Return-Path: Message-Id: Date: Sat, 25 May 91 04:20 EDT From: lojbab (Bob LeChevalier) To: lojban-list Subject: binxo, the "logic" of Lojban, and terminology (very long) Status: RO X-From-Space-Date: Sat May 25 04:21:17 1991 X-From-Space-Address: lojbab The following, if long, may be worthwhile even for new people. I am attempting to explain some of the logical aspects of Lojban, as well as clarify some terms that are frequently misused. My apologies if this comes out a little dense though. jimc finally made one thing clear in his latest discussion of binxo that I didn;t see he was saying before. >Returning to the head of the discussion, my major objection to the >(sumti) binxo (sumti) form is that for good reason we discourage (sumti) >du (sumti) when a predicate form is possible, e.g. > > la banthas. mlatu la banthas. du lo mlatu > Bantha cats (preferred) Bantha is a cat (deprecated) If I read what jimc is not quite saying here, he is relating the meaning of binxo in contrast to "du" as opposed to the contrast with "cenba" and "galfi" that was our motivation for "binxo". In short, he sees our "binxo" sentence as a type of identity sentence, and not as a predication. If so, he may have a point in that "become" is seen as the future tense of "to be" in English; however, I am yet not convinced that a change is needed, other than the one already done: to take the discussion of "du" out from the start of the textbook to prevent people from concentrating on same from the beginning. Because "binxo" is NOT an identity sentence. Similar arguments have been raised on "gasnu", however, and its meaning has been drastically changed/clarified to distinguish it from the English "do". We may need to make similar changes to the definition of "binxo" - for clarity. The following sticks my logically inexpert neck out, in an attempt to clarify what I see as the meanings of some of these words, and why jimc's problem disappears. I may be off-base, and will therefore be quite prepared to back off from any point - this is NOT any formal LLG prescription of the language (unless I'm right) though it summarizes a lot of intentions. If there are no logical flaws, I think it is a safe claim that learning Loglan/Lojban has had a significant effect onmy thinking, since I would never have gotten this right after nearly flunking college logic class. On the other hand, even if I may be a little off base, I am reasonably sure that I have my terminology straight, and this may reduce confusion about things jimc and others have been writing. "du" IS an identity 'predicate', and its morphology alone flags it as different from other predicate words. It claims that the two sumti on either side are alternate and equivalent designations for the same thing. Translate it best as the mathematical "=" sign. (Nora adds that she sees "du", other than in a mathematical context, as having a somewhat metalinguistic effect. It equates two labels for the same thing. No other words in Lojban, other than the relativizers "po'u" and "no'u", and the assigners "goi" and "cei", have this metalinguistic effect.) In: > la banthas. du lo mlatu (1) > Bantha = a cat (deprecated) (Bob correcting=> some cat(s)), we have a legal/grammatical but probably false statement. "lo mlatu" is a description that can apply to a cat, or the members of any collection of cats, in the universe of discourse (possibly including the non-domesticated species). I doubt that there exists anyone that would apply the name "la banthas." to all of these cats. If the name had been the Latin name for the cat family, well, maybe ... "lo" might be referring to a specific cat or set of cats, but it might not. We can't say, because there is no logically quantified variable. Let us look at a similar sentence: la banthas. du da poi [ke'a] mlatu (2) la banthas. du da poi [ke'a] mlatu Bantha = something such-that it="da" is-a-cat (ke'a is the usually omitted-as-understood relative pro-sumti, in this case referring back to "da") I say that this does not mean the same thing as (1) in that "da" is an existential variable, logically quantified as "some (at least one) x". In prenex form, (2) is: da poi [ke'a] mlatu zo'u la banthas. du da (2a) da poi [ke'a] mlatu zo'u la banthas. du da There exists some x such-that it="x" is-a-cat such-that Bantha = x (inverted E) and this statement is probably true, since I presume jimc did not coin the name at random but actually knows a cat with that name. There is a 'predication' (as opposed to 'identity') "predicate word" that is near-equivalent to "du", and that is "mintu" - "x1 is identical to x2" ("du" while etymologically tied to "dunli" is not really related due to place structure differences). There have been some probably legitimate but inconclusive debates about whether "du" and "mintu" are the same predicate. (Nora thinks not. She feels that "mintu" can be used more broadly, as in "this plate is the same as that one", when the two are interchangeable for the intended function. "du" would not be correct in translating such a statement, since presumably "this plate" and "that one" refer to different objects.) la banthas. mintu da poi [ke'a] mlatu (3) la banthas. mintu da poi [ke'a] mlatu Bantha is-identical-to something such-that it="da" is-a-cat da poi [ke'a] mlatu zo'u la banthas. mintu da (3a) da poi [ke'a] mlatu zo'u There exists some x such-that it="x" is-a-cat such-that (inverted E) la banthas. mintu da Bantha is-identical-to x I think that means approximately the same thing as (2), but we have now expressed a predication rather than an identity. In symbolic logic, we might write this as a predicate: Ex | M(Bantha, x) I believe that predicate logic does not write identity sentences as predicates. Lojban's predicate grammar requires even an identity sentence to be phrased as a predication, and as such is a mirror image of natural languages. One difference I can see that (may be) true about a predication and not an identity is tense. Lojban is tense-optional, but it does have the concept. I think it is meaningful to put a tense on "mintu", but not on "du". (Lojban's grammar allows both, but I would have trouble interpreting: ? la djan. ba du le speni be la salis. (4) ? John will mathematically-equal the spouse of Sally. = as having any meaning at all, while the following is at least meaningful to me: la djan. ba mintu le speni be la salis. (5) John will be-identical-to the spouse of Sally Assuming the sentence: la djan. speni la salis. (6) John is-the-spouse-of Sally. will some day be true, I would class (5) as true. Indeed, both may be true now, since "mintu" says nothing about change. "binxo" does. "le pu'u mintu" (the process of [x1] being identical to [x2]) is a strange concept, hard to think about. "le pu'u binxo" (the process of [x1] becoming [x2]) is not. jimc's claims the following 3 sentences are equivalent to "binxo": > x1 changes (7a) > x1 doesn't (pred) before (7b) > x1 does (pred) afterward (7c) Well, I'm not sure I agree. Certainly (7a) is involved in "binxo", but (7b) and (7c) are more like steps on the way to deducing (7a) - we identify change by relationships that come into being and others that cease. We have thus moved from linguistics to epistemology. So jimc's "semantic universal" isn't. I'll qualify this by saying that (7c) presumably is at least momentarily true at the end of the "binxo" process, though I've known some marriages that failed to last very long. But what can we make of: la djan. binxo la. djan. (8) John becomes John This violates (7b), but might be true in Lojban, by analogy with: le djacu cu binxo le djacu (9) The water (after freezing into ice and then melting) becomes the water (again). Turning now to jimc's: > loi bisli cu likbi'o (likti binxo) (10) > Some ice melts (liquid become) (I prefer Ice melts. or expanding to Some of the mass of all ice melts. but this is a side point.) jimc has recognized that there is an obvious interpretation to "likbi'o" (from "liquid-becomes") that allowed him to make this lujvo compound. This word is DIFFERENT from "binxo". All jimc's and mine and your desire to deduce its meaning analytically will fail to some extent, when we start playing at the level of semantics that we are in this discussion. Human language just doesn't work that analytically at the semantic level, and we do not have the goal in Lojban of making a semantically analytical language. Perhaps Loglan-sub-n+1 will. There is no argument in the place structure of "likbi'o" containing a description of the final state of the process. It is the metaphorical aspect of the source tanru that tells us that there is some liquid in the process, and based on binxo being roughly a "change with result", we know that the liquid is probably either the thing that changes or the result. In the case of "binxo" we the speakers of the language may make it a convention that "...bi'o" is "becomes lo ..." but we are debating that type of convention now and until the 5-year baseline ends since that is NOT part of what I see LLG's charter for the pre-baseline prescription. (Of course this one may be sufficiently stable-and-general that we may note it in the dictionary as a >descriptive< guideline based on prior usage before the baseline.) I think the x1 place of binxo is a description of some prior state that changes into x2, without necessarily any external agent involved. I think the x1 place of likbi'o is a description of some prior state that changes into a liquid, without necessarily an external agent involved. What you put in that x1 place should not change the meaning of the predicate word "binxo" or "likbi'o" (I should note that pc does not even claim this latter - he says that pragmatics overrides logic in interpreting the semantics of natural language use.) >In other words, every bridi (with arguments even if not specified by >words) expresses an event, but only some of them express predications, >called "claims" by some, "calling it to the listener's attention" by >others. Specifically, jufra (main-level sentences) and clauses linked >with "noi" always call attention. No. Every bridi is a predication, with the possible exception of one with predicate (selbri) "du". A predication (bridi) is a specification of a relationship between 1 or more arguments (sumti) which has a truth value: it is true if the relationship holds under the conditions of the sentence and false if it does not, (and is possibly indeterminate). Main-level bridi-sentences (jufra) usually make claims on the basis of that truth value. Some jufra-bridi may not make claims if modified by certain discursives and attitudinals (these can change whether a claim is being made, but do not change the truth value of the bridi), or when embedded in a logical structure. In a disjunction (XOR) between two sentences, it is not the case that both sentences are claimed as true. A description is a part of a sentence, most commonly a sumti, marked with "le", "lo", "loi", or other "descriptors" in selma'o LE and LA, or a vocative marked with COI or DOI vocative markers. By omitting the x1 sumti of a predication, it describes that sumti as something that can fill that place so as to make the descriptive predication true in the case of the "lo" series or agreeably identifiable in the case of most other descriptors and vocatives. "le", for example, makes no claim about the descripted thing, while "lo" does (we say "lo" is 'veridical'.) bridi in relative clauses are 'veridical' as well. The clause as a whole makes claims about the relative pronoun that is referenced in the clause, that it is part of the indicated relation(s). This MIGHT be modified if certain attitudinals are present, but there is no usage history or analysis of what such sentences might mean (in other words, I'm not going out very far on this limb). Events, properties, amounts, in the form of NU abstraction clauses, are just that - abstractions. Something concrete is not its abstract and the abstract is not its concretion(s). This is why I object to jimc's "... binxo lenu ...". You can evaluate the truth value of the bridi within an abstraction; we even have an abstraction cmavo for this: "jei". But the abstraction itself is a different predicate (a selbri), with its own sumti (usually only an x1): x1 is the event/property/truth value/amount/etc. of the predication (x1a abstraction-selbri x2a ...) Lojban has no defined semantics of "attention-calling", although there is a pattern, reflected in the observative construct, that particular attention is focussed on the beginning of the sentence, with lesser focus on the end of the sentence, and on any deviations from the speaker's normal word order. The following is an exchange between John Cowan (jc) and jimc (unmarked): >jc> ... >jc> Therefore your "x1 changes so that event x2 is true" should be rewritten as >jc> "x1 changes so that property x2 (a one-place predicate) is true of it". > >I pretty close to agree. How about "x1 changes so bridi-tail x2 becomes >true (was false and is later true) when x1 is replicated as its first >argument after conversion"? You've introduced the previously undefined term "bridi-tail". By your usage, regarding it as something that is missing an x1 that can be filled in (whether by replication or whatever), you want the word "description" as I defined above. The only propoer way to incorporate a description into a sumti is with a descriptor, as described above. An abstraction operator would turn that description (now merely a bridi with an elliptically unspecified x1) into something else, only abstractly related to the original, and the abstraction itself becomes a selbri, possibly a description, which with a descriptor can become a sumti. "bridi-tail" is a non-terminal figment of the grammar, consisting of the selbri and any and all sumti that come afterwards. The grammar says nothing about which sumti is x1 or how many sumti are found either before or after the selbri, so a bridi-tail may or may not be missing any sumti, or it may be missing more than one. A bridi-tail has no semantics - it doesn't mean anything (unless you decide that it is a complete expression, in which case it is an observative). The following, with my mild reformatting, and insertion of "cu" was from John Cowan, quoted by jimc, with the translation marked as un-correct ("*") by me. >jc> lemi ratcu cu binxo le du'u morsi >jc> *my rat changes-so-that the predication-of (it)-is-dead (is true) >jc> >jc> where the x1 place of "morsi" is elliptically the rat. >jc> Of course, this is not official LLG doctrine. :-) A correct translation, for those looking on for the first time, is, my rat becomes the predication that ...is-dead Regardless of the actual translation, the bridi implied by the English is a relation between: lemi ratcu a rat le du'u morsi a predication about a dead thing Rats do not "become" predications, so that if this place structure were adopted, "become" would be a truly inappropriate keyword. I daresay that no natural language includes many sentences relating rats and predications. One (to show the INTENDED usage of "du'u") might be: lemi ratcu cu jinvi le du'u morsi lemi ratcu cu jinvi le du'u morsi My rat opines-that the predication (...(unspecified) is-dead) is true _________ Hope this is neither clear-as-mud nor tinder-for-flaming. I would like comments, especially on what is unclear, since this is my first attempt to cover logical aspects in writing, and I WILL have to talk about these aspects in the textbook. lojbab