![[Cartoon]](chap15.gif)
The grammatical expression of negation is a critical part of Lojban's claim
to being logical. The problem of negation, simply put, is to come up with a
complete definition of the word ``not''. For Lojban's unambiguous grammar,
this means further that meanings of ``not'' with different grammatical effect
must be different words, and even different grammatical structures.
Logical assertions are implicitly required in a logical language; thus,
an apparatus for expressing them is built into Lojban's logical connectives
and other structures.
In natural languages, especially those of Indo-European grammar, we
have sentences composed of two parts which are typically called ``subject''
and ``predicate''. In the statement
1. Introductory
1.1) John goes to the store
``John'' is the subject, and ``goes to the store'' is the predicate. Negating
Example 1.1 to produce
1.2) John doesn't go to the store.has the effect of declaring that the predicate does not hold for the subject. Example 1.2 says nothing about whether John goes somewhere else, or whether someone else besides John goes to the store.
We will call this kind of negation ``natural language negation''. This kind of negation is difficult to manipulate by the tools of logic, because it doesn't always follow the rules of logic. Logical negation is bi-polar: either a statement is true, or it is false. If a statement is false, then its negation must be true. Such negation is termed contradictory negation.
Let's look at some examples of how natural language negation can violate the rules of contradictory negation.
1.3) Some animals are not white. 1.4) Some animals are white.
Both of these statements are true; yet one is apparently the negation of the other. Another example:
1.5) I mustn't go to the dance. 1.6) I must go to the dance.
At first thought, Example 1.5 negates Example 1.6. Thinking further, we realize that there is an intermediate state wherein I am permitted to go to the dance, but not obligated to do so. Thus, it is possible that both statements are false.
Sometimes order is significant:
1.7) The falling rock didn't kill Sam. 1.8) Sam wasn't killed by the falling rock.
Our minds play tricks on us with this one. Because Example 1.7 is written in what is called the ``active voice'', we immediately get confused about whether ``the falling rock'' is a suitable subject for the predicate ``did kill Sam''. ``Kill'' implies volition to us, and rocks do not have volition. This confusion is employed by opponents of gun control who use the argument ``Guns don't kill people; people kill people.''
Somehow, we don't have the same problem with Example 1.8. The subject is Sam, and we determine the truth or falsity of the statement by whether he was or wasn't killed by the falling rock.
Example 1.8 also helps us focus on the fact that there are at least two questionable facts implicit in this sentence: whether Sam was killed, and if so, whether the falling rock killed him. If Sam wasn't killed, the question of what killed him is moot.
This type of problem becomes more evident when the subject of the sentence turns out not to exist:
1.9) The King of Mexico didn't come to dinner. 1.10) The King of Mexico did come to dinner.
In the natural languages, we would be inclined to say that both of these statements are false, since there is no King of Mexico.
The rest of this chapter is designed to explain the Lojban model of negation.
In discussing Lojban negation, we will call the form of logical negation
that simply denies the truth of a statement ``bridi negation''. Using bridi
negation, we can say the equivalent of ``I haven't stopped beating my wife''
without implying that I ever started, nor even that I have a wife, meaning
simply ``It isn't true that I have stopped beating my wife.'' Since
Lojban uses bridi as smaller components of complex sentences, bridi negation
is permitted in these components as well at the sentence level.
For the bridi negation of a sentence to be true, the sentence being
negated must be false. A major use of bridi negation is in making a
negative response to a yes/no question; such responses are usually
contradictory, denying the truth of the entire sentence. A negative answer to
The most important rule about bridi negation is that if a bridi is true,
its negation is false, and vice versa.
The simplest way to express a bridi negation is to use the cmavo ``na''
of selma'o NA before the selbri of the affirmative form of the bridi
(but after the ``cu'', if there is one):
Note that we have used a special convention to show in the English
that a bridi negation is present. We would like to use the word ``not'',
because this highlights the naturalness of putting the negation marker just
before the selbri, and makes the form easier to learn. But there is a major
difference between Lojban's bridi negation with ``na'' and natural language
negation with ``not''. In English, the word ``not'' can apply to a single
word, to a phrase, to an English predicate, or to the entire sentence.
In addition, ``not'' may indicate either contradictory negation or another
form of negation, depending on the sentence. Lojban's internal bridi
negation, on the other hand, always applies to an entire bridi, and is
always a contradictory negation; that is, it contradicts the claim of
the whole bridi.
Because of the ambiguity of English ``not'', we will use ``[false]'' in the
translation of Lojban examples to remind the reader that we are expressing
a contradictory negation. Here are more examples of bridi negation:
Although there is this fundamental difference between Lojban's internal bridi
negation and English negation, we note that in many cases, especially when
there are no existential or quantified variables (the cmavo ``da'', ``de'', and
``di'' of selma'o KOhA, explained in Chapter 16) in the bridi, you can indeed
translate Lojban ``na'' as ``not'' (or ``isn't'' or ``doesn't'', as appropriate).
The most important rule about bridi negation is that if a bridi is true,
its negation is false, and vice versa.
In Lojban, there are several structures that
implicitly contain bridi, so that Lojban sentences may contain more than
one occurrence of ``na''. For example:
A more extreme (and more indefinite) example is:
The claim of Example 2.10 could apply to anyone except a person who is
fond of no one at all, since the relation within the description is false
for everyone. You cannot readily express these situations in colloquial
English.
Negation with ``na'' applies to an entire bridi, and not to just part of a
selbri. Therefore, you won't likely have reason to put ``na'' inside a tanru.
In fact, the grammar currently does not allow you to do so (except in a lujvo
and in elaborate constructs involving GUhA, the forethought connector for
selbri). Any situation where you might want to do so can be expressed
in a less-compressed non-tanru form. This grammatical restriction helps
ensure that bridi negation is kept separate from other forms of negation.
The grammar of ``na'' allows multiple adjacent negations, which cancel out,
as in normal logic:
When a selbri is tagged with a tense or a modal, negation with ``na'' is
permitted in two positions: before or after the tag. No semantic difference
between these forms has yet been defined, but this is not finally determined,
since the interactions between tenses/modals and bridi negation have not
been fully explored. In particular, it remains to be seen whether sentences
using less familiar tenses, such as:
A final caution on translating English negations into Lojban: if
you translate the English literally, you'll get the wrong one. With
English causal statements, and other statements with auxiliary clauses,
this problem is more likely.
Thus, if you translate the English:
Such mistranslations result from the ambiguity of English compounded by
the messiness of natural language negation. A correct
translation of the normal interpretation of Example 2.14 is:
In Example 2.16, the negation is clearly confined to the event abstraction
in the x1 sumti, and does not extend to the whole sentence. The English
could also have been expressed by two separate sentences joined by a causal
connective (which we'll not go into here).
The problem is not confined to obvious causals. In the English:
It is possible that someone will want to incorporate bridi negations
into lujvo. For this reason, the rafsi ``-nar-'' has been reserved for ``na''.
However, before using this rafsi, make sure that you intend the
contradictory bridi negation, and not the scalar negation described in
Section 3, which will be much more common in tanru and lujvo.
Let us now consider some other types of negation. For example, when we say:
Whether we agree that the chair is brown or not, the fact that the
statement refers to color has significant effect on how we interpret some
responses. If we hear the following exchange:
What is going on in these statements is something called ``scalar
negation''. As the name suggests, scalar negation presumes an implied scale.
A negation of this type not only states that one scalar value is false, but
implies that another value on the scale must be true. This can easily lead
to complications. The following exchange seems reasonably natural (a little
suspension of disbelief in such inane conversation will help):
We have acknowledged a scalar negation by providing a correct value which
is another color in the set of colors permissible for houses. While a
little less likely, the following exchange is also natural:
Again, we have acknowledged a scalar negation, and substituted a different
object in the universe of discourse of things that can be blue.
Now, if the following exchange occurs:
Another even more confusing example of scalar negation is to the sentence:
Might Example 3.9 imply that John went to Paris from somewhere else?
Or did he go somewhere else from Rome? Or perhaps he didn't go anywhere at
all: maybe someone else did, or maybe there was no event of going whatsoever.
One can devise circumstances where any one, two or all three of these
statements might be inferred by a listener.
In English, we have a clear way of distinguishing scalar negation
from predicate negation that can be used in many situations. We can use
the partial word ``non-'' as a prefix. But this is not always considered
good usage, even though it would render many statements much clearer. For
example, we can clearly distinguish
We can't always use ``non-'' though, because of the peculiarities of
English's grammar. It would sound strange to say:
Finally, we have natural language negations that are called
polar negations, or opposites:
To be immoral is much more than to just be not moral: it implies the
opposite condition. Statements like Example 3.15 are strong negations which
not only deny the truth of a statement, but assert its opposite.
Since, ``opposite'' implies a scale, polar negations are a special variety
of scalar negations.
To examine this concept more closely, let us draw a linear scale, showing
two examples of how the scale is used:
Some scales are more binary than the examples we diagrammed. Thus
we have ``not necessary'' or ``unnecessary'' being the polar opposite of
necessary. Another scale, especially relevant to Lojban, is interpreted
based on situations modified by one's philosophy: ``not true'' may be
equated with ``false'' in a bi-valued truth-functional logic, while in
tri-valued logic an intermediate between ``true'' and ``false'' is permitted,
and in fuzzy logic a continuous scale exists from true to false. The
meaning of ``not true'' requires a knowledge of which variety of truth scale
is being considered.
We will define the most general form of scalar negation as
indicating only that the particular point or value in the scale or range is
not valid and that some other (unspecified) point on the scale is correct.
This is the intent expressed in most contexts by ``not mild''.
Using this paradigm, contradictory negation is less restrictive
than scalar negation --- it says that the point or value stated is incorrect
(false), and makes no statement about the truth of any other point or
value, whether or not on the scale.
In English, scalar negation semantically includes phrases such as
``other than'', ``reverse of'', or ``opposite from'' expressions and their
equivalents. More commonly, scalar negation is expressed in English by the
prefixes ``non-'', ``un-'', ``il-'', and ``im-''. Just which form and
permissible values are implied by a scalar negation is dependent on the
semantics of the word or concept which is being negated, and on the
context. Much confusion in English results from the uncontrolled
variations in meaning of these phrases and prefixes.
In the examples of Section 4, we will translate the general case of
scalar negation using the general formula ``other than'' when a phrase is
scalar-negated, and ``non-'' when a single word is scalar-negated.
All the scalar negations illustrated in Section 3 are expressed in Lojban
using the cmavo ``na'e'' (of selma'o NAhE). The most common use of ``na'e''
is as a prefix to the selbri:
Comparing these two, we see that the negation operator being used in
Example 4.2 is ``na'e''. But what exactly does ``na'e'' negate? Does the
negation include only the gismu ``klama'', which is the entire selbri in this
case, or does it include the ``le zarci'' as well? In Lojban, the answer
is unambiguously ``only the gismu''. The cmavo ``na'e'' always applies only
to what follows it.
Example 4.2 looks as if it were parallel to:
In tanru, we may wish to negate an individual element before combining it
with another to form the tanru. We in effect need a shorter-than-selbri-scope
negation, for which we can use ``na'e'' as well. The positive sentence
These negations show the default scope of ``na'e'' is close-binding
on an individual brivla in a tanru. Example 4.5 says that I am going to
the market, but in some kind of a non-walking manner. (As with most tanru,
there are a few other possible interpretations, but we'll assume this
one --- see Chapter 5 for a discussion of tanru meaning).
In neither Example 4.5 nor Example 4.6 does the ``na'e'' negate the entire
selbri. While both sentences contain negations that deny a particular
relationship between the sumti, they also have a component which makes
a positive claim about such a relationship. This is clearer in Example 4.5,
which says that I am going, but in a non-walking manner. In Example 4.6,
we have claimed that the relationship between me and the market in some way
involves walking, but is not one of ``going to'' (perhaps we are walking
around the market, or walking-in-place while at the market).
The ``scale'', or actually the ``set'', implied in Lojban tanru negations is
anything which plausibly can be substituted into the tanru. (Plausibility
here is interpreted in the same way that answers to a ``mo'' question must be
plausible --- the result must not only have the right number of places and
have sumti values appropriate to the place structure, it must also be
appropriate or relevant to the context.) This minimal condition allows a
speaker to be intentionally vague, while still communicating meaningful
information. The speaker who uses selbri negation is denying one
relationship, while minimally asserting a different relationship.
We also need a scalar negation form that has a scope longer than a single
brivla. There exists such a longer-scope selbri negation form, as
exemplified by (each Lojban sentence in the next several examples is
given twice, with parentheses in the second copy showing the scope of the
``na'e''):
This negation uses the same ``ke'' and ``ke'e'' delimiters (the ``ke'e'' is
always elidable at the end of a selbri) that are used in tanru. The
sentence clearly negates the entire selbri. The ``ke'e'', whether elided or
not, reminds us that the negation does not include the trailing sumti.
While the trailing-sumti place-structure is defined as that of the final
brivla, the trailing sumti themselves are not part of the selbri and are
thus not negated by ``na'e''.
Negations of just part of the selbri are also permitted:
In Example 4.8, only the ``sutra cadzu'' tanru is negated, so the speaker
is indeed going to the market, but not by walking quickly.
Negations made with ``na'e'' or ``na'eke'' also include within their scope any
sumti attached to the brivla or tanru with ``be'' or ``bei''. Such attached
sumti are considered part of the brivla or tanru:
Note that Example 4.10 and Example 4.11 do not express the
same thing:
The translations show that the negation in Example 4.10 is more restricted
in scope; i.e. less of the sentence is negated with respect to x1 (``mi'').
Logical scope being an important factor in Lojban's claims to be
unambiguous, let us indicate the relative precedence of ``na'e'' as an
operator. Grouping with ``ke'' and ``ke'e'', of course, has an overt scope,
which is its advantage. ``na'e'' is very close binding to its brivla.
Internal binding of tanru, with ``bo'', is not as tightly bound as ``na'e''.
``co'', the tanru inversion operator has a scope that is longer than all
other tanru constructs.
In short, ``na'e'' and ``na'eke'' define a type of negation, which
is shorter in scope than bridi negation, and which affects all or part of a
selbri. The result of ``na'e'' negation remains an assertion of some specific
truth and not merely a denial of another claim.
The similarity becomes striking when it is noticed that the rafsi
``-nal-'', representing ``na'e'' when a tanru is condensed into a lujvo, forms
an exact parallel to the English usage of ``non-''. Turning a series of
related negations into lujvo gives:
Note: ``-kem-'' is the rafsi for ``ke'', but it is omitted in the final lujvo
as superfluous --- ``ke'e'' is its own rafsi, and its inclusion in the lujvo
implies a ``ke'' after the ``-nal-'', since it needs to close something; only a
``ke'' immediately after the negation would make the ``ke'e'' meaningful in the
tanru expressed in this lujvo.
In a lujvo, it is probably clearest to translate ``-nal-'' as ``non-'',
to match the English combining forms, except when the ``na'e'' has single
word scope and English uses ``un-'' or ``im-'' to negate that single word.
Translation style should determine the use of ``other than'', ``non-'', or
another negator for ``na'e'' in tanru; the translator must render the Lojban
into English so it is clear in context. Let's go back to our simplest
example:
Note that to compare with the English translation form using ``non-'',
we've translated the Lojban as if the selbri were a noun. Since Lojban
``klama'' is indifferently a noun, verb, or adjective, the difference is
purely a translation change, not a true change in meaning. The English
difference seems significant, though, due to the strongly different English
grammatical forms and the ambiguity of English negation.
Consider the following highly problematic sentence:
The selbri ``krecau'' negates with ``na'e'' as:
Since there is no current King of France, it is false to say that he
is bald, or non-bald, or to make any other affirmative claim about him.
Any sentence about the current King of France containing only a selbri
negation is as false as the sentence without the negation. No amount of
selbri negations have any effect on the truth value of the sentence, which
is invariably ``false'', since no affirmative statement about the current
King of France can be true. On the other hand, bridi negation does
produce a truth:
Note: ``lo'' is used in these sentences because negation relates to truth
conditions. To meaningfully talk about truth conditions in sentences
carrying a description, it must be clear that the description actually
applies to the referent. A sentence using ``le'' instead of ``lo'' can be true
even if there is no current king of France, as long as the speaker and
the listener agree to describe something as the current king of France.
(See the explanations of ``le'' in Chapter 6.)
In expressing a scalar negation, we must provide some indication of the
scale, range, frame-of-reference, or universe of discourse that is being
dealt with in an assertion. As stated in Section 4, the default is the set
of plausible alternatives. Thus if we say:
However, if we have reason to be more explicit (an obtuse or
contrary listener, or simply an overt logical analysis), we can clarify
that we are referring to a color by saying:
We might also have reduced the pragmatic ambiguity by making the two
trailing sumti values explicit (the ``as perceived by'' and ``under conditions''
places have been added to the place structure of ``xunre''). But assume
we have a really stubborn listener (an artificially semi-intelligent
computer?) who will find a way to misinterpret Example 5.3 even with three
specific sumti provided.
In this case, we use a sumti tagged with the sumti tcita ``ci'u'', which
translates roughly as ``on a scale of X'', where ``X'' is the sumti. For
maximal clarity, the tagged sumti can be bound into the negated selbri
with ``be''. To clarify Example 5.3, we might say:
We can alternately use the sumti tcita ``teci'e'', based on ``ciste'', which
translates roughly as ``of a system of components X'', for universes of
discourse; in this case, we would express Example 5.3 as:
Other places of ``ciste'' can be brought out using the grammar of selma'o BAI
modals, allowing slightly different forms of expression, thus:
The cmavo ``le'a'', also in selma'o BAI, can be used to specify a
category:
The cmavo ``na'e'' is not the only member of selma'o NAhE. If we want to
express a scalar negation which is a polar opposite, we use the cmavo
``to'e'', which is grammatically equivalent to ``na'e'':
Likewise, the midpoint of a scale can be expressed with the cmavo ``no'e'',
also grammatically equivalent to ``na'e''. Here are some parallel
examples of ``na'e'', ``no'e'', and ``to'e'':
The cmavo ``to'e'' has the assigned rafsi ``-tol-'' and ``-to'e-''; the cmavo
``no'e'' has the assigned rafsi ``-nor-'' and ``-no'e-''. The selbri in
Example 5.10 through Example 5.12 could be replaced by the lujvo
``nalmle'', ``normle'', and ``tolmle'' respectively.
This large variety of scalar negations is provided because different scales
have different properties. Some scales are open-ended in both directions:
there is no ``ultimately ugly'' or ``ultimately beautiful''. Other scales,
like temperature, are open at one end and closed at the other: there is
a minimum temperature (so-called ``absolute zero'') but no maximum
temperature. Still other scales are closed at both ends.
Correspondingly, some selbri have no obvious ``to'e'' --- what is the
opposite of a dog? --- while others have more than one, and need ``ci'u''
to specify which opposite is meant.
There are two ways of negating sumti in Lojban. We have the
choice of quantifying the sumti with zero, or of applying the sumti-negator
``na'ebo'' before the sumti. It turns out that a zero quantification serves
for contradictory negation. As the cmavo we use implies, ``na'ebo'' forms a
scalar negation.
Let us show examples of each.
Is Example 6.1 true? Yes, because it merely claims that of the current
Kings of France, however many there may be, none are bald, which is plainly
true, since there are no such current Kings of France.
Now let us look at the same sentence using ``na'ebo'' negation:
In place of ``na'ebo'', you may also use ``no'ebo'' and ``to'ebo'', to be more
specific about the sumti which would be appropriate in place of the
stated sumti. Good examples are hard to come by, but here's a valiant try:
It is not possible to transform sumti negations of either type into bridi
negations or scalar selbri negations. Negations of sumti will be used in
Lojban conversation. The inability to manipulate these negations logically
will, it is hoped, prevent the logical errors that result when natural
languages attempt corresponding manipulations.
We have a few other constructs that can be negated, all of them
based on negating individual words. For such negation, we use the
suffix-combining negator, which is ``nai''. ``nai'', by the way, is almost
always written as a compound into the previous word that it is negating,
although it is a regular separate-word cmavo and the sole member of selma'o
NAI.
Most of these negation forms are straightforward, and should be
discussed and interpreted in connection with an analysis of the particular
construct being negated. Thus, we will not go into much detail here.
The following are places where ``nai'' is used:
When attached to tenses and modals (see Chapter 10), the ``nai'' suffix
usually indicates a contradictory negation of the tagged bridi. Thus
``punai'' as a tense inflection means ``not-in-the-past'', or ``not-previously'',
without making any implication about any other time period unless explicitly
stated. As a result,
Tenses and modals can be logically connected, with the logical
connectives containing contradictory negations; this allows negated tenses
and modals to be expressed positively using logical connectives. Thus
``punai je ca'' means the same thing as ``pu naje ca''.
As a special case, a ``-nai'' attached to the interval modifiers of selma'o
TAhE, ROI, or ZAhO (explained in Chapter 10) signals a scalar negation:
In indicators and attitudinals of selma'o UI or CAI, ``nai'' denotes a polar
negation. As discussed in Chapter 13, most indicators have an implicit
scale, and ``nai'' changes the indicator to refer to the opposite end of the
scale. Thus ``.uinai'' expresses unhappiness, and ``.ienai'' expresses
disagreement (not ambivalence, which is expressed with the neutral or
undecided intensity as ``.iecu'i'').
Vocative cmavo of selma'o COI are considered a kind of indicator, but
one which identifies the listener. Semantically, we could dispense with
about half of the COI selma'o words based on the scalar paradigm. For
example, ``co'o'' could be expressed as ``coinai''. However, this is not
generally done.
Most of the COI cmavo are used in what are commonly called protocol
situations. These protocols are used, for example, in radio conversations,
which often take place in a noisy environment. The negatives of protocol
words tend to convey diametrically opposite communications situations (as
might be expected). Therefore, only one protocol vocative is dependent
on ``nai'': negative acknowledgement, which is ``je'enai'' (``I didn't get
that'').
Unlike the attitudinal indicators, which tend to be unimportant in noisy
situations, the protocol vocatives become more important. So if, in a noisy
environment, a protocol listener makes out only ``nai'', he or she can presume
it is a negative acknowledgement and repeat transmission or otherwise respond
accordingly. Chapter 13 provides more detail on this topic.
The abstractors of selma'o NU follow the pattern of the tenses and modals.
NU allows negative abstractions, especially in compound abstractions
connected by logical connectives: ``su'ujeninai'', which corresponds to
``su'u jenai ni'' just as ``punai je ca'' corresponds to ``pu naje ca''.
It is not clear how much use logically connected abstractors will
be: see Chapter 13.
A ``nai'' attached to a non-logical connective (of selma'o JOI or BIhI) is
a scalar negation, and says that the bridi is false under the specified
mixture, but that another connective is applicable. Non-logical connectives
are discussed in Chapter 14.
One application of negation is in answer to truth questions (those which
expect the answers ``Yes'' or ``No''). The truth question cmavo ``xu'' is in
selma'o UI; placed at the beginning of a sentence, it asks whether the
sentence as a whole is true or false.
You can now use each of the several kinds of negation we've
discussed in answer to this (presuming the same question and context for
each answer).
The straightforward negative answer is grammatically equivalent to the
expanded sentence with the ``na'' immediately after the ``cu'' (and before
any tense/modal):
The respondent can change the tense, putting the ``na'' in either before
or after the new tense:
We stated in Section 3 that sentences like Example 8.5 and Example 8.7
appear to be semantically identical, but that subtle semantic distinctions
may eventually be found.
You can also use a scalar negation with ``na'e'', in which case, it is
equivalent to putting a ``na'eke'' immediately after any tense:
He might have telephoned the two cities instead of going there. The
unnecessary ``ke'' and ``ke'e'' would have been essential if the selbri
had been a tanru.
There is an explicit positive form for both selma'o NA (``ja'a'') and selma'o
NAhE (``je'a''), each of which would supplant the corresponding negator in
the grammatical position used, allowing one to assert the positive in
response to a negative question or statement without confusion. Assuming the
same context as in Section 8:
The obvious, but incorrect, positive response to this negative question is:
A plain ``go'i'' does not mean ``Yes it is''; it merely abbreviates repeating
the previous statement unmodified, including any negators present; and
Example 9.3 actually states that it is false that John went to both Paris
and Rome.
When considering:
It was decided that substitution, the latter alternative, is the preferable
choice, since it is then clear whether we intend a positive or a negativ
sentence without performing any manipulations. This is the way English
usually works, but not all languages work this way --- Russian, Japanese,
and Navajo all interpret a negative reply to a negative question as
positive.
The positive assertion cmavo of selma'o NA can also replace the
``na'' in the context, giving:
The question of truth or falsity is not entirely synonymous with
negation. Consider the English sentence
If I never started such a heinous activity, then this sentence is neither
true nor false. Such a negation simply says that something is wrong with
the non-negated statement. Generally, we then use either tone of voice or
else a correction to express a preferred true claim: ``I never have beaten my
wife.''
Negations which follow such a pattern are called ``metalinguistic
negations''. In natural languages, the mark of metalinguistic negation is
that an indication of a correct statement always, or almost always,
follows the negation. Tone of voice or emphasis may be further used to
clarify the error.
Negations of every sort must be expressible in Lojban; errors are inherent
to human thought, and are not excluded from the language. When such
negations are metalinguistic, we must separate them from logical claims
about the truth or falsity of the statement, as well as from scalar negations
which may not easily express (or imply) the preferred claim. Because Lojban
allows concepts to be so freely combined in tanru, limits on what is plausible
or not plausible tend to be harder to determine.
Mimicking the muddled nature of natural language negation would destroy this
separation. Since Lojban does not use tone of voice, we need other means to
metalinguistically indicate what is wrong with a statement. When the statement
is entirely inappropriate, we need to be able to express metalinguistic
negation in a more non-specific fashion.
Here is a list of some different kinds of metalinguistic negation with
English-language examples:
The set of possible metalinguistic errors is open-ended.
Many of these forms have a counterpart in the various examples that
we've discussed under logical negation. Metalinguistic negation doesn't
claim that the sentence is false or true, though. Rather, it claims that,
due to some error in the statement, ``true'' and ``false'' don't really apply.
Because one can metalinguistically negate a true statement intending a
non-contradictory correction (say, a spelling error); we need a way (or
ways) to metalinguistically negate a statement which is independent of our
logical negation schemes using ``na'', ``na'e'' and kin. The cmavo ``na'i'' is
assigned this function. If it is present in a statement, it indicates
metalinguistically that something in the statement is incorrect. This
metalinguistic negation must override any evaluation of the logic of the
statement. It is equally allowed in both positive and negative statements.
Since ``na'i'' is not a logical operator, multiple occurrences of
``na'i'' need not be assumed to cancel each other. Indeed, we can use the
position of ``na'i'' to indicate metalinguistically what is incorrect,
preparatory to correcting it in a later sentence; for this reason, we give
``na'i'' the grammar of UI. The inclusion of ``na'i'' anywhere in a sentence
makes it a non-assertion, and suggests one or more pitfalls in
assigning a truth value.
Let us briefly indicate how the above-mentioned metalinguistic
errors can be identified. Other metalinguistic problems can then be marked
by devising analogies to these examples:
Existential failure can be marked by attaching ``na'i'' to the
descriptor ``lo'' or the ``poi'' in a ``da poi''-form sumti. (See Chapter
6 and Chapter 16 for details on these constructions.) Remember that
if a ``le'' sumti seems to refer to a non-existent referent, you may not
understand what the speaker has in mind --- the appropriate response is
then ``ki'a'', asking for clarification.
Presupposition failure can be marked directly if the presupposition is overt;
if not, one can insert a ``mock presupposition'' to question with the sumti
tcita (selma'o BAI) word ``ji'u''; ``ji'uku'' thus explicitly refers to an
unexpressed assumption, and ``ji'una'iku'' metalinguistically says that
something is wrong with that assumption. (See Chapter 10.)
Scale errors and category errors can be similarly expressed with
selma'o BAI. ``le'a'' has meaning ``of category/class/type X'', ``ci'u'' has
meaning ``on scale X'', and ``ci'e'', based on ``ciste'', can be used to
talk about universes of discourse defined either as systems or sets of
components, as shown in Section 8. ``kai'' and ``la'u'' also exist in BAI for
discussing other quality and quantity errors.
We have to make particular note of potential problems in the areas of undue
quantity and incorrect scale/category. Assertions about the relationships
between gismu are among the basic substance of the language. It is thus
invalid to logically require that if something is blue, that it is colored,
or if it is not-blue, then it is some other color. In Lojban, ``blanu''
(``blue'') is not explicitly defined as a ``skari'' (``color''). Similarly,
it is not implicit that the opposite of ``good'' is ``bad''.
This mutual independence of gismu is only an ideal. Pragmatically, people
will categorize things based on their world-views. We will write dictionary
definitions that will relate gismu, unfortunately including some of these
world-view assumptions. Lojbanists should try to minimize these assumptions, but this seems a likely
area where logical rules will break down (or where Sapir-Whorf effects
will be made evident). In terms of negation, however, it is vital that we
clearly preserve the capability of denying a presumably obvious scale or
category assumption.
Solecisms, grammatical and spelling errors will be marked by
marking the offending word or phrase with ``na'i'' (in the manner of any
selma'o UI cmavo). In this sense, ``na'i'' becomes equivalent to the English
metalinguistic marker ``[sic]''. Purists may choose to use ZOI or LOhU/LEhU
quotes or ``sa'a''-marked corrections to avoid repeating a truly
unparsable passage, especially if a computer is to analyze
the speech/text. See Chapter 19 for explanations of these usages.
In summary, metalinguistic negation will typically take the form of
referring to a previous statement and marking it with one or more ``na'i'' to
indicate what metalinguistic errors have been made, and then repeating the
statement with corrections. References to previous statements may be full
repetitions, or may use members of selma'o GOhA. ``na'i'' at the beginning of
a statement merely says that something is inappropriate about the
statement, without specificity.
In normal use, metalinguistic negation requires that a corrected statement
follow the negated statement. In Lojban, however, it is possible to completely
and unambiguously specify metalinguistic errors without correcting them. It
will eventually be seen whether an uncorrected metalinguistic negation
remains an acceptable form in Lojban. In such a statement, metalinguistic
expression would involve an ellipsis not unlike that of tenseless expression.
Note that metalinguistic negation gives us another kind of legitimate
negative answer to a ``xu'' question (see Section 8). ``na'i'' will be used
when something about the questioned statement is inappropriate, such as in
questions like ``Have you stopped beating your wife?'':
Responses could include:
One can also specifically qualify the metalinguistic negation, by
explicitly repeating the erroneous portion of the bridi to be
metalinguistically negated, or adding on of the selma'o BAI qualifiers
mentioned above:
Finally, one may metalinguistically affirm a bridi with ``jo'a'', another
cmavo of selma'o UI. A common use for ``jo'a'' might be to affirm that
a particular construction, though unusual or counterintuitive, is in
fact correct; another usage would be to disagree with --- by overriding ---
a respondent's metalinguistic negation.
2. bridi negation
2.1) Did you go to the store?
is taken as a negation of the entire sentence, equivalent to
2.2) No, I didn't go to the store.
2.3) mi klama le zarci
I go-to the store.
when negated becomes:
2.4) mi na klama le zarci
I [false] go-to the store.
2.5) mi [cu] na ca klama le zarci
I [false] now am-a-go-er to the market.
I am not going to the market now.
2.6) lo ca nolraitru
be le fasygu'e cu na krecau
The-actual present noblest-governor
of the French country [false] is-hair-without.
The current king of France isn't bald.
2.7) ti na barda prenu co melbi mi
This [false] is a big-person of-type (beautiful to me).
This isn't a big person who is beautiful to me.
2.8) mi na gleki le nu
na klama le nu dansu
I [false] am-happy-about the event-of(
[false] going-to the event-of dancing).
It is not the case that I am happy about it not being
the case that I am going to the dance.
I am not happy about not going to the dance.
In the previous example, we used internal negations in abstraction
bridi; bridi negation may also be found in descriptions within
sumti. For example:
2.9) mi nelci le na melbi
I am fond of the-one-described-as ([false] beautiful)
I am fond of the one who isn't beautiful.
2.10) mi nelci lo na ca nolraitru
be le frasygu'e
I am-fond-of one-who-is ([false] the current king
of the French-country).
I am fond of one who isn't the current king of France.
2.11) ti na na barda prenu co
melbi mi
This [false] [false] is-a-big person
that is (beautiful to me).
which is the same as:
2.12) ti barda prenu co melbi mi
This is a big-person that is (beautiful to me).
2.13) mi [cu] ta'e klama le zarci
I habitually go to the market.
mean the same thing with ``na'' before the ``ta'e'', as when the negation
occurs afterwards; we'll let future, Lojban-speaking, logicians decide on
how they relate to each other.
2.14) I do not go to the market because the car is broken.
as:
2.15) mi na klama le zarci ki'u lenu le karce cu spofu
I [false] go-to the market because the car is broken.
It is false that: ``I go to the market because the car
is broken.''
you end up negating too much.
2.16) lenu mi na klama le zarci
cu se krinu
lenu le karce cu spofu
The event-of (my [false] going-to the market)
is justified by
the event-of (the car being broken).
My not going to the market is because the car is broken.
2.17) I was not conscripted into the Army with the help of
my uncle the Senator.
we do not intend the uncle's help to be part of the negation. We must thus
move the negation into an event clause or use two separate sentences.
The event-clause version would look like:
2.18) The event-of (my [false] being-conscripted-into
the Army) was aided by my uncle the Senator.
3. Scalar Negation
3.1) The chair is not brown.
we make a positive inference --- that the chair is some other color. Thus,
it is legitimate to respond:
3.2) It is green.
3.3) The chair is not brown.
Correct. The chair is wooden.
we immediately start to wonder about the unusual wood that isn't brown. If
we hear the exchange:
3.4) Is the chair green?
No, it is in the kitchen.
we are unsettled because the response seems to be a non-sequitur. But
since it might be true and it is a statement about the chair, one can't say
it is entirely irrelevant!
3.5) That isn't a blue house.
Right! That is a green house.
3.6) That isn't a blue house.
Right! That is a blue car.
3.7) That isn't a blue house.
Right! That is a green car.
we find the result unsettling. This is because it seems that two
corrections have been applied when there is only one negation. Yet out of
context, ``blue house'' and ``green car'' seem to be reasonably equivalent
units that should be mutually replaceable in a sentence. It's just that we
don't have a clear way in English to say:
3.8) That isn't a ``blue-house''.
aloud so as to clearly imply that the scalar negation is affecting the pair
of words as a single unit.
3.9) John didn't go to Paris from Rome.
3.10) That is a non-blue house.
from the related sentence
3.11) That is a blue non-house.
Example 3.10 and Example 3.11 have the advantage that, while they contain a
negative indication, they are in fact positive assertions. They say what
is true by excluding the false; they do not say what is false.
3.12) John went to non-Paris from Rome.
or
3.13) John went to Paris from non-Rome.
although these would clarify the vague negation. Another circumlocution for
English scalar negation is ``other than'', which works where ``non-'' does not,
but is wordier.
3.14) John is moral
3.15) John is immoral
Affirmations (positive) Negations (negative)
|-----------|-----------|-----------|-----------|
All Most Some Few None
Excellent Good Fair Poor Awful
4. selbri and tanru negation
4.1) mi klama le zarci
I go to the market.
4.2) mi na'e klama le zarci
I non-go to the market.
4.3) mi na klama le zarci
I [false] go-to the market.
but in fact there is no real parallelism at all. A negation using ``na'' denies
the truth of a relationship, but a selbri negation with ``na'e'' asserts that a
relationship exists other than that stated, one which specifically involves
the sumti identified in the statement. The grammar allotted to ``na'e''
allows us to unambiguously express scalar negations in terms of scope,
scale, and range within the scale. Before we explain the scalar aspects,
let us show how the scope of ``na'e'' is determined.
4.4) mi cadzu klama le zarci
I walking-ly go to the market.
can be subjected to selbri negation in several ways. Two are:
4.5) mi na'e cadzu klama le zarci
I (other-than-walkingly)-go-to the market.
4.6) mi cadzu na'e klama le zarci
I walkingly-(other-than-go-to) the market.
4.7) mi na'eke cadzu klama [ke'e] le zarci
mi na'e (ke cadzu klama [ke'e]) le zarci
I other-than-(walkingly-go-to) the market.
4.8) mi na'eke sutra cadzu ke'e klama le zarci
mi na'e (ke sutra cadzu ke'e) klama le zarci
I other-than-(quickly-walkingly) go-to the market.
4.9) mi na'e ke sutra cadzu be le mi birka ke'e
klama le zarci
I other-than-(quickly walking-on-my-arms-ly)
go-to the market.
4.10) mi na'eke sutra cadzu [ke'e] lemi birka
mi na'e (ke sutra cadzu [ke'e]) lemi birka
I other-than-(quickly-walk-on) my-arms.
4.11) mi na'eke sutra cadzu be lemi birka [ke'e]
mi na'e (ke sutra cadzu be lemi birka [ke'e])
I other-than-(quickly-walk-on my-arms).
4.12) na'e klama becomes nalkla
na'e cadzu klama becomes naldzukla
na'e sutra cadzu klama becomes nalsu'adzukla
nake sutra cadzu ke'e klama becomes nalsu'adzuke'ekla
4.13) mi na'e klama le zarci
I am other-than-(going-to) the market.
?I am not going-to the market.
4.14) mi nalkla le zarci
I am-a-non-go-er-to the market.
4.15) lo ca nolraitru
be le fasygu'e
cu krecau
An-actual currently noblest-governor
of the French country
is-hair-without.
The current King of France is bald.
4.16) lo ca nolraitru
be le fasygu'e
cu na'e krecau
An-actual currently noblest-governor
of the French country
is-other-than hair-without.
The current King of France is other-than-bald.
or, as a lujvo:
4.17) lo ca nolraitru
be le fasygu'e
cu nalkrecau
An-actual currently noblest-governor
of the French country
is-non-hair-without.
The current King of France is a non-bald-one.
Example 4.16 and Example 4.17 express the predicate negation forms using a
negation word (``na'e'') or rafsi (``-nal-''); yet they make positive assertions
about the current King of France; ie., that he is other-than-bald or
non-bald. This follows from the close binding of ``na'e'' to the brivla. The
lujvo form makes this overt by absorbing the negative marker into the word.
4.18) lo ca nolraitru
be le fasygu'e
cu na krecau
An-actual current noblest-governor
of the French Country
[false] is-hair-without.
It is false that the current King of France is bald.
5. Expressing scales in selbri negation
5.1) le stizu cu na'e xunre
The chair is a non-(red-thing).
the pragmatic interpretation is that we mean a different color and not
5.2) le stizu cu dzukla be le zarci
The chair walkingly-goes-to-the-market.
5.3) le stizu cu na'e xunre skari
The chair is of a non-(red)-color
(as perceived by something under some conditions).
5.4) le stizu cu na'e xunre be ci'u loka skari
The chair is a non-(red on-a-scale-of-colorness)-thing.
5.5) le stizu cu na'e xunre
be teci'e le skari
The chair is a non-(red
of-a-system-with-components-the-colors)-thing.
5.6) le stizu cu na'e xunre
be ci'e lo'i skari
The chair is a non-(red
of-a-system-which-is-the-set-of-colors)-thing.
5.7) le stizu cu na'e xunre
be le'a lo'i skari
The chair is a non-(red
of-a-category-which-is-the-set-of-colors)-thing.
which is minimally different in meaning from Example 5.6.
5.8) le stizu cu to'e xunre
be ci'u loka skari
The chair is a (opposite-of red)
on-scale a-property-of color-ness.
5.9) ta melbi
That is-beautiful.
5.10) ta na'e melbi
That is-non-beautiful.
That is other than beautiful.
That is ugly [in one sense].
5.11) ta no'e melbi
That is-neutrally beautiful.
That is plain/ordinary-looking
(neither ugly nor beautiful).
5.12) ta to'e melbi
That is-opposite-of beautiful.
That is ugly/very ugly/repulsive.
6. sumti negation
6.1) no lo ca nolraitru
be le fasygu'e cu krecau
Zero of those who are currently noblest-governors
of the French country are-hair-without.
No current king of France is bald.
6.2) na'ebo lo ca nolraitru
be le fasygu'e cu krecau
[Something] other-than-(the-current-noblest-governor
of the French country) is-hair-without.
Something other than the current King of France is bald.
Example 6.2 is true provided that something reasonably describable as
``other than a current King of France'', such as the King of Saudi Arabia,
or a former King of France, is in fact bald.
6.3) mi klama to'ebo la bastn.
I go to the-opposite-of Boston.
I go to Perth.
(Boston and Perth are nearly, but not quite, antipodal cities. In a
purely United States context, San Francisco might be a better ``opposite''.)
Coming up with good examples is difficult, because attaching ``to'ebo'' to
a description sumti is usually the same as attaching ``to'e'' to the selbri
of the description.
7. Negation of minor grammatical constructs
7.1) mi na pu klama le zarci
I [false] [past] go-to the store.
I didn't go to the store.
and
7.2) mi punai klama le zarci
I [past-not] go-to the store.
I didn't go to the store.
mean exactly the same thing, although there may be a difference of emphasis.
7.3) mi paroinai dansu le bisli
I [once] [not] dance-on the ice
means that I dance on the ice either zero or else two or more times within
the relevant time interval described by the bridi. Example 7.3 is very
different from the English use of ``not once'', which is an emphatic way
of saying ``never'' --- that is, exactly zero times.
8. Truth questions
8.1) xu la djan. pu klama la paris. .e la rom.
Is it true that:
(John previously went-to [both] Paris and Rome.)
8.2) na go'i
[false] [repeat previous]
No.
which means
8.3) la djan. [cu] na pu klama la paris. .e la rom.
John [false] previously went-to [both] Paris and Rome.
It's not true that John went to Paris and Rome.
8.4) na ba go'i
[false] [future] [repeat previous]
meaning
8.5) la djan. [cu] na ba klama la paris. .e la rom.
John [false] later-will-go-to [both] Paris and Rome.
It is false that John will go to Paris and Rome.
or alternatively
8.6) ba na go'i
[false] [future] [repeat previous]
meaning
8.7) la djan. [cu] ba na klama la paris. .e la rom.
John later-will [false] go-to [both] Paris and Rome.
8.8) na'e go'i
other-than [repeat previous]
which means
8.9) la djan. [cu] pu na'eke klama
[ke'e] la paris. .e la rom.
John previously other-than(went-to)
[both] Paris and Rome.
9. Affirmations
9.1) xu na go'i
Is-it-true-that [false] [repeat previous]?
or equivalently
9.2) xu la djan. [cu] na pu klama
la paris. .e la rom.
Is it true that: John [false] previously-went-to
[both] Paris and Rome.]
9.3) go'i
[repeat previous]
9.4) na go'i
[false] [repeat previous]
as a response to a negative question like Example 9.2, Lojban designers
had to choose between two equally plausible interpretations with opposite
effects. Does Example 9.4 create a double negative in the sentence by
adding a new ``na'' to the one already there (forming a double negative
and hence a positive statement), or does the ``na'' replace the previous one,
leaving the sentence unchanged?
9.5) ja'a go'i
(John truly-(previously went-to) [both] Paris and Rome.)
``ja'a'' can replace ``na'' in a similar manner wherever the latter is used:
9.6) ja'a go'i
John indeed previously went-to [both] Paris and Rome.
``je'a'' can replace ``na'e'' in exactly the same way, stating that scalar
negation does not apply, and that the relation indeed holds as stated.
In the absence of a negation context, it emphasizes the positive:
9.7) ta je'a melbi
that is-indeed beautiful.
10. Metalinguistic negation forms
10.1) I have not stopped beating my wife.
10.2) I have not stopped beating my wife
(I never started --- failure of presupposition).
10.3) 5 is not blue
(color does not apply to abstract concepts --
failure of category).
10.4) The current King of France is not bald.
(there is no current King of France ---
existential failure)
10.5) I do not have THREE children.
(I have two --- simple undue quantity)
10.6) I have not held THREE jobs previously, but four.
(inaccurate quantity; the difference from the previous
example is that someone who has held four jobs has also
held three jobs)
10.7) It is not good, but bad.
(undue quantity negation indicating that the value on a
scale for measuring the predicate is incorrect)
10.8) She is not PRETTY; she is beautiful
(undue quantity transferred to a non-numeric scale)
10.9) The house is not blue, but green.
(the scale/category being used is incorrect, but a
related category applies)
10.10) The house is not blue, but is colored.
(the scale/category being used is incorrect, but a
broader category applies)
10.11) The cat is not blue, but long-haired.
(the scale/category being used is incorrect, but an
unrelated category applies)
10.12) A: He ain't coming today.
B: ``Ain't'' ain't a word.
(solecism, or improper grammatical action)
10.13) I haven't STOOPED beating my wife; I've STOPPED.
(spelling or mispronunciation error)
10.14) Not only was it a sheep, it was a black sheep.
(non-contradictory correction)
10.15) xu do sisti lezu'o do rapydarxi
ledo fetspe
Have you ceased the activity of repeat-hitting
your female-spouse?
10.16) na'i go'i
The bridi as a whole is inappropriate in some way.
10.17) go'i na'i
The selbri (sisti) is inappropriate in some way.
10.18) go'i ji'una'iku
Some presupposition is wrong with the previous bridi.
11. Summary --- Are All Possible Questions About Negation Now Answered?
11.1) na go'i .ije na'e go'i .ije na'i go'i