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Ongoing discussion with TLI rep on Loglan/Lojban and logic - 3 of 3
Part 3 of 3+ of the exchange between lojbab and Randall Holmes.
|Message 6:
|Date: Tue, 21 Jun 94 23:15:40 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|How do you define the set of all x such that ...x..., where ...x... is a
|_sentence_ in which x may occur several times? This is the standard way
|in which sets are defined in mathematics. All of the constructions you
|describe seem to have close Loglan analogues or to be refinements which
|do not address this particular problem. You need a device for
|converting a subordinate clause into a predicate.
|
| --Randall Holmes
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|Having trouble coming up with an example of a sentence where "x" occurs
|several times that is not a compound (i.e logically connected) sentence.
|Part of the problem is that most Loglan arguments start out as
|descriptions, and the effect of "me" in the formal sentence would be
|simply to remove the descriptor.
|
|I think that if we got stuck with something sufficiently difficult, and
|wanted to make it a SET, though, we would simply use the "set" predicate
|"cmima" with the argument(s) defining the membership, collectively
|converted to a set using the appropriate member of LAhE (which is
|"lu'i").
|
|It has just occured to me that I want to see if Colin Fine will get
|involved in this discussion. Nick is in the middle of a thesis and
|probably doesn't want to get into such a technical discussion right now.
|Colib has the advantage of being knowledgeable of both TLI Loglan and
|Lojban - he has been around since the mid-70s. He also has served on
|occasion in lieu of pc for posing and answering logical problems with
|the language, and is much more qualified than I am (after all, I
|practically flunked Symbolic Logic in college - not from inability to
|understand, but lack of time to study a course that was self-paced - but
|I am the last person who should be arguing about formal logic
|expressions). If he is interested, I'll send him the entirety of our
|exchange so far so he can comment, and include him on future cc: lines
|so he keeps up thereafter.
|
|lojbab
|Cc: nick lojbab
|
|
|Message 6:
|Date: Thu, 23 Jun 94 07:13:05 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|Da me le to mrenu
|
|means "X is one of the three men I have in mind".
|
|ME <designator> is one-place.
|
|The "difficulty" (if it is that) is that X itself may validly designate
|more than one object (not in the sense of designating a set or mass, but
|in the sense that a designator like Le mrenu indifferently means "the
|man" or "the men" I have in mind).
|
|By the way, here is a way to use ME in my sense:
|
|Le mrenu pa vizka le bakso (the man/men saw the box).
|
|I te ba me le mrenu.
|
|(there were three of them that I had in mind that did this).
|
|Notice that I am not using a set or mass usage here; the "plural
|reference" of Le mrenu is expressed (as JCB would say) by there being a
|conjunction of three sentences expressed by the first sentence (one for
|each of the originally indeterminate class of men which the second
|sentence tells us has three elements).
|
|Now it would be easy in this case to say
|
|Le te mrenu pa vizka le bakso
|
|and reveal at the outset that we have three men in mind. But it is not
|so easy to express the claim made by the second sentence once the first
|has gone without a precise predicator.
|
|Suppose we said
|
|Te mrenu pa vizka le bakso
|
|instead; how do we know that the individuals we had in mind are not a
|proper subset of the three men mentioned (or not a subset at all; maybe
|one of the "men" we have in mind is about to be revealed to be a woman
|in disguise :-) ) Of course, we could actually _say_ "I had three men in
|mond in the last sentence", but that would be awfully long-winded.
|
|I'm not so sure that JCB would disagree with your response to his column
|in Lognet. I think that was part of what he had in mind.
|
| --Randall
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|I'm going to have to think about your posting off-line. Abit too late
|for me to be fully coherent. I think that the way we would in
|afterthought indicate that "le mrenu" were three individuals would be by
|using our equivalent of "le mrenu, tera" (in Lojban: "le nanmu cu
|cimei" for the non- TLI kibbitzers that I hope to eventually comment %^)
|Our cardinality predicate has places for the set, the mass, and the
|individuals comprising the set membership.
|
|Having said something like
|RH> Le mrenu pa vizka le bakso (the man/men saw the box)
| le nanmu pu viska le tanxe [in Lojban]
|
|it would be inappropriate to say
|
|RH> Te mrenu pa vizka le bakso
| ci nanmu pu viska le tanxe
|
|to clarify the number, because for us "ci nanmu" not restricted is a)
|veridical rather than intensional like a "le" description and b) because
|it is non- restricted in the example, there is no way to tie it to the
|previous usage. We do have a discursive operator ("bi'u", I think) that
|has grammar of UI and can attach to such an argument indicating "old
|information" vs. "new information ("bi'unai"?), where "old information"
|explicitly means that we are referring to some previously discussed
|(three) men - thereby in this context making the usage clear. But I
|think we would be more likely to use the cardinality predicate to
|specify the number in after thought, perhaps even as a relative clause:
|
|le nanmu noi cimei cu zvati ti
|?le mrenu jio tera, hijra ti
|The men, a threesome, are here (at place indicated).
|
|lojbab
|Cc: lojbab nick
|
|Message 7:
|Date: Thu, 23 Jun 94 07:20:44 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|I'm not sure how the set predicate is going to help you. Sets defined
|by complex sentences where multiple occurrences of x cannot be
|eliminated by compounding are everywhere in mathematical discourse,
|certainly. Here's an easy one, though (if Lojban lacks a reflexive, as
|Loglan does):
|
|The set of all x such that x loves x
|
|Lea meba jio ba cluva ba
|
|How would you propose to say this?
|
|Reflexives are a linguistic universal; I have proposed nuo preda here so
|that A cluva A would be A nuo cluva (with a series of these for later
|argument positions. And it is no fair to coin a new predicate in order
|to carry out a clearly logical transformation!
|
| --Randall
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|Lojban has a reflexive, indeed a variety fo them for specific purposes,
|but I don;t have them firmly in mind. I am sure that we have one for
|this simple case though I can't think of it off-hand (if we don't, we
|should ...) My first thought was "le prami be ke'a", but "ke'a" is
|normally for use in a relative clause, not in a specified description,
|for reflexivity, and we probably can't use it for both relative clauses
|and specified descriptions without ambiguity. [the descriptor should be
|"lo'i" and not "le" to correspond to TLI lea]. But if this is a problem
|for us, it is not limited to set manipulations, but to a whole class of
|reflexive usages. I need to talk to others to get this straight. (If
|this discussion were taking place on Lojban List, I would probably have
|a few people piping up with comments. Maybe I oughta be sending this to
|the List rather than to selected people for comment. This discussion is
|starting to range rather widely over our grammar features and thus would
|be informative to those who are learning as well as those who could
|comment intelligently.
|
|lojbab
|Cc: lojbab nick
|
|Message 8:
|Date: Thu, 23 Jun 94 07:39:30 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|JCB does say something like what you say; see page 5, column on the
|right. (in the Lognet article). We are not used to making the dis-
|tinctions required in speech; most of us were not aware of themn
|(explicitly -- we _do_ know about them in some sense) until we
|encountered Loglan/Lojban. He makes the point that Loglan doesn't just
|offer the _opportunity_ to speak with precision; in some snse it forces
|us to. Some kinds of fuzziness we are used to can't be expressed in
|Loglan!
|
|My feeling about Loglan is that there is going to be serious trouble
|keeping the uses of quantifiers in line without giving everyone formal
|logical training. The other day, I wrote
|
|Lemi sunho prozymao ri steti na ra le denli
|
|My son writes a few sentences each day
|
|and on reflection rewrote this as
|
|Lemi sunho prozymao na ra le denli gu ri steti
|
|(I think the "gu" is optional)
|
|Can you see why?
|
| --Randall
|
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|I see why, even if I am not up to figuring out the distinction in
|meaning between the two versions at this time of night. Order of
|quantifiers is certainly important to logical meaning. I think Lojban
|usage, or at least MY Lojban usage, is a bit richer in prenex
|expressions because I don't like to take chances with such ordering
|rules at the default sentence level. By going to prenexes, I
|intuitively go into "logical mode" and make fewer mistakes.
|
|Cc: lojbab nick
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|I talked to pc tonight, and mentioned your interest in talking with him,
|and passed along your interest in theorem proving software. He is not
|yet on line and UMSL apparently is completely confused about its slow
|net-attaching - he mentioned that they have had something like 8
|different people in charge of the project over the 3 years that it has
|been promised. At the moment things are somewhat behind where they were
|6 months ago.
|
|I will be talking with our voting membership about having LLG payt for
|him to get net access that is independent of his unoversity bureaucracy.
|Our annual meeting at LogFest is in 3 weeks. If this happens, he will
|be able to speak for himself.
|
|He indicated that, since UMSL is a teaching rather than research
|oriented university, he has been working mostly with software tools to
|aid teaching. His major work in the last few years has been with
|automated proof constructors using SNOBOL, with the intent that a
|student could be given exercises, attempt to solve them himself, and get
|help from teh software on a plausible next step in the proof as well as
|have the computer check the prrof that the student generated for
|correctness. At least that is what I think I understood he has been
|trying for. he got a good way on this project last school year when he
|had a time and/or money grant to support the work, but I think he's been
|stalled out on the project recently.
|
|lojbab
|Cc: lojbab
|
|
|
|Message 4:
|Date: Fri, 24 Jun 94 09:16:04 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|I will read your letter in more detial later, but here is an obvious
|problem I've been through in Loglan:
|
|le mrenu jio tera
|
|will not have the desired effect; it asserts that each of the men you
|have in mind is a threesome, not the set of three men whose individual
|members you have in mind. Plural reference is very different from set
|reference!
|
| --Randall
|
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|Our equivalent of "tera", "cimei", has multiple places - one of which is
|a set, one of which are the individuals which are members of the set.
|
|lojbab
|Cc: lojbab nick
|
|Message 5:
|Date: Fri, 24 Jun 94 09:19:34 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|Am I correct in assuming that ke'a is an argument form meaning "itself"
|or something of that sort? My proposed solution to the reflexive
|problem is somewhat different. I would be interested in hearing more
|about Lojban reflexives, though.
|
| --Randall
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|Actually, "ke'a" was intended to be a floating relative pronoun with
|usage like "it" in "the box such that it is green". It is generally
|ellipsized right after the relative marker, but explicit when in other
|possitions: "the man such that she kissed him" would be likely to have
|the pronoun after the predicate for kissed (though here again, if the
|speaker usually uses SVO order in relative clauses, the implicature
|would be to assume an eelipsized pronoun would go into the first
|available place, so ellipsis is possible here to). A better example:
|"the man such that his (le ke'a) car is in front of the house".
|
|What isn;t coming to mind at the moment: we have pronouns that go 'out
|a level' from the current predicate. It isn't clear what such a pronoun
|in a specified description would be, and I'll have to check and see if
|we have discussed it ( aproblem since I can't even remember the word
|right now).
|
|lojbab
|Cc: lojbab nick
|
|Message 6:
|Date: Fri, 24 Jun 94 09:22:41 -0600
|From: Randall Holmes <holmes@diamond.idbsu.edu>
|To: holmes@diamond.idbsu.edu, lojbab@access.digex.net
|Subject: Re: Lojban
|Cc: nsn@krang.vis.mu.oz.au
|
|Interesting; I would think that such forms would be avoided in speech at
|all costs (with a resultant freight of errors)!
|
|By the way, what is the current Lojban convention on scopes of implicit
|quantifiers in connected sentences? Is it the same as the convention
|described in L1 (there are some problems with the latter).
|
| --Randall
|
|Mail>r
|To: holmes@diamond.idbsu.edu
|Subject: Re: Lojban
|
|I'll have to defer to pc or someone else on this one, as that is way too
|much in my weak area. I know that pc and I went into great detail on
|scopes of negation in connected sentences, and I think quantifiers were
|to be handled by the same rules. In general, though, we have added in
|prenexes at most lesser clause levels, and I seem to recall that we do
|not presume a quantifier exports any further than the nearest avbailable
|prenex. But I could very well be wrong on this. This however is one
|reason why I tend to make my prenexes explicit rather than relying on
|implicit quanti- fication.
|
|lojbab
|Cc: lojbab nick
|