Lojban Wave Lessons/More on abstractions

Lesson 28: 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 an earlier disclaimer 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 one’s 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, "Tlön, 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 they’re 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.

Lesson 29: 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:

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:

lo 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 painful 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 lo 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 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 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 .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 lo nu mi facki ce'o lo nu mi jai tolsti ce'o 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 zu'o 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 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 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 du'u 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 ‘'du'u, 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 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 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 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 su'u, these can be explicitly differentiated:

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

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

lo su'u mi do prami kei be lo klani is an amount.

Using su'u 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 sa'ordzifa'a ke nalmatma'e sutyterjvi.

Lesson 30: 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 ‘’ce’u’’ 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: 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 xasli na’e 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: 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 ‘’ce’u’’ 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'us! These ce'us, 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 it’s made out of shadow and flame, but also suggesting that it’s 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.