Constructing worlds

According to the classical approach to modality, possible worlds are static struc- tures, namely sets of objects with relations defined on them. One might wonder how a logical construct that is a possible world is actually constructed. Two main approaches can be proposed here:

• objects are treated as primitive

• laws are treated as primitive

In the latter approach, we have some laws that define a possible world and “force” the existence of some objects. In the former, we first select some ob- jects and then just “throw” them into the world. We can, for example, create a world by selecting some real and fictitious objects and arranging them into a certain configuration; on the other hand, we can think of a possible world as an initially empty container that satisfies some global conditions, e.g. some physical or magical laws, and welcome into that world those very objects that are forced by these laws. To give an example of this approach: if in some world elves are like humans with respect to reproduction, then the existence of some elf in this world forces the existence of her parents. (In this case, we can also meaningfully speak of ontological commitment with respect to possible objects.) Those approaches need not, however, be viewed as mutually exclusive. In most cases, a possible world will be constructed heterogeneously with some primitive laws and some primitive objects. Possible worlds are hence hybrid monsters and the process of their construction is dynamic. This means that first we throw some objects from our world, postulating also some laws and, by their power, other objects are born into the world. One might think this approach faces a vicious circle problem. If some laws force the existence of a given object in a given world, does this object already exist in this world? If so, do the laws really force anything? The answer to this objection lies in the dynamics of the process of world construction. Possi- ble worlds are not static. It makes little sense to speak of a world as a complete construction – what is given to us is just a world-description from the appropriate stage of the dynamic world-building process.

Another hybrid aspect of possible worlds is the possibility of having mixed worlds – possible worlds that are a mixture of the actual world and some fictional elements (or fictional world and some real elements). This possibility comes from allowingindividual objects to “travel” between worlds. Of course, in most possible worlds there are some real objects, such as tress, animals, humans, etc. However, there is a difference between individual objects and the objects denoted by general terms. The latter are possible objects of a real species rather then real objects by themselves, and the individual designata of such species-terms do not have to come from the actual world. With objects denoted by individual terms the matter is altogether different. Let us consider a fable in which the author of this

4.3. An existential journey into many worlds 113 thesis discovers a magical gate to some fairy-land, where she meets elves. The possible world of such a story would be a hybrid of the real world and the “elvish” world. And more importantly, the main character in this world would be the real object (real individual human-being) from the actual world. In this sense, we believe in therigid designation of individual terms. The identity of the author of this thesis is not changed in all possible worlds as far as she is referred to by her proper name.

Possible objects and paradoxes

First of all we observe that if existence is not a predicate but a modal index the problems that arise by using existence in the characteristics of an object (e.g. the ontological argument for existence of God) are avoided. What about the status of objects? Of course it might seem that we reject the Humean account that “to be an object” is “to be an existent object”, but on the contrary we agree with this account, however we assume that existence has two meanings: the “real”, when it indexes the actual world and the “possible”, when it indexes some possible, but not actual, worlds. Thus “to be an object” is to be “existent object in some possible world”. What is distinguished is hence not the existence itself, but the actual world.

The final questions concern how to cope with so-called “incomplete” (“the blue”) and contradictory (“round squares”) objects. In the case of contradictory objects we follow Priest’s proposal that they can exist in those worlds in which the law of contradiction does not hold, so worlds with paraconsistent logics. Actually, we consider contradictory objects neither troublesome nor interesting enough to focus on them. Objects like “the blue” require, however, devoting few sentences to cope with them. We think that there are no such objects as “the blue”. Not everything that can be characterized qualitatively, or that seems to be character- ized qualitatively, is an object. One might ask, what is then “an object”. The reply is that the notion of “an object” is primitive, which is why the statement that “to be an object is to be an existent object (in some possible world)” does not include a vicious circle. It is rather a claim than a definition. Defective objects are no objects, in no possible world in the universe of universes.

To see why defective objects like “blue” are rejected, we need to observe first that in a sense all possible objects are incomplete. This follows from the fact that they are, like whole worlds, dynamic constructs, or rather more precisely they are either real objects form the actual world or dynamic constructs. In both cases they are incomplete. The final complete descriptions of such objects are never available to us. What are available are only certain object-states i.e. descriptions of certain states of given objects. In the case of real objects incompleteness concerns how they will develop along the time dimension10, whereas possible

10_{It is another philosophical question to reply whether past real objects, that existed and}

objects may change in all possible dimensions, and hence may be incomplete also intheir pastness. Let us take as an example Tolkien’s elves. We know a lot about them as entities, how they looked, what kind of family relations they had, what was their history, what languages they spoke, and that they all sailed away to Valinor. But what about a sentence “Arwen wore a blue cloak on the day of her three-hundredth birthday” or “Arwen has a mole on the left side of her neck”. The verity of such sentences may depend on other facts about the world she lives in, but most probably it is just a matter of the incompleteness of both the world and Arwen as an object. Then, both the world and Arwen may develop so that those sentences will be true or false. This leads us to even more interesting conclusions. Imagine that someone writes a new story set in Tolkien’s world, with some new characters participating along with the ones already existing in the text. Do we want to say that it is still Tolkien’s world or that it is a new possible world, let us say “Tolkien-plus”? Probably it would depend on how much the new author added to the original setting. From this point of view, possible worlds are fuzzy!11

Thus, if all possible objects are incomplete, why do we reject objects like “blue”. The problem is that Meinongean “incomplete objects” are not really incomplete, they pretend to be incomplete but in fact they are ex definitione

complete. If “blue” has one and only one property, then it is a static, complete, though defective quasi-object, whereas possible objects may be incomplete con- structs but they must bepotentially completeand non-defective infinite collections of properties – like real objects, which they imitate.