[om-list] Sense and Tense

[Mark Butler]

Sense and Tense

I submit that natural language tenses can be accurately modeled as a 
time dependent functions of the sense of the proposition with the tense 
removed.  For example, given time-dependent base proposition P we might 
have:

(1) P is always true
(2) P has always been true (at least until now)
(3) P was true (at some time in the past)
(4) P has been true (from some time in the past until now)
(5) P is true  (now)
(6) P will have been true (at some time in the future)
(7) P will be true (at some time in the future)

Other verbs have more complex tenses, but this gives you the idea.  We 
can easily translate these example tenses into functions.

Definitions:
   ts:   the time the statement is made or held to be true.
   tx,ty:  unbound context times
   S:   [-1,+1] linear sense of base proposition
  
Then the following sense functions match the corresponding tenses listed 
above

(1)  S = 1   (for all time)
(2)  S = 1 for t < ts, 0 otherwise
(3)  S = delta(t-tx) for some time tx < ts where delta() is the Dirac 
delta function or some reasonable equivalent.
(4)  S = 0 for t < tx, 1 for tx < t < ts,  0 otherwise for some time tx 
< ts.
(5)  S = delta(ts)
(6)  S = delta(tx) - delta(ty) for some times tx and ty where ty > tx > ts.
(7)  S = delta(tx) for some time tx > ts.

Notice how wonderfully non-commital most of these tenses are. The sense 
for common tenses at most times is roughly zero - most act as simple 
existential predicates that there exists or will exist at least one time 
where the base proposition is true.  If you can't handle existential 
predicates, most tenses have to be qualified with specific times to be 
clear, which is usually only the case in subject areas like history (or 
anything else where you have a specified context time tx for all of your 
statements).

There is one major caveat to this - the sense functions should be 
contigent on whether P is a time-dependent or time-independent 
proposition.  For time independent propositions (e.g. 2+2 = 4), most of 
the more elaborate tenses are redundant and all seven example tenses 
should generally reduce to "is always true" (S = 1).  Otherwise they 
show metaphysical doubt ( e.g. two plus two was equal to four yesterday 
but I don't know about today...).  Of course if the temporality of the 
subject is open to debate, then the less committal form must be 
preserved (...yes the French Revolution occurred in 1789, but will it 
always have occured in 1789?)

- Mark


Note: Intentional tenses, e.g. ones that contain "would" or that are 
contingent on the speakers free will, must be factored appropriately.  
For example "I would have gone" is an existential predicate about the 
state of the speaker's intention to go at some time in the past plus an 
implication that he did not go at the same time that he would have 
gone.  Likewise, "I will go" expresses both an intent and a belief in a 
future state of affairs.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://six.pairlist.net/pipermail/om-list/attachments/20031010/29cbaf6e/attachment.html