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15.xml
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<chapter xml:id="chapter-negation">
<title> <quote>No</quote> Problems: On Lojban Negation</title>
<mediaobject xml:id="chapter-negation-picture">
<alt>The picture for chapter 15</alt>
<imageobject>
<imagedata fileref="media/chapter-negation.gif"/>
</imageobject>
</mediaobject>
<section xml:id="section-negation-introduction">
<title>Introductory</title>
<para>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
<quote>not</quote>. For Lojban's unambiguous grammar, this means further that meanings of
<quote>not</quote> with different grammatical effect must be different words, and even different grammatical structures.</para>
<para>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.</para>
<para>In natural languages, especially those of Indo-European grammar, we have sentences composed of two parts which are typically called
<quote>subject</quote> and
<quote>predicate</quote>. In the statement</para>
<example xml:id="example-random-id-vrXe">
<title>
<anchor xml:id="c15e1d1"/>
</title>
<para>John goes to the store</para>
</example>
<para>
<quote>John</quote> is the subject, and
<quote>goes to the store</quote> is the predicate. Negating
<xref linkend="example-random-id-vrXe"/> to produce</para>
<example xml:id="example-random-id-gm3I">
<title>
<anchor xml:id="c15e1d2"/>
</title>
<para>John doesn't go to the store.</para>
</example>
<para>has the effect of declaring that the predicate does not hold for the subject.
<xref linkend="example-random-id-gm3I"/> says nothing about whether John goes somewhere else, or whether someone else besides John goes to the store.</para>
<para>We will call this kind of negation
<quote>natural language negation</quote>. 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.</para>
<para>Let's look at some examples of how natural language negation can violate the rules of contradictory negation.</para>
<example xml:id="example-random-id-qGWR">
<title>
<anchor xml:id="c15e1d3"/>
</title>
<para>Some animals are not white.</para>
</example>
<example xml:id="example-random-id-qgXI">
<title>
<anchor xml:id="c15e1d4"/>
</title>
<para>Some animals are white.</para>
</example>
<para>Both of these statements are true; yet one is apparently the negation of the other. Another example:</para>
<example xml:id="example-random-id-qgxL">
<title>
<anchor xml:id="c15e1d5"/>
</title>
<para>I mustn't go to the dance.</para>
</example>
<example xml:id="example-random-id-qGXL">
<title>
<anchor xml:id="c15e1d6"/>
</title>
<para>I must go to the dance.</para>
</example>
<para>At first thought,
<xref linkend="example-random-id-qgxL"/> negates
<xref linkend="example-random-id-qGXL"/>. 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.</para>
<para>Sometimes order is significant:</para>
<example xml:id="example-random-id-qgyb">
<title>
<anchor xml:id="c15e1d7"/>
</title>
<para>The falling rock didn't kill Sam.</para>
</example>
<example xml:id="example-random-id-qGYX">
<title>
<anchor xml:id="c15e1d8"/>
</title>
<para>Sam wasn't killed by the falling rock.</para>
</example>
<para>Our minds play tricks on us with this one. Because
<xref linkend="example-random-id-qgyb"/> is written in what is called the
<quote>active voice</quote>, we immediately get confused about whether
<quote>the falling rock</quote> is a suitable subject for the predicate
<quote>did kill Sam</quote>.
<quote>Kill</quote> implies volition to us, and rocks do not have volition. This confusion is employed by opponents of gun control who use the argument
<quote>Guns don't kill people; people kill people.</quote></para>
<para>Somehow, we don't have the same problem with
<xref linkend="example-random-id-qGYX"/>. 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.</para>
<para>
<xref linkend="example-random-id-qGYX"/> 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.</para>
<para>This type of problem becomes more evident when the subject of the sentence turns out not to exist:</para>
<example xml:id="example-random-id-qgzq">
<title>
<anchor xml:id="c15e1d9"/>
</title>
<para>The King of Mexico didn't come to dinner.</para>
</example>
<example xml:id="example-random-id-qgzv">
<title>
<anchor xml:id="c15e1d10"/>
</title>
<para>The King of Mexico did come to dinner.</para>
</example>
<para>In the natural languages, we would be inclined to say that both of these statements are false, since there is no King of Mexico.</para>
<para>The rest of this chapter is designed to explain the Lojban model of negation.</para>
</section>
<section xml:id="section-bridi-negation">
<title>bridi negation</title>
<para>In discussing Lojban negation, we will call the form of logical negation that simply denies the truth of a statement
<quote>bridi negation</quote>. Using bridi negation, we can say the equivalent of
<quote>I haven't stopped beating my wife</quote> without implying that I ever started, nor even that I have a wife, meaning simply
<quote>It isn't true that I have stopped beating my wife.</quote> Since Lojban uses bridi as smaller components of complex sentences, bridi negation is permitted in these components as well at the sentence level.</para>
<para>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</para>
<example xml:id="example-random-id-sCNE">
<title>
<anchor xml:id="c15e2d1"/>
</title>
<para>Did you go to the store?</para>
</example>
<para>is taken as a negation of the entire sentence, equivalent to</para>
<example xml:id="example-random-id-vFYC">
<title>
<anchor xml:id="c15e2d2"/>
</title>
<para>No, I didn't go to the store.</para>
</example>
<para>The most important rule about bridi negation is that if a bridi is true, its negation is false, and vice versa.</para>
<para>The simplest way to express a bridi negation is to use the cmavo
<valsi>na</valsi> of selma'o NA before the selbri of the affirmative form of the bridi (but after the
<valsi>cu</valsi>, if there is one):</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-7nrv">
<title>
<anchor xml:id="c15e2d3"/>
</title>
<interlinear-gloss>
<jbo>mi klama le zarci</jbo>
<gloss>I go-to the store.</gloss>
</interlinear-gloss>
</example>
<para>when negated becomes:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-bV3b">
<title>
<anchor xml:id="c15e2d4"/>
</title>
<interlinear-gloss>
<jbo>mi na klama le zarci</jbo>
<gloss>I [false] go-to the store.</gloss>
</interlinear-gloss>
</example>
<para>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
<quote>not</quote>, 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
<valsi>na</valsi> and natural language negation with
<quote>not</quote>. In English, the word
<quote>not</quote> can apply to a single word, to a phrase, to an English predicate, or to the entire sentence. In addition,
<quote>not</quote> 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.</para>
<para>Because of the ambiguity of English
<quote>not</quote>, we will use
<quote>[false]</quote> in the translation of Lojban examples to remind the reader that we are expressing a contradictory negation. Here are more examples of bridi negation:</para>
<example xml:id="example-random-id-qgzz" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e2d5"/>
</title>
<interlinear-gloss>
<jbo>mi [cu] na ca klama le zarci</jbo>
<gloss>I [false] now am-a-go-er to the market.</gloss>
<natlang>I am not going to the market now.</natlang>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qh10" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e2d6"/>
</title>
<interlinear-gloss>
<jbo>lo ca nolraitru be le fasygu'e cu na krecau</jbo>
<gloss>The-actual present noblest-governor of the French country [false] is-hair-without.</gloss>
<natlang>The current king of France isn't bald.</natlang>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qh2i" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e2d7"/>
</title>
<interlinear-gloss>
<jbo>ti na barda prenu co melbi mi</jbo>
<gloss>This [false] is a big-person of-type (beautiful to me).</gloss>
<natlang>This isn't a big person who is beautiful to me.</natlang>
</interlinear-gloss>
</example>
<para>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
<valsi>da</valsi>,
<valsi>de</valsi>, and
<valsi>di</valsi> of selma'o KOhA, explained in
<xref linkend="chapter-quantifiers"/>) in the bridi, you can indeed translate Lojban
<valsi>na</valsi> as
<quote>not</quote> (or
<quote>isn't</quote> or
<quote>doesn't</quote>, as appropriate).</para>
<para>The most important rule about bridi negation is that if a bridi is true, its negation is false, and vice versa.</para>
<para>In Lojban, there are several structures that implicitly contain bridi, so that Lojban sentences may contain more than one occurrence of
<valsi>na</valsi>. For example:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-WU9u">
<title>
<anchor xml:id="c15e2d8"/>
</title>
<interlinear-gloss>
<jbo>mi na gleki le nu na klama le nu dansu</jbo>
<gloss>I [false] am-happy-about the event-of ([false] going-to the event-of dancing).</gloss>
<gloss>It is not the case that I am happy about it not being the case that I am going to the dance.</gloss>
<natlang>I am not happy about not going to the dance.</natlang>
</interlinear-gloss>
</example>
<para>In the previous example, we used internal negations in abstraction bridi; bridi negation may also be found in descriptions within sumti. For example:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-N65f">
<title>
<anchor xml:id="c15e2d9"/>
</title>
<interlinear-gloss>
<jbo>mi nelci le na melbi</jbo>
<gloss>I am fond of the-one-described-as ([false] beautiful).</gloss>
<natlang>I am fond of the one who isn't beautiful.</natlang>
</interlinear-gloss>
</example>
<para>A more extreme (and more indefinite) example is:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-eQaI">
<title>
<anchor xml:id="c15e2d10"/>
</title>
<interlinear-gloss>
<jbo>mi nelci lo na ca nolraitru be le frasygu'e</jbo>
<gloss>I am-fond-of one-who-is ([false] the current king of the French-country).</gloss>
<natlang>I am fond of one who isn't the current king of France.</natlang>
</interlinear-gloss>
</example>
<para>The claim of
<xref linkend="example-random-id-eQaI"/> 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.</para>
<para>Negation with
<valsi>na</valsi> applies to an entire bridi, and not to just part of a selbri. Therefore, you won't likely have reason to put
<valsi>na</valsi> 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.</para>
<para>The grammar of
<valsi>na</valsi> allows multiple adjacent negations, which cancel out, as in normal logic:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-RJKu">
<title>
<anchor xml:id="c15e2d11"/>
</title>
<interlinear-gloss>
<jbo>ti na na barda prenu co melbi mi</jbo>
<gloss>This [false] [false] is-a-big person that is (beautiful to me).</gloss>
</interlinear-gloss>
</example>
<para>which is the same as:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-2UpW">
<title>
<anchor xml:id="c15e2d12"/>
</title>
<interlinear-gloss>
<jbo>ti barda prenu co melbi mi</jbo>
<gloss>This is a big-person that is (beautiful to me).</gloss>
</interlinear-gloss>
</example>
<para>When a selbri is tagged with a tense or a modal, negation with
<valsi>na</valsi> 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:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-fgmv">
<title>
<anchor xml:id="c15e2d13"/>
</title>
<interlinear-gloss>
<jbo>mi [cu] ta'e klama le zarci</jbo>
<natlang>I habitually go to the market.</natlang>
</interlinear-gloss>
</example>
<para>mean the same thing with
<valsi>na</valsi> before the
<valsi>ta'e</valsi>, as when the negation occurs afterwards; we'll let future, Lojban-speaking, logicians decide on how they relate to each other.</para>
<para>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.</para>
<para>Thus, if you translate the English:</para>
<example xml:id="example-random-id-hEa7">
<title>
<anchor xml:id="c15e2d14"/>
</title>
<para>I do not go to the market because the car is broken.</para>
</example>
<para>as:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-q8su">
<title>
<anchor xml:id="c15e2d15"/>
</title>
<interlinear-gloss>
<jbo>mi na klama le zarci ki'u lenu le karce cu spofu</jbo>
<gloss>I [false] go-to the market because the car is broken.</gloss>
<natlang>It is false that:
<quote>I go to the market because the car is broken.</quote></natlang>
</interlinear-gloss>
</example>
<para>you end up negating too much.</para>
<para>Such mistranslations result from the ambiguity of English compounded by the messiness of natural language negation. A correct translation of the normal interpretation of
<xref linkend="example-random-id-hEa7"/> is:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-R3GU">
<title>
<anchor xml:id="c15e2d16"/>
</title>
<interlinear-gloss>
<jbo>lenu mi na klama le zarci cu se krinu lenu le karce cu spofu</jbo>
<gloss>The event-of (my [false] going-to the market) is justified by the event-of (the car being broken).</gloss>
<natlang>My not going to the market is because the car is broken.</natlang>
</interlinear-gloss>
</example>
<para>In
<xref linkend="example-random-id-R3GU"/>, 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).</para>
<para>The problem is not confined to obvious causals. In the English:</para>
<example xml:id="example-random-id-MGvB">
<title>
<anchor xml:id="c15e2d17"/>
</title>
<para>I was not conscripted into the Army with the help of my uncle the Senator.</para>
</example>
<para>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:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-NILi">
<title>
<anchor xml:id="c15e2d18"/>
</title>
<interlinear-gloss>
<gloss>The event-of (my [false] being-conscripted-into the Army) was aided by my uncle the Senator.</gloss>
</interlinear-gloss>
</example>
<para>It is possible that someone will want to incorporate bridi negations into lujvo. For this reason, the rafsi
<rafsi>-nar-</rafsi> has been reserved for
<valsi>na</valsi>. However, before using this rafsi, make sure that you intend the contradictory bridi negation, and not the scalar negation described in
<xref linkend="section-scalar-negation"/>, which will be much more common in tanru and lujvo.</para>
</section>
<section xml:id="section-scalar-negation">
<title>Scalar Negation</title>
<para>Let us now consider some other types of negation. For example, when we say:</para>
<example xml:id="example-random-id-GJga">
<title>
<anchor xml:id="c15e3d1"/>
</title>
<para>The chair is not brown.</para>
</example>
<para>we make a positive inference – that the chair is some other color. Thus, it is legitimate to respond:</para>
<example xml:id="example-random-id-DDN8">
<title>
<anchor xml:id="c15e3d2"/>
</title>
<para>It is green.</para>
</example>
<para>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:</para>
<example xml:id="example-random-id-muQB">
<title>
<anchor xml:id="c15e3d3"/>
</title>
<para>The chair is not brown.</para>
<para>Correct. The chair is wooden.</para>
</example>
<para>we immediately start to wonder about the unusual wood that isn't brown. If we hear the exchange:</para>
<example xml:id="example-random-id-MxWM">
<title>
<anchor xml:id="c15e3d4"/>
</title>
<para>Is the chair green?</para>
<para>No, it is in the kitchen.</para>
</example>
<para>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!</para>
<para>What is going on in these statements is something called
<quote>scalar negation</quote>. 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):</para>
<example xml:id="example-random-id-s5DJ">
<title>
<anchor xml:id="c15e3d5"/>
</title>
<para>That isn't a blue house.</para>
<para>Right! That is a green house.</para>
</example>
<para>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:</para>
<example xml:id="example-random-id-M472">
<title>
<anchor xml:id="c15e3d6"/>
</title>
<para>That isn't a blue house.</para>
<para>Right! That is a blue car.</para>
</example>
<para>Again, we have acknowledged a scalar negation, and substituted a different object in the universe of discourse of things that can be blue.</para>
<para>Now, if the following exchange occurs:</para>
<example xml:id="example-random-id-sq36">
<title>
<anchor xml:id="c15e3d7"/>
</title>
<para>That isn't a blue house.</para>
<para>Right! That is a green car.</para>
</example>
<para>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,
<quote>blue house</quote> and
<quote>green car</quote> 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:</para>
<example xml:id="example-random-id-hd0I">
<title>
<anchor xml:id="c15e3d8"/>
</title>
<para>That isn't a
<quote>blue-house</quote>.</para>
</example>
<para>aloud so as to clearly imply that the scalar negation is affecting the pair of words as a single unit.</para>
<para>Another even more confusing example of scalar negation is to the sentence:</para>
<example xml:id="example-random-id-JTrd">
<title>
<anchor xml:id="c15e3d9"/>
</title>
<para>John didn't go to Paris from Rome.</para>
</example>
<para>Might
<xref linkend="example-random-id-JTrd"/> 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.</para>
<para>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
<quote>non-</quote> 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</para>
<example xml:id="example-random-id-gN3C">
<title>
<anchor xml:id="c15e3d10"/>
</title>
<para>That is a non-blue house.</para>
</example>
<para>from the related sentence</para>
<example xml:id="example-random-id-GtQC">
<title>
<anchor xml:id="c15e3d11"/>
</title>
<para>That is a blue non-house.</para>
</example>
<para>
<xref linkend="example-random-id-gN3C"/> and
<xref linkend="example-random-id-GtQC"/> 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.</para>
<para>We can't always use
<quote>non-</quote> though, because of the peculiarities of English's grammar. It would sound strange to say:</para>
<example xml:id="example-random-id-A3yR">
<title>
<anchor xml:id="c15e3d12"/>
</title>
<para>John went to non-Paris from Rome.</para>
</example>
<para>or</para>
<example xml:id="example-random-id-sn2I">
<title>
<anchor xml:id="c15e3d13"/>
</title>
<para>John went to Paris from non-Rome.</para>
</example>
<para>although these would clarify the vague negation. Another circumlocution for English scalar negation is
<quote>other than</quote>, which works where
<quote>non-</quote> does not, but is wordier.</para>
<para>Finally, we have natural language negations that are called polar negations, or opposites:</para>
<example xml:id="example-random-id-qh2s">
<title>
<anchor xml:id="c15e3d14"/>
</title>
<para>John is moral</para>
</example>
<example xml:id="example-random-id-qh3s">
<title>
<anchor xml:id="c15e3d15"/>
</title>
<para>John is immoral</para>
</example>
<para>To be immoral is much more than to just be not moral: it implies the opposite condition. Statements like
<xref linkend="example-random-id-qh3s"/> are strong negations which not only deny the truth of a statement, but assert its opposite. Since,
<quote>opposite</quote> implies a scale, polar negations are a special variety of scalar negations.</para>
<para>To examine this concept more closely, let us draw a linear scale, showing two examples of how the scale is used:</para>
<programlisting xml:space="preserve">
Affirmations (positive) Negations (negative)
|-----------|-----------|-----------|-----------|
All Most Some Few None
Excellent Good Fair Poor Awful
</programlisting>
<para>Some scales are more binary than the examples we diagrammed. Thus we have
<quote>not necessary</quote> or
<quote>unnecessary</quote> being the polar opposite of necessary. Another scale, especially relevant to Lojban, is interpreted based on situations modified by one's philosophy:
<quote>not true</quote> may be equated with
<quote>false</quote> in a bi-valued truth-functional logic, while in tri-valued logic an intermediate between
<quote>true</quote> and
<quote>false</quote> is permitted, and in fuzzy logic a continuous scale exists from true to false. The meaning of
<quote>not true</quote> requires a knowledge of which variety of truth scale is being considered.</para>
<para>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
<quote>not mild</quote>, for example.</para>
<para>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.</para>
<para>In English, scalar negation semantically includes phrases such as
<quote>other than</quote>,
<quote>reverse of</quote>, or
<quote>opposite from</quote> expressions and their equivalents. More commonly, scalar negation is expressed in English by the prefixes
<quote>non-</quote>,
<quote>un-</quote>,
<quote>il-</quote>, and
<quote>im-</quote>. 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.</para>
<para>In the examples of
<xref linkend="section-nahe"/>, we will translate the general case of scalar negation using the general formula
<quote>other than</quote> when a phrase is scalar-negated, and
<quote>non-</quote> when a single word is scalar-negated.</para>
</section>
<section xml:id="section-nahe">
<title>selbri and tanru negation</title>
<para>All the scalar negations illustrated in
<xref linkend="section-scalar-negation"/> are expressed in Lojban using the cmavo
<valsi>na'e</valsi> (of selma'o NAhE). The most common use of
<valsi>na'e</valsi> is as a prefix to the selbri:</para>
<example xml:id="example-random-id-qh42" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d1"/>
</title>
<interlinear-gloss>
<jbo>mi klama le zarci</jbo>
<natlang>I go to the market.</natlang>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qH4n" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d2"/>
</title>
<interlinear-gloss>
<jbo>mi na'e klama le zarci</jbo>
<gloss>I non-go to the market.</gloss>
</interlinear-gloss>
</example>
<para>Comparing these two, we see that the negation operator being used in
<xref linkend="example-random-id-qH4n"/> is
<valsi>na'e</valsi>. But what exactly does
<valsi>na'e</valsi> negate? Does the negation include only the gismu
<valsi>klama</valsi>, which is the entire selbri in this case, or does it include the
<jbophrase>le zarci</jbophrase> as well? In Lojban, the answer is unambiguously
<quote>only the gismu</quote>. The cmavo
<valsi>na'e</valsi> always applies only to what follows it.</para>
<para>
<xref linkend="example-random-id-qH4n"/> looks as if it were parallel to:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-tqX1">
<title>
<anchor xml:id="c15e4d3"/>
</title>
<interlinear-gloss>
<jbo>mi na klama le zarci</jbo>
<gloss>I [false] go-to the market.</gloss>
</interlinear-gloss>
</example>
<para>but in fact there is no real parallelism at all. A negation using
<valsi>na</valsi> denies the truth of a relationship, but a selbri negation with
<valsi>na'e</valsi> asserts that a relationship exists other than that stated, one which specifically involves the sumti identified in the statement. The grammar allotted to
<valsi>na'e</valsi> 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
<valsi>na'e</valsi> is determined.</para>
<para>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
<valsi>na'e</valsi> as well. The positive sentence</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-ETuV">
<title>
<anchor xml:id="c15e4d4"/>
</title>
<interlinear-gloss>
<jbo>mi cadzu klama le zarci</jbo>
<gloss>I walking-ly go to the market.</gloss>
</interlinear-gloss>
</example>
<para>can be subjected to selbri negation in several ways. Two are:</para>
<example xml:id="example-random-id-qh4w" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d5"/>
</title>
<interlinear-gloss>
<jbo>mi na'e cadzu klama le zarci</jbo>
<gloss>I (other-than-walkingly)-go-to the market.</gloss>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qH6w" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d6"/>
</title>
<interlinear-gloss>
<jbo>mi cadzu na'e klama le zarci</jbo>
<gloss>I walkingly-(other-than-go-to) the market.</gloss>
</interlinear-gloss>
</example>
<para>These negations show the default scope of
<valsi>na'e</valsi> is close-binding on an individual brivla in a tanru.
<xref linkend="example-random-id-qh4w"/> 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
<xref linkend="chapter-selbri"/> for a discussion of tanru meaning).</para>
<para>In neither
<xref linkend="example-random-id-qh4w"/> nor
<xref linkend="example-random-id-qH6w"/> does the
<valsi>na'e</valsi> 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
<xref linkend="example-random-id-qh4w"/>, which says that I am going, but in a non-walking manner. In
<xref linkend="example-random-id-qH6w"/>, we have claimed that the relationship between me and the market in some way involves walking, but is not one of
<quote>going to</quote> (perhaps we are walking around the market, or walking-in-place while at the market).</para>
<para>The
<quote>scale</quote>, or actually the
<quote>set</quote>, 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
<valsi>mo</valsi> 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.</para>
<para>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
<valsi>na'e</valsi>):</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-t20b">
<title>
<anchor xml:id="c15e4d7"/>
</title>
<interlinear-gloss>
<jbo>mi na'eke cadzu klama [ke'e] le zarci</jbo>
<jbo>mi na'e (ke cadzu klama [ke'e]) le zarci</jbo>
<gloss>I other-than-(walkingly-go-to) the market.</gloss>
</interlinear-gloss>
</example>
<para>This negation uses the same
<valsi>ke</valsi> and
<valsi>ke'e</valsi> delimiters (the
<valsi>ke'e</valsi> is always elidable at the end of a selbri) that are used in tanru. The sentence clearly negates the entire selbri. The
<valsi>ke'e</valsi>, 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
<valsi>na'e</valsi>.</para>
<para>Negations of just part of the selbri are also permitted:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-PVct">
<title>
<anchor xml:id="c15e4d8"/>
</title>
<interlinear-gloss>
<jbo>mi na'eke sutra cadzu ke'e klama le zarci</jbo>
<jbo>mi na'e (ke sutra cadzu ke'e) klama le zarci</jbo>
<gloss>I other-than-(quickly-walkingly) go-to the market.</gloss>
</interlinear-gloss>
</example>
<para>In
<xref linkend="example-random-id-PVct"/>, only the
<jbophrase>sutra cadzu</jbophrase> tanru is negated, so the speaker is indeed going to the market, but not by walking quickly.</para>
<para>Negations made with
<valsi>na'e</valsi> or
<jbophrase>na'eke</jbophrase> also include within their scope any sumti attached to the brivla or tanru with
<valsi>be</valsi> or
<valsi>bei</valsi>. Such attached sumti are considered part of the brivla or tanru:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-MYYa">
<title>
<anchor xml:id="c15e4d9"/>
</title>
<interlinear-gloss>
<jbo>mi na'e ke sutra cadzu be le mi birka ke'e klama le zarci</jbo>
<gloss>I other-than-(quickly walking-on-my-arms-ly) go-to the market.</gloss>
</interlinear-gloss>
</example>
<para>Note that
<xref linkend="example-random-id-qh7T"/> and
<xref linkend="example-random-id-qH8J"/> do not express the same thing:</para>
<example xml:id="example-random-id-qh7T" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d10"/>
</title>
<interlinear-gloss>
<jbo>mi na'eke sutra cadzu [ke'e] lemi birka</jbo>
<jbo>mi na'e (ke sutra cadzu [ke'e]) lemi birka</jbo>
<gloss>I other-than-(quickly-walk-on) my-arms.</gloss>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qH8J" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d11"/>
</title>
<interlinear-gloss>
<jbo>mi na'eke sutra cadzu be lemi birka [ke'e]</jbo>
<jbo>mi na'e (ke sutra cadzu be lemi birka [ke'e])</jbo>
<gloss>I other-than-(quickly-walk-on my-arms).</gloss>
</interlinear-gloss>
</example>
<para>The translations show that the negation in
<xref linkend="example-random-id-qh7T"/> is more restricted in scope; i.e. less of the sentence is negated with respect to x1 (
<valsi>mi</valsi>).</para>
<para>Logical scope being an important factor in Lojban's claims to be unambiguous, let us indicate the relative precedence of
<valsi>na'e</valsi> as an operator. Grouping with
<valsi>ke</valsi> and
<valsi>ke'e</valsi>, of course, has an overt scope, which is its advantage.
<valsi>na'e</valsi> is very close binding to its brivla. Internal binding of tanru, with
<valsi>bo</valsi>, is not as tightly bound as
<valsi>na'e</valsi>.
<valsi>co</valsi>, the tanru inversion operator has a scope that is longer than all other tanru constructs.</para>
<para>In short,
<valsi>na'e</valsi> and
<jbophrase>na'eke</jbophrase> 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
<valsi>na'e</valsi> negation remains an assertion of some specific truth and not merely a denial of another claim.</para>
<para>The similarity becomes striking when it is noticed that the rafsi
<rafsi>-nal-</rafsi>, representing
<valsi>na'e</valsi> when a tanru is condensed into a lujvo, forms an exact parallel to the English usage of
<jbophrase>non-</jbophrase>. Turning a series of related negations into lujvo gives:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-2buq"> <!-- FIXME: this "example" should probably just be a simplelist -->
<title>
<anchor xml:id="c15e4d12"/>
</title>
<interlinear-gloss>
<jbo>na'e klama becomes nalkla</jbo>
<jbo>na'e cadzu klama becomes naldzukla</jbo>
<jbo>na'e sutra cadzu klama becomes nalsu'adzukla</jbo>
<jbo>nake sutra cadzu ke'e klama becomes nalsu'adzuke'ekla</jbo>
</interlinear-gloss>
</example>
<para>Note:
<rafsi>-kem-</rafsi> is the rafsi for
<valsi>ke</valsi>, but it is omitted in the final lujvo as superfluous –
<valsi>ke'e</valsi> is its own rafsi, and its inclusion in the lujvo implies a
<valsi>ke</valsi> after the
<rafsi>-nal-</rafsi>, since it needs to close something; only a
<valsi>ke</valsi> immediately after the negation would make the
<valsi>ke'e</valsi> meaningful in the tanru expressed in this lujvo.</para>
<para>In a lujvo, it is probably clearest to translate
<rafsi>-nal-</rafsi> as
<quote>non-</quote>, to match the English combining forms, except when the
<valsi>na'e</valsi> has single word scope and English uses
<quote>un-</quote> or
<quote>im-</quote> to negate that single word. Translation style should determine the use of
<quote>other than</quote>,
<quote>non-</quote>, or another negator for
<valsi>na'e</valsi> in tanru; the translator must render the Lojban into English so it is clear in context. Let's go back to our simplest example:</para>
<example xml:id="example-random-id-qh9c" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d13"/>
</title>
<interlinear-gloss>
<jbo>mi na'e klama le zarci</jbo>
<gloss>I am other-than-(going-to) the market.</gloss>
<gloss>I am not going-to the market.</gloss>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qH9e" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e4d14"/>
</title>
<interlinear-gloss>
<jbo>mi nalkla le zarci</jbo>
<gloss>I am-a-non-go-er-to the market.</gloss>
</interlinear-gloss>
</example>
<para>Note that to compare with the English translation form using
<quote>non-</quote>, we've translated the Lojban as if the selbri were a noun. Since Lojban
<valsi>klama</valsi> 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.</para>
<para>Consider the following highly problematic sentence:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-GFFo">
<title>
<anchor xml:id="c15e4d15"/>
</title>
<interlinear-gloss>
<jbo>lo ca nolraitru be le fasygu'e cu krecau</jbo>
<gloss>An-actual currently noblest-governor of the French country is-hair-without.</gloss>
<natlang>The current King of France is bald.</natlang>
</interlinear-gloss>
</example>
<para>The selbri
<valsi>krecau</valsi> negates with
<valsi>na'e</valsi> as:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-2maY">
<title>
<anchor xml:id="c15e4d16"/>
</title>
<interlinear-gloss>
<jbo>lo ca nolraitru be le fasygu'e cu na'e krecau</jbo>
<gloss>An-actual currently noblest-governor of the French country is-other-than hair-without.</gloss>
<natlang>The current King of France is other-than-bald.</natlang>
</interlinear-gloss>
</example>
<para>or, as a lujvo:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-wGXL">
<title>
<anchor xml:id="c15e4d17"/>
</title>
<interlinear-gloss>
<jbo>lo ca nolraitru be le fasygu'e cu nalkrecau</jbo>
<gloss>An-actual currently noblest-governor of the French country is-non-hair-without.</gloss>
<natlang>The current King of France is a non-bald-one.</natlang>
</interlinear-gloss>
</example>
<para>
<xref linkend="example-random-id-2maY"/> and
<xref linkend="example-random-id-wGXL"/> express the predicate negation forms using a negation word (
<valsi>na'e</valsi>) or rafsi (
<rafsi>-nal-</rafsi>); 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
<valsi>na'e</valsi> to the brivla. The lujvo form makes this overt by absorbing the negative marker into the word.</para>
<para>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
<quote>false</quote>, since no affirmative statement about the current King of France can be true. On the other hand, bridi negation does produce a truth:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-Bwdy">
<title>
<anchor xml:id="c15e4d18"/>
</title>
<interlinear-gloss>
<jbo>lo ca nolraitru be le fasygu'e cu na krecau</jbo>
<gloss>An-actual current noblest-governor of the French Country [false] is-hair-without.</gloss>
<natlang>It is false that the current King of France is bald.</natlang>
</interlinear-gloss>
</example>
<para>Note:
<valsi>lo</valsi> 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
<valsi>le</valsi> instead of
<valsi>lo</valsi> 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
<valsi>le</valsi> in
<xref linkend="section-basic-descriptors"/>.)</para>
</section>
<section xml:id="section-scales-negation">
<title>Expressing scales in selbri negation</title>
<para>In expressing a scalar negation, we can 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
<xref linkend="section-nahe"/>, the default is the set of plausible alternatives. Thus if we say:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-mw3B">
<title>
<anchor xml:id="c15e5d1"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu na'e xunre</jbo>
<gloss>The chair is a non-(red-thing).</gloss>
</interlinear-gloss>
</example>
<para>the pragmatic interpretation is that we mean a different color and not</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-7iMz">
<title>
<anchor xml:id="c15e5d2"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu dzukla be le zarci</jbo>
<gloss>The chair walkingly-goes-to-the-market.</gloss>
</interlinear-gloss>
</example>
<para>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:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-yWSC">
<title>
<anchor xml:id="c15e5d3"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu na'e xunre skari</jbo>
<gloss>The chair is of a non-(red)-color (as perceived by something under some conditions).</gloss>
</interlinear-gloss>
</example>
<para>We might also have reduced the pragmatic ambiguity by making the two trailing sumti values explicit (the
<quote>as perceived by</quote> and
<quote>under conditions</quote> places have been added to the place structure of
<valsi>xunre</valsi>). But assume we have a really stubborn listener (an artificially semi-intelligent computer?) who will find a way to misinterpret
<xref linkend="example-random-id-yWSC"/> even with three specific sumti provided.</para>
<para>In this case, we use a sumti tagged with the sumti tcita
<valsi>ci'u</valsi>, which translates roughly as
<quote>on a scale of X</quote>, where
<varname>X</varname> is the sumti. For maximal clarity, the tagged sumti can be bound into the negated selbri with
<valsi>be</valsi>. To clarify
<xref linkend="example-random-id-yWSC"/>, we might say:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-a8S1">
<title>
<anchor xml:id="c15e5d4"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu na'e xunre be ci'u loka skari</jbo>
<gloss>The chair is a non-(red on-a-scale-of-colorness)-thing.</gloss>
</interlinear-gloss>
</example>
<para>We can alternately use the sumti tcita
<valsi>teci'e</valsi>, based on
<valsi>ciste</valsi>, which translates roughly as
<quote>of a system of components X</quote>, for universes of discourse; in this case, we would express
<xref linkend="example-random-id-yWSC"/> as:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-I0eV">
<title>
<anchor xml:id="c15e5d5"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu na'e xunre be teci'e le skari</jbo>
<gloss>The chair is a non-(red of-a-system-with-components-the-colors)-thing.</gloss>
</interlinear-gloss>
</example>
<para>Other places of
<valsi>ciste</valsi> can be brought out using the grammar of selma'o BAI modals, allowing slightly different forms of expression, thus:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-Rj71">
<title>
<anchor xml:id="c15e5d6"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu na'e xunre be ci'e lo'i skari</jbo>
<gloss>The chair is a non-(red of-a-system-which-is-the-set-of-colors)-thing.</gloss>
</interlinear-gloss>
</example>
<para>The cmavo
<valsi>le'a</valsi>, also in selma'o BAI, can be used to specify a category:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-5ibb">
<title>
<anchor xml:id="c15e5d7"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu na'e xunre be le'a lo'i skari</jbo>
<gloss>The chair is a non-(red of-a-category-which-is-the-set-of-colors)-thing.</gloss>
</interlinear-gloss>
</example>
<para>which is minimally different in meaning from
<xref linkend="example-random-id-Rj71"/>.</para>
<para>The cmavo
<valsi>na'e</valsi> 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
<valsi>to'e</valsi>, which is grammatically equivalent to
<valsi>na'e</valsi>:</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-RuvP">
<title>
<anchor xml:id="c15e5d8"/>
</title>
<interlinear-gloss>
<jbo>le stizu cu to'e xunre be ci'u loka skari</jbo>
<gloss>The chair is a (opposite-of red) on-scale a-property-of color-ness.</gloss>
</interlinear-gloss>
</example>
<para>Likewise, the midpoint of a scale can be expressed with the cmavo
<valsi>no'e</valsi>, also grammatically equivalent to
<valsi>na'e</valsi>. Here are some parallel examples of
<valsi>na'e</valsi>,
<valsi>no'e</valsi>, and
<valsi>to'e</valsi>:</para>
<example xml:id="example-random-id-qH9T" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e5d9"/>
</title>
<interlinear-gloss>
<jbo>ta melbi</jbo>
<gloss>That is-beautiful.</gloss>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qh9U" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e5d10"/>
</title>
<interlinear-gloss>
<jbo>ta na'e melbi</jbo>
<gloss>That is-non-beautiful.</gloss>
<gloss>That is other than beautiful.</gloss>
<natlang>That is ugly [in one sense].</natlang>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qhAI" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e5d11"/>
</title>
<interlinear-gloss>
<jbo>ta no'e melbi</jbo>
<gloss>That is-neutrally beautiful.</gloss>
<natlang>That is plain/ordinary-looking (neither ugly nor beautiful).</natlang>
</interlinear-gloss>
</example>
<example xml:id="example-random-id-qHAV" role="interlinear-gloss-example">
<title>
<anchor xml:id="c15e5d12"/>
</title>
<interlinear-gloss>
<jbo>ta to'e melbi</jbo>
<gloss>That is-opposite-of beautiful.</gloss>
<natlang>That is ugly/very ugly/repulsive.</natlang>
</interlinear-gloss>
</example>
<para>The cmavo
<valsi>to'e</valsi> has the assigned rafsi
<rafsi>-tol-</rafsi> and
<jbophrase>-to'e-</jbophrase>; the cmavo
<valsi>no'e</valsi> has the assigned rafsi
<rafsi>-nor-</rafsi> and
<rafsi>-no'e-</rafsi>. The selbri in
<xref linkend="example-random-id-qh9U"/> through
<xref linkend="example-random-id-qHAV"/> could be replaced by the lujvo
<valsi>nalmle</valsi>,
<valsi>normle</valsi>, and
<valsi>tolmle</valsi> respectively.</para>
<para>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
<quote>ultimately ugly</quote> or
<quote>ultimately beautiful</quote>. Other scales, like temperature, are open at one end and closed at the other: there is a minimum temperature (so-called
<quote>absolute zero</quote>) but no maximum temperature. Still other scales are closed at both ends.</para>
<para>Correspondingly, some selbri have no obvious
<valsi>to'e</valsi>- what is the opposite of a dog? – while others have more than one, and need
<valsi>ci'u</valsi> to specify which opposite is meant.</para>
</section>
<section xml:id="section-sumti-negation">
<title>sumti negation</title>
<para>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
<jbophrase>na'ebo</jbophrase> before the sumti. It turns out that a zero quantification serves for contradictory negation. As the cmavo we use implies,
<jbophrase>na'ebo</jbophrase> forms a scalar negation.</para>
<para>Let us show examples of each.</para>
<example role="interlinear-gloss-example" xml:id="example-random-id-PL1E">
<title>
<anchor xml:id="c15e6d1"/>
</title>
<interlinear-gloss>
<jbo>no lo ca nolraitru be le fasygu'e cu krecau</jbo>
<gloss>Zero of those who are currently noblest-governors of the French country are-hair-without.</gloss>