Lojban Wave Lessons/29
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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.
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