| Time to start over again, I think. There is a thing, otherwise
unspecified in and of itself. It has a uniqueness, a distinctiveness, an it-ness, a vishesha. This is, in modern logic, a function that picks out this thing (or its counterpart) in every situation (like worlds but not necessarily complete nor consistent) in which the thing (or -- but we take that as read henceforth) exists. The thing has a Logically Proper Name, a linguistic _expression_ which denotes (refers to) the thing and designates (has as sense) its vishesha, but has no connotations. It consequently denotes this thing in every situation. (is a rigid designator). Assuming the thing is of the right sort, it has, in this situation (world in this case), a conventional name -- perhaps several -- and a number of descriptions that fit it as a result of the classes it belongs to, the events it participates in -- and, indeed, what other people think about it. All of these expressions have senses, but none of these senses is the vishesha of the thing nor logically equivalent to it. Consequently, there are situations in which any of the conventional names or descriptions that here apply to the thing continue to apply and others where they do not (either apply to nothing or to something else), and, by parity, situations where the thing has conventional names and descriptions which do not apply to it here. (Since the sense of a conventional name is little more than the fact that it is used to name something, we can consider it as a description, too, for simplicity.) I take it that one rule of the possible-worlds game is that, the closer a possible world is to the real one, the more descriptions cluster in the alternate world as they do in the real (this seems to fit nicely with the temporal model). In particular, in close alternate worlds, the same thing tends to get the same name and have the same history and properties. Indeed, the distance of a world can almost be read off from the number - and centrality (but that may come down to numbers too, a central change entails more peripheral changes) -- of changes in the focus individual. Certain kinds of intensional contexts seem to require close alternate worlds: "practical" intensions like beliefs, hopes, expectations, etc. which seem to be "about" the real world though situations of their own in fact. More theoretical or hypothetical intensions have fewer restrictions and are, thus, harder to deal with ("If Socrates were an Irish washerwoman, ...."). In the close worlds, it does not usually matter what linguistic line we follow from world to world, since they usually hang together at the core ("George Eliot", "Mary Anne Evans", "the author of Middlemarch," "the author of Silas Marner," "the author of The Mill on the Floss", for example). The farther away we get, however, the more important it is to be clear which of the descriptions that in fact attach to our thing we are following: "If Socrates had fled Athens,..." might take some major changes in character but could preserve most of the normal actions in the life history, "If Socrates were an Irish washerwoman, ..." seems dangerously close to only talking about the thing who happens to be Socrates in fact, but carries over almost no other descriptions (maybe some "characteristic" personality traits?), taking a "Socrates" whose sense is simply the vishesha. [I skip over the question of whether this Irish washerwoman is in a world which did not have someone who was otherwise the known Socrates, in which case we don't even know what it means to be an Irish washerwoman, because Western civilization is now fundamentally changed in unpredictable but major ways.] Thus, conventional proper names and even widely recognized descriptions serve in the practical cases almost as well as rigid designators, but even here we need sometimes to note that that cannot quite be right. And more remotely, we need to be very careful about what is intended, even though the convention continues to be to use names as though they were clear, when they often either are not (some particular aspect is being covertly stressed) or are not helpful (as logical proper names). Interestingly, for most cases, even of the closest worlds, keeping the same thing in the cluster is usually less important than keeping the cluster of descriptions applying to a single object, even if it is a different thing (why counterparts do so often work - but note they do not do so well in very remote cases. But then, nothing does.) The case of classes is rather similar, but affects the individual case as well, since what various classes are affects what descriptions apply to a thing. The basic situation for a class is axiomatically its members. So the fundamental _expression_ for a class is "that whose members are exactly ...." And this neatly summarizes the sense of the expressions as well: it picks out a unique class in every world in which all those members exist (their visheshas have loci) and otherwise it does not exist in a world. In this world, in which it exists, it is a subset of other sets, and has other sets included in it. It may have a special name ("cats," say), as may have some of its supersets ("mammals," "animals") and some of its subsets ("Persians," "Scottish Folds"). Thus it gets other descriptions ("the subset of carnivores differentiated by..."), which tend to go together in the same way in near worlds and then gradually diverge ("the class of America's most popular pets" leaves early, perhaps before being the superset to "Scottish Folds"). Now what seems to be important for the sense of class names - once we get away from bare membership notions - is the relationship to other classes, where the class lies in some hierarchy, and this seems to work both ways -- up and down: the species gets its meaning from its genus, and the genus (perhaps less so) from its species. But the question of which superclasses of a given class are genera and which subclasses are species are one of the things that possible-world games are meant to answer and also something that the notion of a possible world seems to require to be clear already. It is "clearly possible" (and in fact historically happened) that whales were not classified as mammals, but as fishes. Yet nowadays, we are inclined to say that being a mammal is essential to being a whale, that among the superclasses of the class of whales, the mammal class is a genus and, indeed, the fish class is not even a superclass, though a number of other classes which are super to fish are (but not, short of Chordata, genera). Notice, that the actual members (under there logically proper names) of these classes no longer plays any role here - and, in a peculiar sense, neither do the actual properties being associated with sets (why the alternate languages alternative to alternate worlds works so well sometimes). Sense become Platonic definitions in which the ultimate terms - but genera and differentia - are defined only formally, where they stand in the hierarchy and what they separate. Incidental classes in this world - not "natural classes" like genera and species - are even harder to deal with, since they are, like individuals, often defined by a variety of incidental descriptions, "the gang I used to hang out with at the Pub." This might work across close worlds until it turned out that certain people or people with certain attributes were essential, so that, even in a world where the description picked out a groups, it would not be the right groups without that person/type, just as a male George Eliot, even after writing all those books, might well not be the right George Eliot for what one was working on. Summary: an individual per se has a logically proper name - rarely pronounced, if ever - whose sense is the individual's vishesha (NOT a property but a function across worlds). An individual also may have in a world a number of descriptions that apply to it in that world, including conventional names. Most of these, apparently especially conventional names, also apply in near worlds, but gradually thin out in remote ones until none of them strictly apply any more. Folks have a tendency to use some conventional name as tough it were the logical proper name even when that name no longer applies to the same individual (then as a disguised descriptions whose content is to be discovered somehow - indeed, what individual the name or the description applies to become irrelevant). Classes have fundamental descriptions that refer to their members by logical proper names and whose sense then picks out the same class (by members) in every world in which it occurs (all its members exist). Some classes also have names, whose senses are properties: functions that pick out classes in every world (sometimes the empty class). These functions are usually said not to be arbitrary; that is, what class a particular function picks out is related in specfic ways to what class another function picks out in that same world. Dogs and cats are both carnivorous mammals and nothing can be both a dog and a cat, but neither has to be a pet, for example. [If we could - as we cannot, as xod noted - look into another world, we might find that there cats looked for all the world like vipers and dogs like constrictors, and mammals like snakes and so on up the line as long as all the structural relations held.] The extent of this transworld restriction is unclear (to put it kindly) but it affects not only what is essential to being a certain kind of thing but also, consequently, the extent to which a description continues to apply to an individual as otherwise characterized. So, the line between what is merely a fact about something or class and what is essential to its being that thing or class is fuzzy at best (and not in the technical sense, though we could do that, too) running on to meaningless. The point of the exercise then is merely to provide a framework within which we can try to isolate what position a person who goes into hypothetical or other intensional mode is taking on these boundaries in the particular case. What he gets out of his world back to this one is aprroximately what he put in: if he is sure that whales are mammals, then he wrote "mammal" in as a genus for "whale." |