(Originally appeared in Lognet 99/1)
Letters policy: Unless otherwise stated, letters addressed to logli in general, to The Institute, JCB, or any editor of Lognet will be considered as offered for publication. But it would be good if the writer explicitly offers. We reserve the right to edit letters, mostly just tc drop material that has to do with ordering books, etc. Sometimes a given correspondent will have several letters in the hopper, so to speak, and we will combine them into one purely for the sake of clarity. If you are not on e-mail and your letter is a long one, we’d be grateful if you 'd enclose a soft copy on a di skette. We can translate most word-processors into the one we use and having your letters on disk could .save us a lot of typing.
The first letter is from our former Cefli Lodtua, Randall Holmes:
Please note that there is no personal animus involved in my recent note on the subject of sets 1/2 and the different proposed senses of LO [see his Sets, Masses, & JCB’s Multiples” in LN 97/1, p.23 ff]. What is involved is my very firmly held notions of the standards which a “logical language” should meet. If the Loglan community does not agree, I will resign as a lodtua, not because I feel personally slighted but because the language will in my professional judgement have gone off the rails logically. I will not necessarily cease to be interested in Loglan, nor will I be especially annoyed on a personal level.
So far from feeling personally slighted, I think that my views have been given a very careful hearing by all сoncerned.
Sincerely, Randall Holmes
See JCS's article "A Brief History... " in this issue for more on sets1 vs. sets2 and the uses of lo.
The next letter is from our present Cefli Lodtua, Emerson Mitchell:
I tried several ways to work out a proposal for Loglan negative terms, and could not find anything satisfactory. This is not surprising, there is no one accepted logical interpretation. Mathematicians avoid the issue in predicate calculus, and use set complements in other areas of mathematics.
But I do have some examples from logic which may help our thinking. I will use logical notation to make it clear I am not discussing Loglan. Upper case letters near P stand for predicates (e.g., P, R), lower case letters near the beginning of the alphabet for constant terms (e.g., a, b, c), lower case letters near the end of the alphabet for variables (e.g., x, y, z), negation is ~, and quantifiers are [A] for ‘for all’ and [E] for ‘there exists’.
Some observations in no particular order:
A negated sentence does not assert that anything is true, it asserts that something is false. So ~(P(a,b,c)) says P(a,b,c) is false.
Since a sentence is something, doesn’t a negated sentence assert that something, namely that negative sentence, is true?
The opposite of a predicate is a relation that is true of precisely those things of which the predicate is false. So if R is ~P then R(a,b,c) is true just when P(a,b,c) is false.
One would think that this would mean there is no difference between a negated positive sentence and a sentence with the equivalent opposite predicate. This is not quite true. A negated sentence, because it asserts nothing, is on one interpretation always true of nonexistent objects like unicorns. If U is the predicate for Unicorns and V = ~U is the opposite, true of anything not a unicorn, and u is a descriptive term for a unicorn, then on this interpretation both “U(u)” and “V(u)” are false, because nothing is true about ‘u’, and so both “~(U(u))” and “~(V(u))” are true! But one would expect “~(V(u))” would be the same as “~(~U(u))” (by definition) as “U(u)” (by double negation). But I just said “U(u)” was false and “~(V(u))” was true. Ouch.
For those interested, on the interpretation I am discussing I have shown a case when it is not safe to apply double negation. This case is rare, usually ~~P is the same as P. But there are other cases as well.
If you think the above is tricky, terms are worse. Terms have an implicit or explicit set of possible references, and an implicit or explicit quantity: how much of that set is referred to (and how it is referred to, but let’s ignore that here).
So a term ‘a’ either refers to some a ([E]a), or to all a ([A]a). Now consider the same term negated ‘~a’. From a logician’s point of view, there are now four cases: [E]~a, ~[E]a, [A]~a and ~[A]a. But from predicate calculus we would think that ~[A]a is [E]~a and ~[E]a is [A]~a. But we need to be careful.
[E]~a is ‘some non-a’
[A]~a is ‘all non-a’
~[ A]a is ‘not any a’ which is reasonably the same as ‘some non-a’
~[E]a is ‘not some a’, which on one interpretation could be another a! or on another interpretation could be all non-a’s. Ouch.
The lesson I draw is that the problem we are having in Loglan interpreting negated predas and negated terms is not specific to Loglan! It is generic to Logic! No wonder JCB finds us so many problems.
My suggestion is that we decree that Loglan is philosophically neutral on this point. Doing so requires that we not legislate logical transforms shifting negatives and quantifiers around as official interpretations. Instead I suggest that we allow negatives freely but attach them firmly to their grammatical scopes.
So negated sentences would be non-controver- sial.
And a negated preda is a new negative preda defined to be the relational complement of the nonnegated preda. Negating the preda is usually but not always the logical equivalent of negating the sentence.
And a negated term is a special form of a description term, one with potential ambiguities which can often be resolved from context and always the same way any description ambiguity is resolved: by asking. In the case of a negated term, the relevant questions concern the scope of the negation relative to the quantifier(s) on the term.
All this means that a computer attempting to reason about Loglan assertions will either need to resolve any ambiguities before starting to make transformations, or be able to reason with the ambiguities in place. The latter is not impossible; it is currently a very active area of research in computer science.
Obviously, my suggestion does not simplify the work of writing a textbook. Except that we should
avoid the complicated cases, and perhaps warn about the trouble they can cause.
Hue E’mrsn, ji la Lodtua
After much deliberation and with Emerson’s help, the Keugrufound, I believe, a satisfactory way of dealing with the most common double negatives. We deal with all the forms that you might realistically use. There are of course multiply negated sentences which we shall no doubt have fun with in the future. You can find the basics of our treatment in Lesson 14 of L3, Steve Rice’s Understanding Loglan.
The next letter on this topic gives us the anthropologist’s “take" on this matter: from Reed Riner, North Arizona University:
Hoi K, rie:
Talk of double negatives recalls to me this anecdote about double positives ....
A professor side-tracked himself into a discussion about universals in natural languages.
“All languages (that we know of) have a positive case. In fact, all natural languages are written in the positive case. And all languages have a negative case, so that any statement can be negated.
“Some languages, but not all of them, have a double negative, when two negatives in a sentence give an overall positive result.”
Then he added, rather wistfully, “But we know of no language which has a double positive.” ... and he paused.
From the back of the room a sleepy voice remarked, “Yah, right.”
The next item is an excerpt from some correspondence between JCB and RAM, who had mentioned someone's intention to translate the Bible into Loglan:
Bob: They must have found Loglandia if they are proposing to send missionaries there!
Jim: Can I use this in Lognet?
Bob: You may.
The final message came from Slavik Ivanov (Sau la Ro’si,as) just as we were putting this issue to bed:
Hoi Logli, rie, loi!
I continue publishing the text [on my Web page in Russian] I’ve started last Saturday. The next passage now.
Lo tarci sui mela Sol, ice darli mela Sol. I muo fundi lepo bleka lo tarci guo, e jupni lepo tei clufikco.
Riba jie muo gui hanco tokna le darvizrie, ice rei kledja le darli mela Sol lo rorkle, ice rei sirdjano lepo be sui bi le telfoa pe le mela Sol, ice rei feodja lepo lo tarci mutce darli la Ter. Irau lepo tei darli Tai guo le humnu ji trati lepo fadgoi tei gui nu namci le bunbo.
Mela makes a name a predicate, and this I used to say The stars are also suns, and far-off suns. In fact, I must confess, this second passage is not same successful as the first was. Maybe anyone will try to translate better?
Darvizrie = is a telescope. Is clufikco the best way to translate romantic?
La steloj - ili ankaux estas sunoj, nur tre malproksimaj. Ni sxatas rigardi la stelojn kaj opinias, ke ili estas romantikaj. Kelkaj el ni manprenas teleskopojn kaj scias, kiaj diversaj estadas tiuj foraj sunoj, kaj ke iuj ecx havas proprajn planedojn, kaj ke distanco gxis la steloj estas longega. Tiom longega, ke oni nomas revantajn ilin atingi homojn "frenezuloj".
Hue Slavik, ji le ruski logcima.
Let’s fine-tooth-comb S’s L composition. To do so I’ll number its sentences; then translate literally what each L, sentence says; then I’ll correct s if s needs correcting (and can figure out what S meant!); then translate the corrected sentence с literally; and finally express с in idiomatic English...bearing in mind that the composer of these L sentences is a Russian who has learned his L through his E, already a tour de force:
1. Lo tarci sui mela Sol, ice darli mela Sol.
(Observe) Star-also-sort-of Sun-things, and be a distant-sort-of Sun-thing.
This is the conjunction of an observative and an imperative. It's like saying Lo simba, ice briga! = There are lions, and be brave! But S has told us that he meant to say something else: The stars are also suns, and (they are) far-off suns. So let’s say that in L:
Ra tarci ga solfoa sui, e darli solfoa.
All stars are suns (Sun-forms) also, and distant suns.
The stars are also suns, and distant suns.
To do this, I've corrected four things: (a) replaced Lo with Ra, for we're talking about the “exhaustive multiple", each and every star, not about the mass of stars; (b) implied that mela Sol should be replaced with solfoa = Sun-form on the model of telfoa = Earth-form/planet (S could have had another sense of sun in mind, namely something with planets, in which case nu telfoa would be correct); (c) made sui follow the term it modifies, which is the default interpretation of unmarked free-modifiers; and (d) used an ek rather than an eeshek as the connective, for it is predicates we are connecting here, not sentences.
2. I muo fundi lepo bleka lo tarci guo, e jupni lepo tei clufikco.
And each of us (you, I, and others) are fond of the particular act of looking at stars I have in mind (end clause), and have opinions about the condition of tee (stars) being love-fictional.
(a) The first lepo should be lopo; it is not some particular event of looking that we’re fond of, but the mass of such events; (b) we're not opining but believing here, so krido not jupni; and finally (c) it 's not the love-fictional sense of romantic that S probably intends but love-related, so cluperti. (You will note, Hoi Logli, that I make up new words as I go along; that's what you should do.)
I muo fundi lopo bleka lo tarci guo, e krido lepo tei cluperti.
And each of us (you, I, and others) are fond of looking at stars (end clause), and believe that tee (stars) are romantic (love-related).
All of us like looking at stars and believe they’re romantic.
3. Riba jie muo gui hanco tokna le darvizrie, ice rei kledja le darli mela Sol lo rorkle, ice rei sirdjano lepo be sui bi le telfoa pe le mela Sol, ice rei feodja lepo lo tarci mutce darli la Ter.
A few x among us (end ji-clause...but there’s no clause!) by-hand take the telescope (far-see-tool), and r (those few) identify the distant Sun-thing(s) as belonging to the mass of variouses, and r certainly- know that (there is) something у also is-the-same-as the planet(s) of the Sun-thing, and r know-for-a-fact that (I observe?) star-extremely far-things (and) the Earth.
Correcting this without comment:
I ri muo goznurlei lo darvizrie, ice mei kledja lea darli solfoa lea rorkle, ice mei sirdja sui lepo ba bi ne telfoa ne le solfoa, ice mei katcydja lepo ra notbi tarci ji nu telfoa ga mutce darli la Ter.
And a few of us have access to telescopes, and m (those few) identify the class of distant suns as being various (belonging to the class of various things), and m certainly-know also that (there is at least one) something x that is a planet of one of the suns, and m know-by-observation that all other stars that have planets are extremely far from Earth.
4. Irau lepo tei darli Tai guo le humnu ji trati lepo fadgoi tei gui nu namci le bunbo.
This is nearly perfect, but I would insert su before the 2nd tei. Do you see why?
—Hue Braon Djim
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