Chapter 16: “Who Did You Pass On The Road? Nobody”: Lojban And Logic

3. Universal claims

What happens if we substitute “everything” for “something” in ✥2.1? We get:

✥3.1  Everything sees me.

Of course, this example is false, because there are many things which do not see the speaker. It is not easy to find simple truthful examples of so-called universal claims (those which are about everything), so bear with us for a while. (Indeed, some Lojbanists tend to avoid universal claims even in other languages, since they are so rarely true in Lojban.)

The Lojban translation of ✥3.1 is

✥3.2  ro da zo'u da viska mi
For-every X : X sees me.

When the variable cmavo “da” is preceded by “ro”, the combination means “For every X” rather than “There is an X”. Superficially, these English formulations look totally unrelated: c16-§6 will bring them within a common viewpoint. For the moment, accept the use of “ro da” for “everything” on faith.

Here is a universal claim with two variables:

✥3.3  ro da ro de zo'u da prami de
For-every X, for-every Y : X loves Y.
Everything loves everything.

Again, X and Y can represent the same thing, so ✥3.3 does not mean “Everything loves everything else.” Furthermore, because the claim is universal, it is about every thing, not merely every person, so we cannot use “everyone” or “everybody” in the translation.

Note that “ro” appears before both “da” and “de”. If “ro” is omitted before either variable, we get a mixed claim, partly existential like those of c16-§2, partly universal.

✥3.4  ro da de zo'u da viska de
For-every X, there-is-a-Y : X sees Y.
Everything sees something.

✥3.5  da ro de zo'u da viska de
There-is-an-X such-that-for-every-Y : X sees Y.
Something sees everything.

Examples 3.4 and 3.5 mean completely different things. ✥3.4 says that for everything, there is something which it sees, not necessarily the same thing seen for every seer. ✥3.5, on the other hand, says that there is a particular thing which can see everything that there is (including itself). Both of these are fairly silly, but they are different kinds of silliness.

There are various possible translations of universal claims in English: sometimes we use “anybody/anything” rather than “everybody/everything”. Often it makes no difference which of these is used: when it does make a difference, it is a rather subtle one which is explained in c16-§8.