| In a message dated 10/3/2002 7:04:24 PM Central Daylight Time, jjllambias@hotmail.com writes: << 1- <n>-roi, with integer, <n> says that the event happens <n> times, >> I think the analogical argument so far gets no problems: Earth revolves one-twelfth in a month, just as it does once in a year (give or take, of course). << This is different from saying that the event happens in a fraction of an interval. For example, to say that the horse has been running for half of an hour, we say: le xirma cu bajra ze'a lo cacra be li pimu The horse runs for half an hour. and not le xirma cu bajra pimuroi lo cacra The horse runs half-instance in an hour. >> That is because there is not boundaries on running (activity). If you put in a process, where there is a "natural bondary," "runs a mile" say, one could say -- I think -- that a turtle runs a half-instance of running a mile in an hour ("run" being a bit odd here), if it covers half a mile in that time. This does not seem to me to be a flaw in the argument so far, however. << Also, le xirma cu pimuroi bajra ze'a lo cacra The horse half-run for an hour. I think fractional roi then can be interpreted if not exactly as a fuzzy logic function, as something very similar. >> I am not to sure what this one means, for all sorts of reasons. Again, it may make sense with "runs a mile" and seems to mean about the same as the case above, though -- in some not very clear way to me -- not exactly the same (it may be the "for"/"in" contrast that goes with activities v. processes). This seems less a fuzzy value function than an amount of event function ({ni} more than {jei}), but that is too incertain a line yet to say for sure. That is, I can easily see any of these sentences being flat-out true, not requiring a fractional value. And, indeed, I can see the activity sentences at least to be flat out true even if you drop the {pimuroi} part (processes are trickier, but still possible, I think). << 3- <n>-re'u for integer <n> gives the nth instance of an event. Similarly we can say that fractional re'u gives the n-th stage of one instance, as it becomes an instance. Then {piso'ure'u} will be similar to {co'a}. The difference being that whereas {co'a} marks a sharp transition from 0 to 1, {piso'ure'u} would mark the initial stages. {pirore'u} is similar to {mo'u} in the same way. >> The analogy here is weaker, if only because fractional ordinals make so little sense (which, of course, can be an opening for giving them a special sense). And, of course, the notion of stages of events makes clear sense only in the case of processes. Otherwise, it comes down to little more than chopping things up temporally -- which may be enough for this purpose. Also, though we often talk that way, {co'a} doesn't have to be sharp -- as anyone who works knows, getting started can take some time (treating an achievement here as a process, of course -- but reality allows both readings). << 4- Then as {za'ure'u} indicates an additional instance, {piza'ure'u} can indicate an additional increment in the formation of an instance, and then {pime'ire'u} would analogously give a decrement: le xirma cu pime'ire'u bajra The horse is running less. >> Here I think I have lost the analogy. From what went before, I get that {piza'ure'u} would mean getting more of a total instance than just the beginning. So, does {pime'ire'u} mean less that the beginning. Or is it meant to mean "less than all" -- though perhaps much beyond the beginning. I any case, I don't quite see what "The horse is running less" means here -- "than it used to"? =? "covers less distance in unit time" or ?"takes fewer paces in unit time" or (going back to an earlier worry not mentioned) "is falling more nearly into a different gait from running" I missed out on a part of this discussion for some reason and so I don't quite know how it developed. I thought that it got off into questions of intensity/speed, i.e., more like those wedgies on musical scores -- with various patterns of rate of increase in forming a complete instance as it were. Taking the starting case of becoming yellow, I suppose that the initial situation is totally non-yellow, the final one about as yellow as it gets and the question to be covered is then how rapidly distinct items in the sequence of intermediate states succeed one another and whether this rate is constant or increasing or decreasing or all over the place. In that sense, I don't exactly see what your proposal -- which has interest in its own right -- does for the initial problem. But, as I said, I missed some of what happened to that problem along the way. |