Subject: RE: Tenses

From: [email-masked]
Date: Mon, 12 Aug 2002 12:08:32 EDT

Before dealing with various points about Lojban tenses, I find it helpful to 
review the ideal system and its (partial) realizations in logic, natural 
languages and Lojban. This gives an anchor to cling to when the 
controversies get too confusing. So:
Tense is a system of vectors that run from axes to events. An axis comes 
into existence by having a vector originate at it, an event comes into 
language by being at the end of a vector. Vectors have two properties: a 
direction and a length (tensor). In tense vector systems there is a 0-vector, 
which ends where it originates and has a length of (conventionally) 0 in 
every measuring system. Vectors can iterate; that is, the "event" at which 
one vector ends may be simply the start of another vector, a new axis. The 
direction of a vector may be given in any of a number of intertranslatable 
(given some some faaactual information) forms, based on a variety of 
techniques: graph points, angles, egocentric directions, geographical 
directions, direction of known objects, indexicals, and so on. In the case 
of temporal vectors, there are only the three directions, past (-), present 
(0), and future (+) and the reference to a known event, but spatial vectors 
can be specified in a bewildering variety of ways. The same is true of 
tensors, which can be specified numerically according to some system of 
measurement or by reference to some known thing and even by reference to the 
other modality (times can be referenced spatially and spaces temporally). 
The system also allows "events" that are either outside time (to which time 
is irrelevant -- eternal) or simply "occur" at all times (sempiternal) and 
similarly for space (ellocal and ubiquitous). The first axis of a string of 
one or more vectors is usually taken as given: either the here-and-now of the 
speaker or something established by context. It might also be given 
explicitly by some name or description, including some vector from the given 
axis. A vector may be indicated only partially: either the tensor or the 
direction may be omitted or given in a vague way ("a long time" vs. "seven 
and a half hours," for example), and, in spatial tenses, some dimensions may 
be ignored (we omit altitude in giveing street directions, say). 
Tense logical systems tend to be either very vague or (in principle) very 
precise on tensors, precise on direction and to use vectors to define new 
axes. They also (I think because they are generally not predicate logical 
systems), tend to ignore the 0-vector, not distinguishing among, for example, 
-, 0- and -0 temporal vector strings, as some natural languages do. In 
logic, unmarked sentences are typically of the outside or always variety 
(which, combined with the absence of the 0-vector creates problems, usually 
dealt with by introducing a name for the implicit initial axis). Vectors are 
indefinitely iterable in logic, whereas natural languages seem never to have 
more than four temporal vectors in a single string and even that extreme case 
is often a little peculiar, starting to flop outside the tense system. The 
natural systems of spatial tenses is less clear but, on other than observed 
grounds, probably does not allow more than seven vectors in a single string. 
Logic systems typically (for control) use a limited number of ways to 
describe directions, measure tensors and introduce new axes; natural 
languages seem to allow just about all the ways that one can think (in that 
language -- a SW effect?).
Lojban has a full basic temporal tense system: {pu} -, {ca} 0, {ba} +, and a 
set of vague tensors,ZI. It has a spatial 0 {bu'u} and a variety of 
directional device:
egocentric and geographic (much of FAhA, the rest of which I save for another 
time) and another set of vague tensors VI. The directional markers of a given 
type may be iterated indefinitely (though again, I suspect that seven is a 
practical upper limit and pushing one's luck at that), but the iterations 
cannot be mixed either temporals and spatials. There can be both a temporal 
string and a spatial one but they are separate. There can be a string of 
directionals, or of directional+distance (in that order) combinations, but 
not, apparently, of more than one distance nor of a moixture of directionals 
and distances, except for a distance-initial string of directionals.
Unmarked sentences may be of any type, outside-or-all-over or at a 
contextually determned axis -- context decides (Grice rules!). Remote axes 
that are explicit are introduced by name or description of a coincident event 
or object, not by displacement from the given axis (except as that might be 
worked into a name or description). Thje standard way of using a remote axis 
is parallel to using the given one, except the reference to the axis is 
explicit: {vi le cmana [ku]} means "a short way from the mountain", just as 
{vi [ku]} means "a short way from the given axis" and the longer expression 
has about the same range of locations as the shorter one and, like it, needs 
some care to keep its connection with the whole sentence rather than some 
sumti within it. A remote axis expression cannot, therefore, go in the 
normal tense place, since it will there attach to the x1 sumti (and putting 
{cu} before it is illegal).
For the discussion at hand, the point to notice is that in tense+sumti, the 
sumti is always an axis, never an event: {pu lenu mi broda} means "before I 
broda," never "back when I broda" or an equivalent of {mi pu broda}. This 
meets the present problem; the others (like "How do you give precise tensors, 
e.g., 'fifty minutes ago and five miles away'?") will have to wait.