Chapter 15: “No” Problems: On Lojban Negation
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.
✥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.
Is ✥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:
✥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.
✥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.
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:
✥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.
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.