Lesson 9
somoi seltadni
Abstraction
nunsucta
9.1
Introduction
***
You will undoubtedly have noticed in looking at place structures that
it can be very hard to fit the descriptions that you know how to form
into some places. For example, what can you put into the various
'under conditions ...' places. Let us take the brivla "frili" for
example.
la lojban cu frili mi ma Lojban is-easy for me under what conditions?
You are unlikely to be able to insert a name. You cannot point at
something and use a demonstrative like "ti". (Well, you could wave
your hands around and say "ti", intending to indicate the current
conditions, but this is a very limited answer.) Even the descriptions
you have don't help unless you fake it by matching up "under
conditions ..." places of different brivla as in:
la lojban cu frili mi le te binxo ku Lojban is-easy for me under
conditions where something is becoming something else.
This technically answers the question but raises the question:
ma binxo ma {...?...} What becomes what under conditions when Lojban
is-easy for me.
We clearly want to somehow take the bridi "la lojban cu frili mi" and
insert it into the "under conditions ..." place. Similarly, we want
to be able to fill in the places of "binxo" in the original answer so
that the question isn't raised.
How?
In the last answer given (binxo), we could use "la'edi'u" to refer to
the referent of the previous sentence (frili). If you look, at what
this means, though, you can probably see that a circular reference is
occurring. "la'edi'u" can sometimes be used for this type of problem,
but can't meet all needs.
We also cannot base the construction on descriptions; "le binxo" means
"the becomer". We want "the event of x1 becoming ...". We can't use
"le frili", either; it means "the easy thing". We want "the state of
x1 being easy ...".
When we introduced descriptions in the last lesson, we indicated that
they were one way to express or convert a bridi into a sumti. We also
said that description with "le" in effect turned the first sumti of
the description bridi into the thing described by the sumti.
We need some way to talk about the events (for verb-like
interpretations of brivla) and states (for noun- and adjective- like
interpretations of brivla). Lojban accomplish this through
'abstraction operators'.
The abstraction operators we will discuss in this lesson are the most
used ones - those that indicate the following abstractions:
- events
- states
- properties
- amounts
We will also mention 'truths' in passing, as a means of comparing
meaning with 'amounts'.
Each of these abstractions is indicated by an abstraction operator
which is a member of selma'o NU. The basic grammar to convert a bridi
into one of these abstractions is to precede it by the NU selma'o
operator, then mark the end with the matching right scope delimiter
"kei". This is shown schematically as:
NU {bridi} kei
kei thus acts something like a closing parenthesis to the NU opening
mark.
The abstraction that results from this construction can be considered
as a '1-place selbri'. It can thus have an x1 sumti and "cu" stuck on
the front, thus becoming a sentence bridi. More frequently, we
precede the abstraction selbri with our friend "le", and turn it into
the description that we need to solve the problems with which we
started this discussion.
After this rapid overview, let us turn to each abstraction in some
more depth, and show with examples how it is used in the construction
we have just described.
9.2
Events and States
fasnu gi'e ***
For right now, we will consider that 'events' and 'states' are the
same thing. We generally think of an event as a short-lived thing.
It has a definite starting and ending point. A state on the other
hand is something that continues for a while. If you think about it,
though, the only real difference is the length of time that is being
referred to. A 'state' is merely an event that takes longer time to
complete (if it completes). If a state is short-lived, it is
indistinguishable from an event.
Let us take a couple of examples based on bridi that are in turn a
noun, a verb, and an adjective in their most common English
interpretations. We will use the event/state abstraction operator
"nu" to show how abstraction affects these bridi.
nanmu
blanu
klama
If you think of "nanmu" as a noun, you can probably understand the
concept of "nu nanmu kei" as "the state of [something] being a man".
(The sumti are being elliptically omitted in this abstracted bridi
example; there is also an implied "vau" at the end of the bridi that
we aren't showing). We don't normally think of being a man as a
single event. But isn't the state of being a man composed of many
'short little events of acting like a man', or better, 'the long
continuous event of acting like a man'. This/these may start with
some type of manhood ritual like the Jewish 'Bar Mitzvah', and
continue with various male human sexual activities and certain
masculine cultural roles in society. All of these can be thought of
as little events. Or the whole of adult manhood can be thought of as
a process or an activity.
Remembering that in Lojban, there isn't necessarily a distinction
between singular and plural, "nu nanmu kei" can refer to a single
small abstract event, or it can refer to the multitude of little
activities and achievements that comprise the life of a man.
Remembering that "nanmu" can be thought of as a verb, as well as a
noun, we can conceptualize manhood as a long continuous 'Act' or
'Event', or as a bunch of little 'acts' or 'events', each evidencing
some trait which we identify as part of the adjectival concept of
"nanmu".
Turning to "blanu", we have already attempted to convey the concept of
a blue object actively engaged in 'blueing', by emitting photons, or
otherwise doing what is necessary to be perceived as blue. These
activities can clearly be described as "events of being blue". Since
being blue can be a temporary 'state' which can be very short, it is
easier to conceive of "blanu" events than of "nanmu" events.
With "klama", we have a concept that is clearly a verb. When we
abstract it with "nu", we get something which is usually thought of as
an 'event':
"x1 klama to x2 from x3 ..." becomes
'the event of "x1 klama to x2 from x3 ..."'
and we have an event of 'klama-ing' or 'coming'.
We can still look upon verbs like klama as 'states', however. During
the time when x1 is coming,
"nu klama kei" clearly refers to a 'state of coming'.
Hopefully, all this has shown you that any bridi can be thought of as
a state or as an event. All bridi remain interchangeable even when
abstraction is involved (although some event abstractions may prove
more useful than others).
We now know what to fill into an 'under conditions ...' place. Such a
place fits a 'state' description perfectly. We can now answer the
original question as:
la lojban. cu frili mi
We have added in parenthesis, brackets and braces in the abstraction
place to show how each of the structures is built, and how each piece
matches with an appropriate closing marker.
The "vau" is still elidable in this sentence. We know, upon reaching
the "kei" that the "nu" abstraction is terminated, and that therefore
the bridi within that abstraction must also be terminated. You can
probably see that the same logic leads to the "kei" being elidable, as
long as the "ku" is there, and the "ku" being elidable because it is
the end of the sentence, and either another ".i" sentence or a stated
or implied "fa'o" means that the final sumti has ended. In short, we
find that all of the closing markers are elidable, and can be omitted,
at the end of any text.
In this lesson we won't omit them (except for "vau"). We will show
elidable terminators such as "ku" and "kei" with brackets when they
are optional (they sometimes are required). In the next lesson, we
will be better able to explain how to tell when elision is permitted,
and when it will cause ambiguity. In this lesson, DO NOT OMIT THEM,
although you can try to get a feel for when they could be omitted.
Meanwhile, get used to the idea that EVERY description has a "ku",
even if it is elided, and that EVERY abstraction bridi has a "kei" at
the end, even if it is elided.
We will similarly show "cu" in brackets when it can be omitted. When
we learn the circumstances under which "cu" can be omitted, you should
still remember that it is implicitly there just before the selbri, and
use that to help you find that selbri.
Let us give look at some examples of abstraction with "nu":
9.2.1
mi cu nelci (le ciska ku)
mi [cu] nelci le ciska [ku]
I like the write-er.
mi cu nelci (le ku)
mi [cu] nelci le nu mi ciska [kei] [ku]
I like the act-of 'me writing'.
mi cu nelci (le se ciska ku)
mi [cu] nelci le se ciska [ku]
I like the thing-which-is-written.
9.2.2
mi cu ckire do
mi [cu] ckire do le nu do [cu] ciksi mi [kei] [ku]
I am-grateful to you for the event-of 'your explaining to me'.
9.3
Properties
selckaji
The second most useful abstraction is that of 'property'. Like
event/state abstractions, we are motivated to allow for property
abstractions by certain place structures where they are particularly
useful. For example, let us look at the 3rd place of "cnino", which
is defined as"
x1 is cnino to x2 in feature x3
Try putting any type of normal description in x3 and you have a
'noun-like' sumti which doesn't seem to fit. Remember that
'adjective-like' brivla like "blanu", become 'nouns' in descriptions
("the blue thing").
You can try putting event/state abstractions into x3. If the result
is seen as an event, it makes no sense at all:
do cu cnino mi
do [cu] cnino mi le nu do [cu] klama ti [kei] [ku]
"You are new to me in the property of the event of 'you come here'." or
"You are new to me in the property 'your coming to here'."
We have real trouble envisioning an event as a quality or property.
If you have an abstraction that is seen as a 'state', it looks better
at first:
do cu cnino mi
do [cu] cnino mi le nu do [cu] blanu [kei] [ku]
"You are new to me in the property of the state of 'you are-blue'." or
"You are new to me in the property of your being blue."
But is 'your being blue' the property? No. It is the blueness which
you 'exhibit' that is the property.
We access the property abstraction of a bridi, with the cmavo "ka",
again a member of selma'o NU, and having identical grammar to "nu":
do cu cnino mi
do [cu] cnino mi le ka do [cu] blanu [kei] [ku]
"You are new to me in the property of 'you are-blue'-ness." or
"You are new to me in your blueness."
"ka" is so powerful that you can sometimes express the x1 and x3
places at once, with but a small change in emphasis:
cu cnino mi
le ka do [cu] blanu [kei] [ku] cu cnino mi
"The property of 'you are-blue'-ness is new to me (in property ...)", or
"Your blueness is new to me ..."
Note that the "cu" of the main bridi cannot be omitted in this sentence.
Another example:
mi cu na nelci le kruji ku .i le kruji ku cu xlali mi le ka ko'a cu
kukte kei ku mi [cu] na nelci le kruji [ku] .i le kruji [ku] cu xlali
mi le ka ko'a [cu] kukte [kei] [ku] "I don't like the cream. The
cream is-bad for me in the-property-of it-is-delicious-ness."
Again, the main bridi "cu" cannot be omitted in the first sentence.
9.4
Amounts
klani
To examine amount abstraction, we have to be more careful in our
choice of brivla. There are many brivla that can use event/state and
property abstractions in one or more positions. Far fewer are the
places where an amount makes sense.
One such place is the second place of cenba:
x1 cenba in quality/quantity x2
Obviously, from the place structure, we can put either a property or a
quantity in x2.
The amount abstractor is "ni". With "blanu" as our brivla to be
abstracted, let us see what the difference is between property
abstraction with "ka" and amount abstraction with "ni":
ta [cu] cenba le ka ta [cu] blanu [kei] [ku]
ta [cu] cenba le ni ta [cu] blanu [kei] [ku]
In the first sentence, that which is varying is the 'blueness' of
'that'. This variation could be a change in shade of blue, or
intermittent periods when "ta" varies from being blue. The change is
qualitative, and not quantitative.
In the second sentence, the quantitative 'amount' of blueing that "ta"
is demonstrating is what changes. This is either an increase or
decrease in the intensity with which the blue-ing takes place.
"ni" does not communicate the quantitative "purity" of the blueness.
A different abstractor, "jei", refers to the 'truth' of the statement
"x1 is blue" such that relative 'purity of blueness' can be seen as
making the statement 'more true'.
For now, think of "jei" as conveying a scale from '0 to 1' as to
fractionally how true, how pure in truth, or even how probably true,
the bridi being abstracted is. "ni" on the other hand, is a pure
"amount", with an arbitrary and possibly open-ended scale of quantity.
9.5
Nested Abstractions
nenri nunsucta
Because of the unambiguous grammar that results from marking the
bounds of each grammatical construct with "kei", "ku" or other such
markers, Lojban has the capability to express abstractions inside of
abstractions with the same clarity as the simpler forms we've just
looked at. We can thus progress from simple to complex, as in:
mi [cu] cilre la lojban.
"I learn Lojban."
mi cu troci
mi [cu] troci le nu mi [cu] cilre la lojban. [kei] [ku]
"I attempt the state of 'I(my) learn(-ing) Lojban'."
mi cu lifri ) kei} ku>
mi [cu] lifri le nu mi [cu] troci le nu mi [cu] cilre la lojban. [kei]
[ku] [kei] [ku]
"I experience the-state-of [I(my) attempt(-ing) the-state-of 'I(my)
learn(-ing) Lojban']."
mi cu kakne ) kei} ku>) kei} ku>
mi [cu] kakne le nu mi [cu] lifri le nu mi [cu] troci le nu mi [cu]
cilre la lojban. [kei] [ku] [kei] [ku] [kei] [ku]
"I am able at the activity of {I(my) experience(-ing) the-state-of
[I(my) attempt(-ing) the-state-of 'I(my) learn(-ing) Lojban']}."
mi cu djica ) kei} ku>) kei} ku>)
kei} ku>
mi [cu] djica le ka mi [cu] kakne le nu mi [cu] lifri le nu mi [cu]
troci le nu mi [cu] cilre la lojban. [kei] [ku] [kei] [ku] [kei] [ku]
[kei] [ku]
"I desire the property of ."
or, more colloquially:
"I want to be able to experience trying to learn Lojban."
You can see how complex a Lojban sentence can get with these
relatively simple constructs, when they are 'nested' inside one
another. Yet, without too much difficulty, you can probably even see
the structure without the bracket markings that we have provided in
the above examples, especially when all of the elidable markers are
present.
You can also see why elision is desirable by looking at the trailing
end, with its alternating "kei"s and "ku"s, not to mention the "vau"
that we omitted from the end of each bridi. All these excess trailers
simply make the language sound humorous, if they are left in
unnecessarily. We really don't want you to think Lojban is "ku ku" as
a language.
9.6
Abstractions With Ellipsis
nalnunsku nunsucta
If abstraction of entire bridi seems a bit much to handle right now,
don't worry. You will seldom be nesting abstractions several layers
deep like in the last example. In fact, much of the time, through our
'old' friend ellipsis, abstraction expressions can be very simple.
First of all, we note that, in even the most complex example above,
each of the x1 sumti of each abstraction level was relatively obvious.
You will find that this is often the case.
In fact, one of two situations is almost universal:
- the x1 place of an abstract description is also found in one of the
other places of the bridi in which the abstraction is inserted; - the
abstraction is talking about a 'universal abstract' where the x1 place
is immaterial.
We'll examine each of these in a moment. Before that, we must also
note that, in abstractions, the non-x1 places tend to be relatively
unimportant or obvious from context.
The result is that quite often, we can use ellipsis to simplify
complex abstract sentences. Just by leaving out 'obvious' x1 sumti,
that last nested abstraction example is significantly shortened and
simplified, since we lose the "cu" as well.
mi cu djica ) kei} ku>) kei} ku>) kei} ku>
mi [cu] djica le ka kakne le nu lifri le nu troci le nu cilre la
lojban. [kei] [ku] [kei] [ku] [kei] [ku] [kei] [ku]
"I desire able-ness at experience-ing the-attempt-ing of 'learn-ing
Lojban']}>."
When we don't need nested abstractions, ellipsis may lead us to even
greater foreshortening. The abstraction then appears just like a bare
selbri, instead of a bridi. The ellipsized sumti are still there, and
so is the "kei".
With this level of ellipsis, we rely a great deal on the understood
context. You can always expand out the abstracted bridi places.
Usually, however, we rely on something that we've glossed over
somewhat: the definition of "le". This cmavo means literally "that
which I am describing as ...", or "that which I have in mind as ...".
In other words, when you use "le", you are warning the listener to
beware, because
YOU MEAN BY YOUR DESCRIPTION EXACTLY WHAT YOU WANT TO MEAN - NO MORE,
NO LESS
If your listener is not sure what you are describing, then she/he had
better ask you to fill in the places, or otherwise be more specific
(using "ki'a", "ma", "mo", etc.).
With elliptical abstractions, you can express very powerful concepts
very simply - as simply as in English, or more so. Yet the logical
structure of your abstractions is revealed so that any level of
questioning is possible to your listener, and you can be as specific
as needed in your replies, without really modifying what you
originally said.
Fully-ellipsized abstractions often translate into simple English
words. For example:
le klama [ku] means "the come-r(s) to ..."
le nu klama [kei] [ku] means "the come-ing to ... (by x1)"
le blanu [ku] means "the blue thing(s)"
le ka blanu [kei] [ku] means "the blue-ness (of x1)"
le slabu [ku] means "the old one(s)"
le ni slabu [kei] [ku] means "the age (of x1)" (the amount of oldness)
As we said above, when abstraction is used, x1 is either somewhere
else in the place structure, or it is a truly unspecified variable and
we are talking about the fully-abstracted nature or property:
le nu bajra [kei] [ku] can mean "Running", the abstract activity.
le ka kakne [kei] [ku] can mean "Able-ness", or "Ability"
le ni barda [kei] [ku] can mean "Size"
9.7
Examples
mupli
Let us now see what we can do with these simpler forms of abstraction:
9.7.1
a'o ko [cu] lifri le ka xamgu [kei] [ku]
(Hopefully) Experience the goodness! [Note: a particular goodness I
have in mind.]
le nu carna [kei] [ku] cu fasnu la rik.
The act-of-turning happens to Rick.
9.7.2
mi [cu] nelci le frili [ku]
I like the easy-thing.
le frili ku ki'a
What-is The easy-thing?
le frili [ku] cu nu klama [kei]
The easy-thing is-a-going.
mi [cu] na nelci le carmi [ku]
I don't like the intense-thing.
le carmi ku ki'a
What is The intense-thing?
le carmi [ku] cu ka blanu [kei]
The intense-thing is-a blue-ness.
9.7.3
la rik. [cu] ckaji le ka pendo [kei] [ku]
Rick has-the-property of friendliness.
mi'o [cu] casnu le ka barda [kei] [ku] .i le ka barda [kei] [ku] cu se
casnu mi'o
We discuss the property-of big-ness. The property-of big-ness
is-a-thing-discussed by us.
la rik. [cu] ckaji le se casnu [ku] .i la rik [cu] ckaji le ka barda
[kei] [ku]
Rick has-the-property of the thing-discussed. Rick has-the-property
of big-ness.
la rik. [cu] ckaji le ka se casnu [kei] [ku]
Rick has-the-property of the-property-of a thing-discussed [i.e. Rick
is topic of discussions].
mi [cu] troci le nu jimpe kei [ku] le nu catlu [kei] [ku]
I try-to-achieve the understanding by the looking.
Exercise 9-1
larnuntoi sopi'epamoi
Give approximate English equivalents for the following (we are leaving
out the "le" and "kei" to avoid distraction):
e.g. nu bajra "running"
1. ka gleki
2. ka fengu
3. ka kluza
4. ka cumki
5. nu darlu
6. nu xusra
7. ka se krici
8. nu djica
9. ka se djica
10. nu jbera
11. ni nitcu
12. nu troci
13. nu jikca
14. ka jikca
15. ni galtu
Answers to Exercise 9-1
1. ka gleki happiness
2. ka fengu anger
3. ka kluza looseness
4. ka cumki possibility
5. nu darlu argument
6. nu xusra declaration, assertion, claim
7. ka se krici credibility (of a concept)
8. nu djica desire, wanting
9. ka se djica desirability
10. nu te jbera loan
11. ni nitcu need (as in "we have great need for ..."
12. nu troci attempt
13. nu jikca interaction
14. ka jikca sociability
15. ni galtu altitude