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!!!Made by la klaku with help from various lojbanists. Based on the work of la .kribacr. Spring 2013.

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of Lojban is for the most part experimental, new or complex, so you should expect a lot of changing definitions, outdated definitions, disagreements and misunderstandings on the part of the author of this text. Sorry about that.

!!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 explains some constructs which resemble 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 zanru'' - "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
__''zanru''__ 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 vi 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 sumka'i 1
__''de''__ logically quantified existential sumka'i 2
__''di''__ logically quantified existential sumka'i 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 sumka'i" for nothing. They are sumka'i, 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 sumka'i:
- If the quantifier ''ro'' is used before ''da'', it instead refers to "all which exists".
- Importantly, the usage of an existential sumka'i only asserts that such a thing exists __in the domain of truth where it's used__. Thus, in the sentence ''so'e verba cu krici lo du'u su'o da crida'', does not state ''da crida'', since its "domain of truth" is only inside the du'u-abstraction. Generally speaking, abstractions contain their own domain of truth, so using ''da'' and friends inside an abstraction is usually safe.
- 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 brika'i instead of sumka'i:
__''bu'a''__ logically quantified existential brika'i 1
__''bu'e''__ logically quantified existential brika'i 2
__''bu'i''__ logically quantified existential brika'i 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 brika'i 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 of ''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: ''su'o bu'a ro da zo'u da bu'a la .bab.'' 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. There are some situation where this will become problematic - lesson twenty-nine will teach how to overcome those problems.


!!Lojban Lessons - Lesson twenty-eight (types)
This lesson along with the following three lessons will be on semantics - how to interpret the meaning of certain constructs. This lesson is on the meaning of different types of sumti, and will get philosophical and a bit hazy. The following two will be on abstractions, which, even though you already became familiar with them twenty-two lessons ago, will become more technical as I attempt to explain their semantic and grammatical properties.

Teaching (and learning) semantics is much more tricky than teaching grammar, especially in Lojban, where grammar is black-or-white, but semantics isn't. Therefore, I find it necessary to repeat the disclaimer from the beginning of the third part of Wavelessonscontinued: The following is not official, but rather an (educated) opinion on the language.

Bad grammar is easy to spot in Lojban - in fact it's unambiguously correct or not. In contrast, saying that a jufra is semantically wrong is the same as saying that the speaker is using Lojban to think wrongly about the world. It's not saying "You can't say X" as much as "You can't interpret X in this way. You should interpret it this way". Placing these restrictions on composing and understanding language is a slippery slope leading to restrictions on creativity, and even presupposing of certain metaphysical viewpoints while excluding others.

Then why include semantic standards in a textbook? Shouldn't any speaker be free to say anything, and any listener be free to let that speech mean whatever they want?
This is a matter of measure. Given that extreme, that is, if no semantic standards were set, everything could mean anything, and all communication would be meaningless. In any language which aims to facilitate communication, one must be able to express oneself in such a way that one can trust that ones message is interpreted in the desired way. Semantic rules of Lojban do not exist in order to prevent people from saying A. They exist to prevent people from saying B and having others think they meant A.

This lesson is on types. The word __type__, informally translated to ''klesi'', is used by Lojbanists to describe the existential nature of the things sumti describe. This nature is, and must be, the same as the nature of the things described by other languages such as English. However, in Lojban, the different ways of making sumti denote which type a sumti belongs to, so while the exact natures of sumti can be ignored in English, Lojbanists have to deal with them.

When speaking of types, Lojbanists often mention what type a sumti __really is__. When beginning from the beginning, we have to remember that this certainty is not philosophically well grounded. Taking a materialistic viewpoint, the natural world of particles and waves does not correspond well with human understanding of say, hatred, which is not defined by any specific particles, nor any specific brain activity. It is a purely abstract concept. Similarly, in an extreme inductionist viewpoint, such as that taken by Hume, all we humans experience are subjective impressions over time - a long string of events, or, some people argue, a bunch of qualia (This is __green__. This is __crispy__. This is __round__. This is __tasty__. => "This is an apple".) This viewpoint, however, does not correspond well to human understanding of say, a cat, whose existence must be presumed to continue even when it invokes no qualia in humans, whose qualia vary among different cats, and whose death smoothly strips it of its catlike qualia.

In other words, while one can take philosophically consistent worldviews where objects and concepts don't exist, such world views are unfruitful for conducting human affairs: In our lives, we simply need to refer to objects, and pretend that they actually exist as such. One famous story tells of a philosopher, Samuel Johnson, who, frustrated about the philosophical soundness and un-refutability of a fellow philosopher's belief that the physical world does not exist, furiously kicks a rock yelling, "I refute it __thus!__"

In Lojban, most sumti are made from selbri one way or the other, which means that at the core of most sumti lies a selbri, an action, something which something __does__. The Sun is not usually referred to as {la solri}, "The Sun", but often {lo solri}, "Something which is being a sun". There are many confusing philosophical implications of this: As stated before, it's hazy at best what it means "to cat" and when something begins catting or "stops catting". A fictional language with similar properties is described in a neat short story, "Tln, Uqbar, Orbis Tertius" (where "The Moon rose over the ocean" is phrased using similar verb/adverb-derived nouns: "Upward behind the onstreaming it mooned"). In that short story, the language is about to lead to the collapse of society because the worldview which such a language implies is unfit for dealing with the realities of Earth.

The take home point of all this is: Precise definitions of the different types of sumti are impossible, because these categories do not correspond to the real world. Nonetheless, we need these categories when speaking.
There may possibly be an infinite amount of types, but I'll go through the ones which are dealt with most often in Lojban:

Material objects are perhaps the easiest to understand, even though they're hard to defend philosophically. They always have a place in both time and space, but they're considered to be a constant existing through time. That is, objects are not considered temporally: A banana carries with it its unchanging banana-ness even as it ages, until it begins breaking down and stop being a banana at all. If one could freeze time for all bananas, they would stay bananas during that frozen time.

Events are, like objects, places in space and time, but events are considered as unfolding over time: The temporal aspect is as important as the spacial. A banana can be considered an event, but in that case, the event of being a banana is composed of the changes the banana undergoes over time, whereas what makes a banana an object is all that which doesn't change. Freezing time would also freeze the event of being a banana.

Functions are a term used by a few Lojbanists to describe a group of types. All functions are abstract concepts and as such don't really exist in the real world on their own. The nuts and bolt of functions is the subject of lesson thirty; here, we focus on their semantics alone. There are a few types of functions:

Selbri are something you're already well familiar with. It describes an act of doing or being. ''crino'' understood as a selbri means "being green", ''darxi'' means "to hit". A selbri on its own is devoid of the sumti who's doing or being that selbri. As such, they're divorced from any particular instance of being green or hitting, and can therefore be understood as a kind of generalized events. They're used for sentences where no particular instance of that selbri being applied comes to mind. For instance, if I'm looking forward to my wedding next Wednesday, I'm thinking about some event placed in space and time (even if the wedding never actually takes place for some sad reason), whereas if I'm saying that I'd like to become married one day, I desire the act of marriage, and thus I desire the selbri, or rather, that the selbri be applied to me.

Amounts have almost the same grammatical properties as selbri, as you'll see in two lessons. Semantically, however, they're quite distinct. An amount is __how much something fits a selbri__, which is something completely different from the selbri itself. An amount is some kind of number, or can be represented by some number, exact or inexact, no matter whether what is quantified is practically measurable.
There is some disagreement about whether it's correct to use an amount abstraction to quantify something which is in principle unmeasurable. Thus, the amount of my greenness is certainly valid, since that could be measured by say, a digital camera, but speaking about the amount of me being Bob's friend may not be accepted philosophically. A great example which demonstrates the difference between amounts and selbri when applied to specific sumti is the following: "I change in blackness": When "blackness" is considered a selbri, it means that change from being black to not being black or the other way around. When "blackness" is considered an amount, it means my skin turns more or less black (as it does during the winter when there's little sunlight).

Concepts are maybe functions and maybe they're not, depending on who you ask. Their position as maybe-functions is explained in lesson thirty. Concepts, unlike selbri and amounts, cannot be applied to sumti. There can be no talk of fitting a concept, like there can be of whether or not you are fitting a selbri or measuring the amount of fitting a selbri. A concept does not exist in the real world. A concept is not even represented in the real world, like amounts or selbri can be when theyre applied to sumti. A concept, say warfare, exists only in the minds of people, and is understood as the meaning of the word war. Thus "love" understood as a concept is the idea of what love is, no matter who loves and who is being loved.
Perhaps an example can demonstrate the difference between amounts, selbri and concepts:
In "I like loving" and "I like being loved", we are speaking of a selbri.
In the sentence "I like how much I love", I like an amount, and when saying "I like love", I refer to the concept of love.

Bridi is a type which you're also familiar with. A bridi is certainly not a function, but it does bear some relation to functions, as we'll see later. Bridi themselves are imaginary; they exist not in the real world, but inside texts, the next type to explain. However, bridi are not composed of whichever specific symbols are used to express them - because bridi are imaginary, different sentences may express the same bridi. It can be that the sentences are in different languages, that the word order is changed, or that different words are used to refer to the same sumti. Thus ''mi do prami''/''mi prami do'', "I love you", ''mi ko prami'' and ''do mi prami'' (when spoken by the person to which ''do'' refers in the first sentence) all refer to the same bridi. Bridi always have their full place structure filled by something with a non-zero value.

The concept of a text is close intertwined with the concept of a bridi. All bridi are contained in texts, though not all texts contain bridi. Indeed, one might define a text as something that can contain a bridi, but this can easily lead to circular definitions when attempting to define what bridi are. The current understanding of what things should be considered texts is vague at best. Like bridi, texts are something ethereal, something we can imagine exist in a realm outside the physical world. While these lessons certainly are a text, the text is not made of the paper these lessons are printed on, nor the magnetic fields which constitutes the bytes it's stored on. Those physical media only __represent__ the text. But what exactly can represent a text? Words, certainly. But what about body language? And do actions really speak __texts__ louder than words? This is not an issue I'll attempt to answer or even give a shot in these lessons.

Sets are much easier to deal with. They're a kind of meta-type: A imaginary box, in which a group of sumti is packed into. This box has very little to do with what's inside it. A big set does not mean that the things in the set are big, but that there are many things in the set. Sets have very few properties, therefore sets are only used when speaking about the number of things in a given category, the number of things shared between several categories, the criteria for including things in the category etc.

The last used type is the truth value. I've only seen it in use a handful of times, and only include it here because it'll be relevant when discussing a certain abstraction in the next lesson. A truth value is some verdict that a bridi is true, false, or anywhere in between. The nature of a truth value is a verdict, "True", "False", "Mostly true" or the like. It's often represented by a number, such as 0 (false), 1 (true) or 0.5 (halfway true), but this a simply a representation of the truth value, and not the value itself. One might as well represent it by a color, ranging from red to blue.

!!Lojban Lessons - Lesson twenty-nine (semantics of simple abstractions)
Having acquired a terminology suitable for the discussion of types, we can now more easily take on the semantics of abstractions. Most often, an abstraction is merely a bridi considered as a certain type. We begin with what I consider the simplest of abstractions:
''__nu__'': x1 is an event of BRIDI happening
You're already familiar with this word and how it's used. A ''nu''-abstraction is always an event, and as such, it's situated in one particular time and space. Thus:
''mi catlu lo nu lo prenu cu darxi lo gerku'' - "I watch a person hitting a dog" is a proper event, whereas
''mi kakne lo nu bajra fi lo mi birka'' - "I can running on my arms" is wrong, because no particular event of running is implied: The running you're able to do is a selbri - a generalized event, and the Lojban sentence above should sound as badly phrased as its English translation.

There are many ways to view an event, and so there are four other abstractors, which all also create events. The meaning of these abstractions are all covered by ''nu'', but more specific. I'll go through them all here:
''__mue__'': x1 is a point-like event of BRIDI happening
''__zai__'' x1 is a state of BRIDI being true
''__puu__'' x1 is a process of BRIDI unfolding through stages x2
''__zuo__'' 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. ''mue'' is akin to the event contour ''coi'' in the sense that both treat the bridi as point-like in time and space:
''lo mue 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 painful chemotherapy, it is plausible that this process is not desired at all. Becoming healthy, in a point-like sense is desired, however.
''zai'' is like the event contour ''cao'' in the sense that ''lo zai BRIDI'' begins to apply when the bridi begins and sharply ends when the bridi ceases to be true, much like ''cao''.
''zao zai mi kanro binxo'' means that the state of me becoming healthy took too much 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 ''puu'', which, like event contours in general, puts emphasis on the entire event as unfolding through time. ''.ii ba zi coa puu mi kanro binxo .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 ''ceo'': ''zeu puu mi kanro binxo kei lo nu mi facki ceo lo nu mi jai tolsti ceo lo nu 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 ''zuo'' treats the abstraction as consisting of a number of repeated actions: ''lo za'a zo'u darxi lo tanxe cu rinka lo ca mu'e porpi'' "The observed activity of beating the box caused its current brokenness" is more accurate than the similar sentence using ''nu'', because ''zu'o'' makes it explicit that it was the repeating of the action of beating, not a particular instance of beating which broke the box.

The x2 of ''zu'o'' is either one event or a sequence which is repeated. To be unnecessarily explicit, we could have stated that the cause of the current brokenness was ''lo zo'u darxi lo tanxe kei lonu lafti lo grana kei ku ce'o lonu muvgau lo grana lo tanxe kei ku ce'o'' ... and so on.
Note the difference between ''mue bajra'', ''zai bajra'', ''puu bajra'', ''zuo 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 aspects are simultaneously covered by the event of running, ''nu bajra''.

Another type of abstractor is the experience abstractor, ''li'i'':
''__li'i__'': Experience abstractor: x1 is x2's internal experience of BRIDI
An experience can be considered an event type. It has almost the same attributes: It's placed in space, there's focus on the time over which it unfolds, and it's not a function.
Unlike event abstractions, however, an experience is explicitly mental - a ''li'i''-abstraction cannot be said to exist outside the mind of a person. This difference is purely semantic, and exchanging event and experience abstractors would not be considered a type failure in the same sense as ''mi kakne lo nu...''. It might not make sense, as in ''lo kacma cu vreji lo li'i lo mi pendo cu cliva kei mi'' - "A camera recorded my experience of my friend leaving". But then again, cinema is dependent on cameras being able to record the actors' emotions.
It does, I think, make complete sense to write ''mi ciksi lo li'i lo mi pendo cu cliva kei mi'', ''lo li'i lo mi tunba cu morsi cu mukti lo nu mi catra'', and the like.
''li'i'' is derived from ''lifri'', and is indeed a ''se lifri'' - an experience.

A ''du'u''-abstraction is probably the other kind of abstraction you're used to seeing, beside ''nu''.
''__du'u__'': Bridi abstractor: x1 is the bridi of BRIDI, as represented by text x2
According to the standard, abstractions like truths, lies, things being discovered or things being believed are all pure bridi:
''.ui sai zi facki lo duu zi citka lo cidjrpitsa'' Yes! I just found out that pizza will be eaten soon!
''mi krici lo du'u la turni cu zbasu pi ro lo munje zi'o'' - "I believe The Lord created all of the universe"
What is being discovered or believed is the truth of an abstract bridi, so ''du'u'' is appropriate.
As you can see from the definition of duu, the x2 of ''du'u'' is used for the text in which the bridi is contained. As stated before, the nature of texts is hard to nail down, but in practice, ''du'u'''s x2 can be used to express indirect quotation:
''.ue do pu cusku ku'i lo se du'u do nelci lo ckafi'' - "Oh! But you said that you liked coffee!"

Out of obligation, this lesson will include the truth value abstractor, ''jei''. Let's see the definition:
''__jei__'': Truth abstraction: x1 is the truth value of BRIDI under epistemology x2
''jei'' is rarely used, not because truth abstractions are infrequently needed, but because most Lojbanists use other mechanisms to obtain them. The real use of ''jei'' is whenever a truth value which is not "true" or "false" is needed, i.e. practically never. I'll give a couple of examples:
''mi di'i pensi lo jei mi merko'' - "I often think about whether I am American or not" (contrast with "I often think about how American I am", which uses an amount abstraction, not a truth value)
''li pi bi jei la tinjin cu mikce'' - "It's 80% true that Tindjin is a doctor" (whatever that might mean)

To conclude this lesson, the abstractor ''su'u'' is a universal abstractor, whose x2 can be used to specify how the abstraction should be considered - for example, which type the abstraction is. It has already been defined, but we might as well do it again:
''__su'u__'': Universal abstractor x1 is the abstraction on BRIDI considered as x2 / x1 is the abstraction of BRIDI of type x2.
The idea of this abstraction is easy, so I'll just give a few examples of it in use and leave it at that:
The English phrase that I love you is definitely a sumti, since its meant to function as a subject or object in a sentence. Its also clearly made from an abstraction. It can therefore be translated ''lo suu mi do prami''. Without the context of the English sentence, though, its hard to guess what kind of abstraction was meant. I will die happy by the time that I love you. treats the abstraction as 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. "You don't know how much I love you" treats the (nearly identical) abstraction as an amount. Using the second sumti place of suu, these can be explicitly differentiated:
''lo suu mi do prami kei be lo fasnu'' is an event.
''lo suu mi do prami kei be lo bridi'' is a bridi.
''lo suu mi do prami kei be lo klani'' is an amount.
Using ''suu'' this way, the semantic (though not grammatical) range of all abstractors can be covered. More usually, though, other abstractors are used.
Finally, Lojbanist J. Cowan translated the title of the book The Crucifixion of Jesus Considered As A Downhill Bicycle Race as ''lo su'u la .iecuas. kuctai selcatra kei be lo saordzifa'a ke nalmatma'e sutyterjvi''.


!!Lojban Lessons - Lesson thirty (semantics of functions)
Functions are a group of two-three types of abstractions. The term's not official, but I'll use it here anyway.
The definition of functions is closely related to the neat little word ''ce'u''. ''ce'u'' is a sumka'i which fills one sumti place. It's only found usage inside abstractions which are also functions. All functions can have at least one ''ce'u'' somewhere in the abstraction - that's what makes them functions. The ''ce'u'' can be elided, in which case it's most often assumed to fill the first elided sumti place of the function, unless context provides a more reasonable alternative.
What does it actually do? Let's have a look at its definition:
''__ce'u''__: Pseudo-quantifier binding a variable within an abstraction that represents an open place.
Well, that wasn't very helpful, so let me try explaining it with another approach:
Putting ''ce'u'' in a sumti place leaves the sumti place empty. The place is not erased, like if you fill it with ''zi'o'', but the place is not filled with anything - not a specific thing, not a ''zu'i'', not a ''zo'e'', nothing. In that manner, the empty sumti places are reminiscent of the x1, x2, and x3's we put in the sumti places of English definitions of brivla - marking "This is where something else can be put".
Thus ''mi citka lo ti badna'' is "I eat this banana", but ''mi citka ce'u'' is "I eat X".
Of course, "I eat X" is meaningless unless that X is filled by something, and indeed the sentence ''mi citka ce'u'' is senseless in Lojban as well.

In order to put it to use, we need a function abstraction. We'll begin with the most often-used: The selbri abstraction ''ka''. Let's see its official gloss:
''__ka__'' Property/quality abstractor (-ness); x1 is quality/property exhibited by BRIDI.
Under the understanding which I will teach, this gloss is mildly misleading. Instead, ''ka'' should probably be glossed such:
''__ka__'' Predicate/selbri abstractor: x1 is the predicate/selbri of BRIDI (needs at least one open variable i.e. a "ce'u")
Using a selbri abstraction, "I eat X" can make sense, as in the following example:
''__ckaji__'' x1 is characterized by selbri x2
''lo ti badna cu ckaji lo ka mi citka ce'u'' - "This banana is characterized by the selbri: "I eat X"", which may be rephrased as "This banana fits the selbri: "Being eaten by me"", which is of course equivalent to ''mi citka lo ti badna'' - "I eat this banana".
For the statement to make sense, the sumti place held open by ''ce'u'' usually, but not always, must be filled by something. The main selbri of the statement, in this case ''ckaji'', gives us a clue how to fill the open sumti place. Such selbri almost always fill it with a sumti from the main selbri. How ''ce'u'' is given a non-zero value has been a subject of minor debate in Lojbanistan, but the issue is more or less settled: ''ce'u'' keeps a sumti place open, and the main selbri then fills it with something, and what fills the place depends on the selbri in question.

Though it often is, the ''ce'u'' place need not always be filled by the selbri in order for the abstraction to make sense: On its own, ''lo ka ce'u te vecnu lo finpe'' means: "buying a fish", or "to buy a fish". This can be used in a sentence without the selbri filling the ceu in:
''lo se lisri cu srana lo ka ce'u te vecnu lo finpe'' - "The plot is about buying a fish". Here, ''srana'' does not apply anything to the ''ce'u''-place, and the abstraction is instead seen as the selbri on its own.

An alternative way of explaining ''ce'u'' is by regarding the word as representing variables in a lambda function. For instance, consider the sentence:
''la .alis. cu djica lo ka ce'u te vecnu lo finpe'' - "Alice wants to buy a fish"
Here, the first argument of ''djica'' is the one who wants something, namely Alice. The second argument is the selbri that Alice wants to fulfill: Buying a fish.
We can view ''ce'u'' as a free variable, which then becomes bound by a lambda abstraction, namely ''ka''. Now, ''ka ce'u terve'u lo finpe'' can be seen as a lambda function:
\ x -> te vecnu(x,lo finpe,zo'e,zo'e),
and in this case ''djica'' supplies the lambda function with Alice.

Lambdas can be stored, allowing them to be passed around and use them in various situations:
''ca'e ko'a ka ce'u dansu .i mi ko'a ckaji .i do ko'a djica .i ma'a ko'a kakne'' - It is dancing. I am doing it. You want it. Everyone can do it."

Now, using ''ka'', you can correctly phrase "I can run on my arms". How?
Answer: ~~grey,grey:mi kakne lo ka {ce'u} bajra fi lo mi birka~~

A lot of often-used gismu take selbri as one of their sumti, which means ''lo ka'' is used quite often. A few notable examples are ''troci'', ''kakne'', ''djica'', ''zukte'', ''snada'' and ''fraxu'':
''lo kasli nae kakne lo ka silcu la'e la'oi X-files'' - "The donkey cannot whistle the X-files song"

''.e'o ko lo jai se zgike cu fraxu lo ka darxi lo damri ca lo nu do sipna'' - "Please forgive the musician for striking the drum when you were sleeping!"

At least one selbri can fill two ''ce'u'' within a ka-abstraction, namely simxu. What does the following jufra mean?

''mi lo pampe'o cu simxu lo ka {ce'u ce'u} gletu''
Answer: ~~grey,grey:''Me and my lover have sex with each other mutually"~~

Of course, the ''ce'u'' need not be placed in the beginning of the ''ka''-abstraction, though it is by default. One could very well speak of:
''lo ka la .bab. melbi ce'u'' - "The selbri of: "Bob is beautiful according to X"", or in other words: "Thinking that Bob is beautiful".
Indeed, moving the ''ce'u'' around in an function creates very different meanings:
''lo ka ce'u panzi la .maik.'' - "The selbri: "X is a child of Mike"" = "Being Mike's child", versus
''lo ka la .maik. panzi ce'u'' - "The selbri: "Mike is a child of X"" = "Being the parent of Mike".
One could even imagine a statement in where the ''ce'u'' is placed in a very unconventional place, that nonetheless is quite intuitive:
''mi .e nai do ckaji lo ka lo bruna cu jbocre'', wherein the ''ce'u'' is elided, but most probably hiding in ''lo bruna be ce'u'', therefore meaning "I and not you is characterized by the selbri: "The brother of X is good at Lojban"", which is the same as "I have a brother who's good at Lojban, but you don't".

One can make a function, like a "ka"-abstraction, and fill all sumti places, leaving no place for a ''ce'u''. The resulting bridi are weird:
''mi kakne lo ka mi merko lo mi bangu'' - "I can my language is American". This is clearly a type error. Some people regard functions without any ''ce'u'' to be equivalent to bridi abstractions, so that:
''mi krici lo ka mi vrude la cevni'' is the same as ''mi krici lo du'u mi vrude la cevni'' - "I believe that I am good in the eyes of God", and is just as good a sentence in Lojban as its translation is in English. In my opinion, one should refrain from using any of the function abstractors if one doesn't want to use a function. If you mean ''du'u'', use ''du'u''.

The other abstractor which clearly can provide a function is ''ni''. Like ''ka'', a ''ce'u'' can be placed in a ''ni'' abstraction, but unlike with ka, using a ceu with ni is not mandatory. Thus, if no ''ce'u'' is placed in a ''ni''-abstraction, one cannot assume that it's elided - it might simply not be there. If the main selbri is not one which clearly tells us how to fill a ''ce'u''-place, such as ''zmadu'' or ''mleca'', there's probably no ''ce'u'' at all.
In all other aspects, the way ''ce'u'' works within the abstraction is just like ''ka'', so the difference is purely semantical. Whereas ''ka'' creates a selbri, ''ni'' creates an amount. Here's the definition of the word:

__''ni''__: Amount abstraction: x1 is the amount of BRIDI on scale x2
Being familiar with ''ka'', the usage of ni should be straightforward:
''mi zmadu do lo ni {ce'u} xekri'' - "I exceed you in amount: "X is black"", or: "I'm blacker than you." As stated in lesson twenty-eight, all agree that this makes total sense because the brightness of one's skin could be measured by a camera. However, some people will not accept the unmeasurable:
''mi zmadu do lo ni mi pendo la .maik.'' - "I am more of a friend of Mike than you are". I think using amounts to quantify the unmeasurable is fine, but that is an issue I swept under the carpet two lessons ago, and I'm not gonna take it on here.

It's absolutely clear, however, that it's wrong to use ''ni'' as a way to enumerate how many objects fit a selbri - it's always about to which extent certain sumti fit a selbri. Thus:
''do mleca mi lo ni panzi ce'u'' means "You are less of a parent than I am", and not "You have fewer children than me".
In case you're curious (I was), the jufra ''zo'e panzi ce'u'' in the previous example actually refers to two distinct bridi, because the selbri fills the open ''ce'u''-place twice, once for ''do'', and once for ''mi'', making the two sub-bridi: ''zo'e panzi do'' and ''zo'e panzi mi''. Since these two bridi are considered different, the ''zo'e'' need not refer to the same object.

What does it mean if you don't use a ''ce'u'' inside a ''ni''-abstraction? Well, then the main selbri can't fill any of the sumti in the abstraction, so when using selbri like zmadu and mleca, there's a good chance it won't make any sense. However, if ''ni'' itself is the main selbri, it's totally fine to avoid using any ''ce'u'' at all:
''li du'e ni do nelci lo vanju'' - "You like wine too much"

The last of the abstractors we treat in this lesson is ''si'o'', the concept abstractor. ''si'o'' may be considered a function, or it may not be considered a function. A ''si'o''-abstraction certainly contains a ''ce'u'' - in fact, under the understanding which I am teaching, a ''si'o''-abstraction always contains nothing but ''ce'u''s! These ''ce'u''s, unlike those of ''ka'' or ''ni'', remain open and cannot be filled by any selbri. In other words, the function cannot be applied to anything, which is what makes it a maybe-function.
''__si'o__'' Concept abstractor: x1 is x2's concept of BRIDI
Let's have a few examples:
''lo si'o xebni'', which, because all the sumti places are filled with ''ce'u'' is equivalent to:
''lo si'o ce'u xebni ce'u'' - "The concept of: "X hates Y"" = "The concept of hate" = Hate

The mythical creatures Balrog from Lord of the Rings are described as being "shadow and flame", the poesy of which appears much stronger in Lojban: ''la balrog cu si'o fagri joi manku'' is asserting not only that its made out of shadow and flame, but also suggesting that its the prototypical Shadow and Flame, from which all other shadow and flame derives.

For good measure, it should be stated that etymologically, "si'o" derives from "sidbo", "idea", but in current usage an idea is considered a text and not a concept.

The difference between the three abstractors ''ka'', ''ni'' and ''si'o'' can be illustrated with a few more examples for comparison:
''lo ka crino cu pluka mi'' - "Being green pleases me"
''lo ni crino cu pluka mi'' - "How much {zo'e} is green pleases me" (no ''ce'u''!)
''lo si'o crino cu pluka mi'' - "Greenness pleases me"

''mi nitcu lo ka sipna ku lo ka kanro'' - "I need sleep in order to be healthy"
''mi nitcu lo si'o sipna lo ka tavla fi lo sipna'' - "I need the concept of sleep in order to speak about sleeping things"
And I was tempted to write ''mi nitcu lo ni sipna ku lo ka vreji ri'' - "I need the amount of how much {zo'e} sleeps", but that doesn't seem to make a lot of sense.


!!Lojban Lessons - Lesson thirty-one (the not-so-cute assorted words)
Yes, this lesson is yet another which focuses on assorted words. This time, however, the content of the lesson is not chosen by common usage: Unlike words like ''jai'' and ''si'', most of the following words see little usage in ordinary conversation. Some of them are, however, important to understanding the following lessons, and so these words must be awkwardly placed before their usage in these lessons.

Before we venture to obscure words, there's one word which I think deserves a more thorough explanation than it has been given so far: ''kau''.
''kau'' was explained in lesson twelve, but the real implications of it was not. If you have forgotten what it means, I advice you to go back and see. Unfortunately, I can't present a theory on what ''kau'' does when it's present in the main bridi, only on what it does inside an abstraction.
A bridi with abstraction containing a ''kau'' makes two claims: The bridi itself makes one claim as usual, and implicit in the abstraction is furthermore the claim that the word ''kau'' is attached to has a real, nonzero meaning.
This should be demonstrated: The bridi ''mi pu viska lo nu ma kau cliva le salci'' (I saw who left the party) makes two claims. First, it makes an implicit claim that the ''ma'' refers to something real. That is, the bridi actually claims that ''da cliva le salci'' (X left the party). Secondly, the main bridi makes the claim that what the ''ma'' refers to is what was being seen, or in lojban ''mi pu viska lo nu da cliva le salci''. (I saw that X left the party)
This principle is not restricted to the abstractor ''nu'', or to the question word ''ma''. The same principle can be extended to any other abstractor and any other question word, as in the following bridi:
''la .bab. na'e birti lo du'u xu kau la .mias. pampe'o'' (Bob isn't sure whether or not Mia has a boyfriend) states firstly that ''xu'' applies, which means that a truth value correctly can be assigned to the bridi, and secondly that what Bob isn't sure about is the correct truth value for the bridi.
''kau'' can also be applied to a non-question word. This doesn't really change the meaning of the word. The same procedure still applies:
''do ca'o djuno lo du'u la krestcen kau cu cinba la an'' = "You already know that it was Kristian, who kissed Anne." states firstly that ''la krestcen cu cinba la an'' and then that ''do ca'o djuno lodu'u la krestcen cu cinba la an''.

Moving on to the more obscure words, we can begin with ''xi''; it's easy.
__''xi''__: Subscript. Converts any following number string to a subscript, which has the grammar of an attitudinal (ie. placable practically anywhere).
There are few officially encouraged uses of ''xi'', but precisely because the construct ''xi''+number has the free grammar of an attitudinal, the possible uses of ''xi'' are almost endless. In general, it's used to enumerate any word, variable or grammatical construct, as opposed to what it refers to. Let's see some examples.
la tsani cu cusku zo coi .i ba bo la .triliyn. cusku lu .ui coi la tsani coi la klaku li'u .i ba bo la klaku cu spuda fi lu coi ty. xi pa .e ty. xi re do'u zo'o li'u - "Tsani said "hi", then Triliyn said "Hey Tsani, hey Klaku :)", then Klaku answered "Hello T1 and T2 :P""
Because it's the standard that ''ty.' refers to the last sumti which began with T, ''ty'' by itself as said by Klaku would have referred to Tsani. Two __different__ ''ty.'' can be made by subscripting with ''xi''.
If the rare situation arises that we need more variables of the type ''da'' or ''bu'a'' that there are in the language, an infinite number can be made by simply subscripting any existing with a number. Note that a non-subscripted variable is not defined af being eqiuvalent to any subscripted one. That is: ''ty'' is not always equal to ''ty xi pa'' or ''ty xi no'' or anything of the sort. I expect this to be rarely used, because any sentence with more than 3 ''da''-like words or more than 10 ''ko'a''-like words would be hard to keep track of.

Second, we have ''ki'', of which I am not aware of a singe usage in my time on IRC; probably not because the word's useless, but because few Lojbanic texts are of the kind where you need it.
__''ki''__ "Sticky tense". Set/use tense default; establishes new open scope space/time/modal reference base.
Any row of tense words can be suffixed with ''ki'' to make the tense(s) apply to all following bridi. When, for instance, telling a story, this can be used to make explicit that the default time - the time as meant without any tense words - is the time the story is placed in. Usually, this will not be necessary; beginning a fairytale with ''pu zu vu ku'', one can assume that the entire tale is happening a long time ago and far away. Let's have an example:
''pu zu vu ki ku zasti fa lo pukclite je cmalu nixli goi koa .i ro da poi ''[''pu zu vu'']'' viska koa cu nelci koa'' - "Once upon a time there was a sweet, little girl. Everyone who saw her liked her". The ''ki'' allows us to elide the three tenses in the second bridi, and in all the bridi to follow.
So, if a bunch of tenses have been make sticky with ''ki'', how do we unstick them? Simple use ''ki'' bu itself, and all sticky tenses are made unsticky.
Lastly, several sets of tenses can be made sticky by subscripting ''ki''. If there are several of such sets in usage at any given time, one can use the subscripted ''ki''s to make the corresponding set of tenses apply. Unsubscripted ''ki'' alone still makes all tense stickiness disappear, so you have to be careful not to use ''ki'' unsubscripted if you plan on using several sets of tenses.

Changing subject. There's a set of sumtcita which are often used, but which I dare not try to define if not under the disclaimer of part three. Let's see official definitions for two of them first.
__''ca'a''__: modal aspect: actuality/ongoing event. Bridi has/is/will happen during under the circumstances of {sumti}
__''ka'e''__: modal aspect: innate capability; possibly unrealized. Bridi is possible under the circumstances of {sumti}
Let's first contrast ''ca'a'' with ''ka'e''. ''ka'e'' means that the bridi is "possible if the event of SUMTI has/is/will occur". ''ca'a'' by contrast, means that the bridi "has, is, or will happen if the event of SUMTI has/is/will occur".
Like all sumtcita, their corresponding sumti can be elided if the sumtcita is placed before the selbri:
''le vi sovda ka'e fulta .i ja'o bo ri fusra'' - "This egg floats. Therefore, it's rotten".
By using ''ka'e'', this sentence does not state that the egg has floated, or ever will float, but rather that it could float.

__''pu'i''__: modal aspect: can and has; demonstrated potential. Bridi could or could not happen, but in fact it is/did/will happen under the circumstance of {sumti}
__''nu'o''__: modal aspect: can but has not; unrealized potential. Bridi is possible, but is/will/have not happened under {sumti}

Understanding ''ka'e'' and ''ca'a'', ''nu'o'' simply means ''ka'e je na ku ca'a'', and ''pu'i'' means ''ca'a je ka'e na ku''.
Historically, these four words was tense sumtcita - therefore the "modal aspect" in their definitions. All tense sumtcita was then not considered sumtcita at all, but rather "selbri tcita". A modern understanding of Lojban is gaining popularity, wherein the tense sumtcita are considered sumtcita, almost exactly like the BAI, and in where selbri tcita are not used.
Because of these four words' history as selbri tcita, they can be freely elided - indeed, since one of the four words always applies, one is always assumed to be elided. This is most often ''ca'a''. Indeed, it's so often ''ca'a'' that one could wonder why ''ca'a'' is not the default.
One reason is that some selbri has two useful definitions, one which implies ''ka'e SELBRI'' and one which implies ''ca'a SELBRI''. For an example, see ''fasnu'', which can mean "x1 is happening" or "x1 is an event", where the first implies ''ca'a fasnu'' and the second ''ka'e fasnu''
Another use of "implied ''ka'e''" is as a way to escape an annoying philosophical problem in the language. A selbri only applies if all its places apply too. For some selbri, like ''kabri'', that's a problem.
__''kabri''__ x1 is a cup containing contents x2 and of material x3
The definition suggests that if the content of the cup is removed, the x2 no longer applies and it stops being ''lo kabri''. Implied ''ka'e'', or more fittingly, ''nu'o'', let us escape that problem.


!!!End of lessons
Sorry, but as of now, there are no more lessons in this series. Perhaps more will be added later. Meanwhile, feel free to visit ((wavelessonscontinued|the first part of Wavelessonscontinued)) or ((wavelessonscontinuedp2|The second part of Wavelessonscontinued)). + {redirect url=http://http://mw.lojban.org/index.php?title=Lojban_Wave_Lessons} *********************************************************** The new page content follows below. *********************************************************** {redirect url=http://http://mw.lojban.org/index.php?title=Lojban_Wave_Lessons} _______________________________________________ Wikineurotic mailing list Wikineurotic@lojban.org http://mail.lojban.org/mailman/listinfo/wikineurotic