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!Lojban Wave Lessons Continued (part three):

!!!by la klaku with help from la .kribacr., la xalbo and others, autumn 2011.



Welcome to the third part of The Wavelessonscontinued. If you want to go back to ((wavelessonscontinued|the first part)) or ((wavelessonscontinuedp2|the second part)), just click on the words representing them in this sentence. This third part is about advanced Lojban. The Lojban in this part is rarely relevant when speaking Lojban in normal contexts, but it pops up quite often when speaking about language and logic. 

These corners of Lojban is for the most part experimental, new and complex, so you should expect a lot of changing definitions, outdated definitions and misunderstandings on the part of the author of this text.



!!Lojban Lessons - Lesson twenty-seven (lojban logic: da, bu'a, zo'u and terms)

The stated topic of this lesson needs some justification: This lesson is not really about how do to logic in Lojban, since firstly, logic is presumably the same in all languages, and secondly, actually teaching logic would be totally impractical in one single lesson. Rather, this lesson is explains some constructs which resembles those which logicians use. It turns out they have a remarkable wide range of uses in Lojban.



Getting involved in the more obscure details of these logical constructs can be mind-warpingly difficult, and there will always be some disagreement in the corners of this part of the language.



Learning these logical constructs requires one to learn a bit about constructs which are not logical in nature. Let's begin with ''zo'u''



__''zo'u''__ Separates prenex from bridi



Before any ''zo'u'' is the prenex, after ''zo'u'' is the bridi. Informally, a prenex is a place in front of the bridi, where you put a bunch of terms. A term is an English word given to some kinds of Lojban constructs: Sumti, sumtcita with or without sumti attached, ''na ku'' and an abomination called __termsets__, which I refuse to include in these lessons. The prenex is not part of the bridi, but any terms put inside it gives us information about the bridi. One can, for example, use it to state a topic as shown thus:



''lo pampe'o je nai speni zo'u mi na zunre'' - "Concerning lovers who are not spouses: I do not approve". The benefits of kind of sentence structuring is questionable, but it's always good to have some variation to play with. Furthermore, constructing sentences this way resembles Mandarin (and other languages) closely, meaning it might seem more intuitive for speakers of that language.

__''pampe'o''__ x1 is a lover of x2

__''zunre''__ x1 approves of x2 (plan, event or action)



Of course, the relation between the terms in the prenex and the bridi is vague. One can imagine any sumti in the prenex bearing the same relevance to the bridi as if they were put in the bridi after a ''do'e'' sumtcita, and any sumtcita in the prenex doing pretty much the same as if they were in the bridi. It is quite possible to put terms in prenexes without any clear hints as to how the term may relate to the bridi:

''le ti gerku zo'u mi to'e nelci lo cidjrpitsa'' - "Concerning this dog here: I dislike pizza." It leaves you guessing about the reason for mentioning the dog.

__''cidjrpitsa''__ x1 is pizza with topping/ingredients x2



If the prenex contains ''na ku'', it's pretty straight forward: The entire bridi is negated, just as if the bridi itself began with ''na ku''.



So how long does a prenex last? It lasts until the following bridi is terminated. If that is not desired, there are two ways to make it apply to several bridi: One is to put some kind of connective after the ''.i'' separating the bridi, and another method is to simply include all of the text in ''tu'e'' ... ''tu'u''-brackets. These brackets work pretty much by gluing all the bridi together and makes all sorts of construct apply to several bridi.



Now that we covered ''zo'u'', the first "logical" words we can use it with are these:

__''da''__ logically quantified existential pro-sumti 1

__''de''__ logically quantified existential pro-sumti 2

__''di''__ logically quantified existential pro-sumti 3



These words are all the same, like the mathematical variables x, y and z. Once you have defined them, however, they keep refering to the same thing. These words are defined in the prenex of bridi, meaning that when the prenex stop applying, the definition of these three words are cancelled.



The words ''da'', ''de'' and ''di'' can refer to literally any sumti, which makes them kind of useless unless restricted in some way. The first and foremost way to restrict them is to quantify them: They are not called "logically quantified existential pro-sumti" for nothing. They are pro-sumti, they are most useful when quantified, and they are existential. What does it mean, being "existential"? It means that if they are used, that implies that they actually refer to something which exists. An example:



The statement ''pa da zo'u da gerku'' has ''pa da'' in the prenex, which means "Concerning one existing thing:", and then ''da'', now defined, is used in the bridi ''da gerku''. Translated to English, this means: "There exists one thing which is a dog". This is obviously false, there are around 400,000,000 of them in the world. If ''da'' and its sisters are not quantified, the number ''su'o'' is the default. Thus ''da zo'u da gerku'' means "There exist at least one thing which is a dog", which is true. Notice here, that any quantification must be more or less exact in order to be true: Of course one dog exists, but in Lojban, ''pa da zo'u da gerku'' means not only that does one dog exists, but also that no more than one does. 



There are a few specific rules to these existential pro-sumti:

- If the quantifier ''ro'' is used before ''da'', it instead refers to "all which exists".  

- If the same variable is quantified several times, the first quantification is the one which sticks: Any later quantified instance of that variable can refer only to things which are also being referred to by the first instance of that variable, and any later non-quantified instance of that variable will gain the first quantifier. To use an example: ''ci da zo'u re da barda .ije da pelxu'' means "There exists three things such that two of them are big and all three are yellow". ''re da'', being after ''ci da'', can only refer to two of the already stated three things. When ''da'' appears without a quantifier, ''ci'' is assumed.

- If there are several terms in the prenex, the terms are always read left to right. Sometimes, this matters: ''ro da de zo'u da prami de'' means "Concerning all the things X that exists, concerning at least one thing Y: X loves Y". This is the same as "All things love at least one thing.", where the "thing(s)" can be anything, including the thing itself. Note here that ''de'' can refer to different things for each ''da'' - the thing which is referred to by ''de'' is dependent on the ''da'', since it came before it in the prenex, therefore each thing might love something different. If we switched the places of ''da'' and ''de'' in the prenex, a different result would arise: ''de ro da zo'u da prami de'' = "Concerning at least one thing Y, concerning all X which exists: X loves Y", meaning "There exists at least one thing which everything loves".



Of course, both claims are completely false. There are many things which loves nothing - rocks, or abstract concepts, for example. Likewise, it's impossible to concieve of something which everything loves, since "everything" also encompasses non-sentient things. We need better ways to restrict what these variables can point to. One good way of doing it is to make them the subject of a relative clause:

''ro di poi remna zo'u birka di'' = "Concerning all X that exists, which is human: X has one or more arms." or "All humans have arms", which is true, at least when speaking in a potential, timeless sense.

__''birka''__ x1 is an arm of x2

When restricting claims using this kind of logical "existential" variable, it's very important to remember that unless there is an explicit ''no'' as a quantifier, these kind of statements always imply that there __actually exists__ something which can be referred to by ''da''. Therefore, any kind of non-negated statement where ''da'' points to something which does not exist is false, as in this example: ''ro da poi pavyseljirna zo'u da se jirna'' - "All unicorns have horns". This is wrong because, since ''da'' is existensial, it also means that there must exist at least one unicorn.

Interestingly, when using a relative clause, the variable is being restricted regardless of whether you use ''poi'' or ''noi''. This is because ''re da noi gerku'' still only can refer to two things which are humans. Therefore, ''noi'' makes little sense with ''da''/''de''/''di''. Any clause is always restrictive, unless it's really stupid and obvious like ''de noi gerku cu gerku''.



In fact, you don't really need the prenex to define the variables. You can use them directly as sumti in the bridi, and quantify them there. You only need to quantify them the first time they appear, though. Thus, the sentence about humans having arms could be turned into ''birka ro di poi remna''. The order of the variables still matters though, and so the prenex can be used to avoid having to mess up your bridi to place the variables in the correct order. When having more variables, a prenex is usually a good idea.



The second kind of logical words are basically the same as the three we have already been though, but these are pro-bridi instead of pro-sumti:



__''bu'a''__ logically quantified existential pro-bridi 1

__''bu'e''__ logically quantified existential pro-bridi 2

__''bu'i''__ logically quantified existential pro-bridi 3



These work pretty much the same way as the other three, but there are a few points which are important to mention:

Since only terms can go in the prenex, these pro-bridi need to have a quantifier in order to make them into sumti. When quantified in the prenex, however, the quantifier works very different from quantifiers with normal selbri: Instead of quantifying the amount of things which fits the x1 of the selbri variable, it directly quantifies the amount of selbri which applies. Again, the default quantifier is ''so'u''. Thus, instead of ''re bu'a zo'u'' meaning "Concerning two things which is in relationship X:", it means "Concerning two relationships X:"



It's probably good to see an example pf ''bu'a'' put to practice:

''ro da bu'a la .bab.'' = "Considering all X which exists: X is in at least one relationship with Bob" = "Everything is related to Bob in at least one way.". Notice again the order matters: ''bu'a ro da zo'u da bu'a Bob'' means: "There is at least one relationship such that everything that exists is in that relationship with Bob". The first statement is true - for any one thing, one can indeed make up some selbri which relates any guy called Bob and it. But I'm not sure the latter is true - that one can make a selbri which can relate anything, no matter what it is, and Bob.



Let's have an example which quantifies selbri:

''ci'i bu'e zo'u mi bu'e do'' - "Concerning an infinite amount of relationships: I am in all those relationship with you." or "There exists an infinite amount of relationships between us"

You can't quantify the selbri variables in the bridi itself, though. Then it will act as a sumti: ''mi ci'i bu'a do'' is not a bridi.



!!Lojban Lessons - Lesson twenty-eight (notes on abstractors)

The notion of abstractions and abstractors is quite fundamental to Lojban, and you have already learned the mechanism twenty-two lessons ago. There are, however, many abstractors with slightly different semantic meaning to explore, as well as a single important mechanism which has not been covered yet. In this lesson, all twelve abstractors will be elaborated on. The fa'orma'o for all of these is ''kei''.



The first and most basic abstractor is ''su'u'', which you already know.

You might remember from lesson six that ''su'u'' had a place structure with two sumti places. The second sumti place of ''su'u'' makes the word versatile, as the x2 can be used to specify how the abstraction should be considered.

The English phrase “that I love you” is definitely a sumti, since it's meant to function as a subject or object in a sentence. It's also clearly made from an abstraction. It can therefore be translated (''lo''/''le'') ''su'u mi do prami''. Without the context of the English sentence, though, it's hard to guess what kind of abstraction was meant. “I will die happy by the time that I love you.” treats the abstraction like an event happening in time. “The truth is that I love you.” treats the abstraction like a bridi, which can be considered true or false. In the sentence “The most beautiful thing in the world is the idea that I love you”, the abstraction is considered an abstract concept. Using the second sumti place of ''su'u'', these can be explicitly distinguished between:

''le su'u mi do prami kei be lo fasnu'' is an event.

''le su'u mi do prami kei be lo bridi'' is a bridi.

''le su'u mi do prami kei be lo sidbo'' is a concept.



Using ''su'u'' this way, the semantic, though not grammatical, range of all abstractors can be covered. More usually, though, other abstractors are used. ''nu'', which you also know, treats the abstraction as an event.

__''nu''__ x1 is an event of BRIDI



There are many ways to view an event, and so there are four other abstractors whose semantic are all covered by nu, but more specific.

__''mu'e''__ x1 is a point-like event of BRIDI happening

__''za'i''__ x1 is a state of BRIDI being true

__''pu'u''__ x1 is a process of BRIDI unfolding through stages x2

__''zu'o''__ x1 is an activity of BRIDI consisting of the repeated event of x2



The understanding of these abstractors is tied to the understanding of event contours. ''mu'e'' is akin to the event contour ''co'i'' in the sense that both treat the bridi as point-like in time and space:

''le mu'e mi kanro binxo cu se djica mi'' – ”Me becoming healthy is desired by me” has the semantic meaning that the process of becoming healthy is not being considered. If it consists of chemotherapy, it is plausible that this process is not desired at all. “Becoming healthy”, in a point-like sense is desired, however.



''za'i'' is like the event contour ''ca'o'' in the sense that ''le za'i BRIDI'' begins to apply when the bridi begins and sharply ends when the bridi ceases to be true, much like ''ca'o''.

''za'o za'i mi kanro binxo'' means that the state of me becoming healthy took too long time; that the time between my health beginning to improve and be actually being healthy was long-winded.



The actual treatment is perhaps better caught by ''pu'u'', which, like event contours in general, puts emphasis on the entire event as unfolding through time. ''.ii ba zi co'a pu'u mi kanro binxo vau .oi'' expresses fear that the painful process of becoming healthy is about to begin.The x2 is filled by a sequence of stages, which can be made by interspacing the stages with the non-logical connective ''ce'o'': ''ze'u pu'u mi kanro binxo kei le nu mi facki ce'o le nu mi jai tolsti ce'o mi renvi'' means “something is a long process of me becoming healthy consisting of the stages A ) I find out B ) something about me begins C ) I endure.”



Finally, the semantics of ''zu'o'' treats the abstraction as consisting of repeated actions: ''jibri mi fa lo zu'o mi zbasu lo karce'' – “The activity of me making cars is my job” is accurate if, for instance, the speaker works at a car-producing factory. Here, her activity of producing cars consists of the repeated actions A ) she lowers frame 1 onto car 1 B ) she welds frame 1 to car 1, C ) repeat with car 2. The x2 here is also a sequence.



Note the difference between ''mu'e bajra'', ''za'i bajra'', ''pu'u bajra'', ''zu'o bajra'' and ''nu bajra''. The point-like event of running puts emphasis on the event happening, but nothing else. The state of running begins when the runner begins and stops when the runner stops. The process of running consists of a warm-up, keeping a steady speed, and the final sprint. The activity of running consists the cycles of lifting one foot, moving it forward, dropping it down, repeat with the other foot. All of these are covered by the event of running.



The abstractor ''du'u'' has nothing to do with events and only considers the bridi inside the abstraction as a bridi:

''.ui sai zi facki le du'u zi citka lo cidjrpitsa'' – “Yes! I just found out that pizza will be eaten soon!”. What is being discovered is the truth of an abstract bridi, not an event. In general, abstractions like truths, lies, things being discovered or believed are all pure bridi, so ''du'u'' is appropriate. 

__''du'u''__ x1 is the bridi of BRIDI expressed in sentence x2

For bridi to exist (or at least to have any relevance), they must be expressed in some medium, whether this is speech, thought or writing. The term “expressed” is misleading if it is expressed only in the mind of someone but the term nonetheless applies. Specifying which medium the bridi is expressed in is what the x2 of ''du'u'' is used for:  ''.ui facki le du'u jai cidjrpitsa kei zo'e pe le mi mamta'' – “Yay, discovered that something about pizza, expressed in something that had to do with my mother!”. The translation is clumsy, but probably means that the speaker's mother told him that pizza was coming.



The next abstractor, ''si'o'', is derived from the gismu ''sidbo'' meaning “idea”. It's relatively easy to understand: ''le si'o mi mamta'' is the very idea that I am a mother. Similarly, ''le si'o prami'' is “The concept that someone loves someone”, which can be translated as merely “Love itself.” All ideas need someone to reflect on them, and the second sumti place of ''si'o'' mirrors this:

__''si'o''__ x1 is an idea of BRIDI as imagined by x2

''le si'o nanmu kei be do cu xlali vau pe'i'' – “Your idea of manliness is harmful, I think,”



The abstractor ''jei'' is very different from those covered so far, because of its place structure:

__''jei''__ x1 is the truth value of BRIDI under epistemology x2

The first sumti place is not an abstracted bridi, but a verdict of truth, which lies between 0 (false) and 1 (truth) inclusive. These two numbers are used to represent falsehood or truth, and while the x1 of the abstraction is technically a number (''li''), it's not very useful to do mathematics on statements such as "true" or "false", so they should probably not be considered mathematical quantities.

The x2 is often left vague.

''.y li pi so'u jei go'i kei tu'a mi'' – “Uuh, that's not very true, according to me.”



''ka'' is glossed "property" or sometimes "aspect", which is not clear at all. It refers to the essence of fitting to a certain selbri, thus ''lo ka clani'' is "tallness", and ''lo ka djica'' is "desire". In fact, for any selbri, "X satisfies the selbri" is the same as "X is characterized by the property of the selbri".

This selbri may have some sumti places filled out, allowing very specific properties to be expressed: ''le ka pendo la xanz.krt gi'e badri'', "The property of being a friend of Hans Kurt and being depressed". This gives rise to strong ambiguity: Since ''ka'' is about fitting to a selbri (or even an entire bridi), one must be able to specify which sumti place we are talking about: "The property of swimming in something" is very different from "The property of something swimming in you". 

Of course, this cannot always be up to context, and so we have a word, ''ce'u'', which identifies which sumti place is being focused on:

__''ce'u''__ Sets focus on sumti place in abstraction.



''ka''-constructs are used in all kinds of selbri, ''zmadu'' and ''mleca'' introduced in lesson nineteen is examples of such selbri. So: what is the difference between ''mi do zmadu lo ka la liz prami ce'u'' and ''mi do zmadu lo ka ce'u prami la liz''?

Answer: ~~grey,grey: The first one means "Liz loves me more than you", the second "I love Liz more than you do"~~

The ''ce'u'' can be elided, in which case it is understood to fill the first unfilled sumti place of the abstraction.



Lastly, we have the word ''ni'', the definition of which is much contested and discussed among Lojbanists. At least two slightly different meanings can be conveyed with ''ni'', possibly more, and it has not been settled which one is the correct use of ''ni''. Let's first see how the word is glossed:

__''ni''__ x1 is the quantity of BRIDI as measured at scale x2

Unlike the x1 of ''jei'', the x1 of ''ni'' __is__ useful to treat as a number. The discussion arises because it's possible to quantify bridi in several ways. The following four examples show two different ways:

__''xamsi''__ x1 is the/a sea/ocean of planet x2 made of fluid x3

__''cenba''__ x1 varies in property/amount x2 by amount/degree x3 under conditions x4

''le xamsi cu cenba le ni ce'u blanu'' - "The ocean varies in blueness" (meaning that it might be less or more blue, contrast with ''le xamsi cu cenba le ka ce'u blanu'', which means that it varies in whether it's blue or not)

''mi zmadu do lo ni pendo ce'u''- "I have more friends than you"

Where the first example uses ''ni'' to quantify how much an object is characterized by a selbri, and the second example to quantify how many x are characterized by a selbri.

This is, of course, a problem to a language like Lojban, which prides itself with unambigiuty. This problem have not been solved yet, and so as of now, we are stuck with ''ni'' having dual meanings.  

There is also slight disagreement about what it makes sense to quantify, though this is a philosophical rather than linguistic debate. Some texts stress that those things which are not easily quantifiable like ''le ni mi tunba do'', the amount of me being your sibling, makes no sense i a ''ni''-construct. For others this is a perfectly reasonable thing to say, even though actually measuring it is not practical, similarly to the English quantification of love in the sentence "I didn't know how much I loved you until now".

Both ''ka'' and ''ni'' always has an explicit or implicit ''ce'u''.



!!!End of lessons

Sorry, but as of now, there are no more lessons in this series. Perhaps more will be added later.


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