Koenig Date: Mon Nov 7 22:34:53 1994 Subject: lo & quantifiers Status: RO X-From-Space-Date: Mon Nov 7 22:34:53 1994 X-From-Space-Address: LOJBAN%CUVMB.BITNET@uga.cc.uga.edu la pycyn pa cusku: We also agree that _lo_ and its ilk are +veridical and -definite. I argue that, both because it is a description and to fill a gap in the pattern, _lo_ and its ilk are +specific. The +veridical is then essential, for without a known referent (-definite), the referent cannot be determined except through its properties. I agree with Xorxes that this means that the default quantifiers are wrong and that set me wondering how those were set. I have a memory of issuing a bunch of obiter dicta on questions like that on the basis of 30 second presentations of issues while I was in my Lojban oblivion phase. If that is the history, I'd like to say I have more information now and would like to change my vote. djer> I would very much like to hear your current opinion on the default quantifiers. It would also be interesting if you could relate a bit of the history of the evolution of predicate calculus and numerical quantifiers into artificial language, as lojbab did. Below are some excerpts from the sumti paper which I believe are up to date, showing the latest version of things. I see it as the beta test version, and not the Rosetta stone final edition. djer sumti paper> 7.3) (many deletions) There are rules for each of the 11 descriptors specifying what the implicit values for the inner and outer quantifiers are. The following table lists the implicit values: le ro le su'o lo su'o lo ro la ro la su'o lei pisu'o lei su'o loi pisu'o lei ro lai pisu'o lei su'o le'i piro le'i su'o lo'i piro lo'i ro la'i piro la'i su'o le'e ro le'e su'o lo'e su'o lo'e ro When examined for the first time, this table looks dreadfully arbitrary. In fact, there are quite a few regularities in it. First of all, the la-series (that is, the descriptors "la", "lai", and "la'i") and the le-series (that is, the descriptors "le", "lei", "le'i", and "le'e") always have corresponding implicit quantifiers, so we may subsume the la-series under the le-series for the rest of this discussion: "le-series cmavo" will refer to both the le-series proper and to the la-series. The rule for the inner quantifier is very simple: the lo-series cmavo (namely, "lo", "loi", "lo'i", and "lo'e") all have an implicit inner quantifier of "ro", whereas the le-series cmavo all have an implicit inner quantifier of "su'o". Why? Because lo-series descriptors always refer to all of the things which really fit into the x1 place of the selbri. They are not restricted by the speaker's intention. Descriptors of the le-series, however, are so restricted, and therefore talk about some number, definite or indefinite, of objects -- but never less than one. A descriptor which involves the speaker's intent, as the le-series cmavo do, cannot refer to zero objects; whereas it might be the case that a lo-series descriptor describes something that doesn't really exist (like a purple rhinoceros). So "ro" does not exclude "no" (zero), but "su'o" does exclude "no" as a possible quantifier. Understanding the implicit outer quantifier requires rules of greater subtlety. In the case of mass and set descriptors, a single rule suffices for each: reference to a mass is implicitly a reference to some part of the mass; reference to a set is implicitly a reference to the whole set. Masses and sets are inherently singular objects: it makes no sense to talk about two distinct masses with the same components, or two distinct sets with the same members. Therefore, the largest possible outer quantifier for either a set description or a mass description is "piro", the whole of it. The case of outer quantifiers for individual descriptors (including "le", "lo", "la", and the typical descriptors "le'e" and "lo'e") is special. When we refer to specific individuals with "le", we mean to refer to all of those we have in mind, so "ro" is appropriate as the implicit quantifier, just as it is appropriate for "do". Reference to non-specific individuals with "lo", however, is typically to only some of the objects which can be correctly described, and so "su'o" is the appropriate implicit quantifier, just as for quotations. From the English-speaking point of view, the difference in structure between the following example using "le": 7.4) [ro] le ci gerku cu blabi [all-of] those-described-as three dogs are-white. The three dogs are white. and the corresponding form with "lo": 7.5) ci lo [ro] gerku cu blabi three-of those-which-are [all] dogs are-white Three dogs are white. looks very peculiar. Why is the number "ci" found as an inner quantifier in Example 7.4 and as an outer quantifier in Example 7.5? The number of dogs is the same in either case. The answer is that the "ci" in Example 7.4 is part of the specification: it tells us the actual number of dogs in the group that the speaker has in mind. In Example 7.5, however, the dogs referred to by "... lo gerku" are all the dogs that exist: the outer quantifier then restricts the number to three; which three, we cannot tell. The implicit quantifiers are chosen to avoid claiming too much or too little: in the case of "le", the implicit outer quantifier "ro" says that each of the dogs in the restricted group is white; in the case of "lo", the implicit inner quantifier simply says that three dogs, chosen from the group of all the dogs there are, are white. 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! (Actually, because "gerku" has an x2 place, namely the breed or variety of dog, it claims that there are three dogs of the breed which is understood from context. This is almost as bad, because no breed of dog has as few as three members.) 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. The name "indefinite description" for this syntactic form is historically based: of course, it is no more and no less indefinite than its counterpart with an explicit "lo". Indefinite descriptions must fit this mold exactly: there is no way to make one which does not have an explicit outer quantifier ("*gerku cu blabi" is ungrammatical), or which has an explicit inner quantifier ("*reboi ci gerku cu blabi" is also ungrammatical -- "re ci gerku cu blabi" is fine, but means "23 dogs are white"). Note: Example 6.3 contains an indefinite description, namely "su'o ci cutci"; another version using an explicit "lo" would be: 8.2) mi ponse su'o ci lo cutci I possess at-least three things-which-really-are shoes I own three (or more) shoes. --------------------------------------------------------------------------- jlk@netcom.com