The map is an interpretation of the expression Vanville, but only under a certain profile: it says nothing about the shape of the houses or the beauty of the river. Since the citizens know their way around town perfectly well, we can assume that each one has a certain knowledge of where the places are and that therefore the diagram that is the map is part of their CT and of the publicly shared NC.21
Let us now suppose that a tourist arrives in Vanville and asks for the Pegwill Center. Depending on the direction from which he enters the town, he will receive instructions of this type:
(1) The Pegwill Center is the place with three large buildings that can be reached by starting off from the corner of Tegucigalpa and Elm and then heading east across Elm before turning at the corner of Pegasus and Elm to take Pegasus in a southerly direction as far as the corner of Pegasus and Willard.
Figure 4.1 (Vanville 1951)
(2) The Pegwill Center is the place with three large buildings that can be reached by starting off from the corner of Tully and Willard and then heading east along Willard as far as the corner between Pegasus and Willard.
(3) The Pegwill Center is the place with three large buildings that can be reached by heading south along Giorgione as far as the corner of Giorgione and Orman, then turning west onto Orman and proceeding to the corner of Orman and Tegucigalpa before turning north and proceeding along Tegucigalpa until the corner of Tegucigalpa and Elm, where you turn east and proceed along Elm before turning southwest at the corner of Elm and Tully and heading along Tully, where you have to cross Riverside and the Rabbit Bridge and then dive into the river Gavagai and swim eastward as far as the corner of Riverside and Giorgione before going north along Giorgione until the corner of Giorgione and Willard, where you go west along Willard until you come to the corner of Pegasus and Willard.
(1), (2), and (3) are all interpretations of the term Pegwill City Center. As such, they are a part of the NC of Pegwill Center, i.e., they are instructions for its retrieval (and, all things considered, for its identification, since there are no other large buildings in the town).
At first sight, instruction (3) may seem bizarre, but it would not be, if it were given to someone who wanted to reach the Pegwill Center after having acquired a sufficient knowledge of Vanville. Given that a characteristic of interpretations is that through them we always learn something more about the Immediate Object interpreted, interpretation (3) makes it possible to know something more about the Pegwill Center with regard to its relations with the rest of the town.
Insofar as they are statements, (1), (2), and (3) are all true, at least within the framework of the map (and the structure of the town). In our case (in which we are simply imagining Vanville and its map) it is clear that they are true only within the bounds of a system of assumptions (the only experience we have is that of the map), but the map is a drawing of a possible world, not a state of the real world). But if Vanville really existed and a real tourist found the Pegwill Center by following these instructions, he could truthfully say I reached the Pegwill Center by following the route described in instruction x.
One fine day, however, around 1953, someone built a house made of bricks on Elm Street, right at the corner of Pegasus. Anyone passing there would now be entitled to say that there is a house made of bricks on Elm Street. This would be an observation sentence, which springs from a perceptual experience (and is probably taken as true by others who put their faith in credible testimony). As such, this sentence does not upset all the other assertions that could have been made previously about Vanville, and it does not make the definitions (1), (2), and (3) any less true. But we cannot say that it is independent of Vanville’s general situation. If someone were to characterize that house as the brick house on Elm-Street, at the very least it would have to be the only one of its kind on Elm Street. In a city full of brick houses, it would still be a true observation sentence to say that there is a brick house on Elm Street, but it would not be a description capable of providing instructions for the identification of the referent.
Suppose, however, that the house on Elm Street is the only brick structure in Vanville. As soon as its existence is registered by the citizens, the possible interpretations of the Pegwill Center will be increased. Without dragging in Ockham (Quodl. Septem, 8), who used to say that you cannot raise a finger without creating an infinity of new entities, because with this movement all relations of position between the finger and all the entities of the universe will be changed, it cannot be denied that one of the new possible interpretations of the Pegwill Center becomes “the group of buildings south of the brick house on Elm Street” or “the group of buildings that can be reached by starting from the brick house on Elm Street and then heading south along Pegasus.”
What will happen if a second brick house is built in Vanville? If the citizens are used to calling the house on Elm the brick house, with the appearance of a second the name of the first will have to be changed. And one of the definitions of Elm Street will also have to change, if someone defines it as that street in which stands the only house made of bricks in the city.
How many new facts, with the observation sentences they involve, are necessary to make a radical change in a system of interconnected definitions? The question recalls the paradox of the heap. But between a heap and a single grain of sand there are many intermediate degrees, and by removing many grains of sand from a heap it is legitimate at least to assert that at a moment t the heap is smaller than it was in the moment t-1.
Let us therefore leap from Vanville 1951 to the present day and see in figure 4.2 how, through a series of transformations, it has become Vanville 1997.
Around the famous brick house skyscrapers have gradually sprung up, and the new Civic Center (to which the Bank, the Town Hall, and the Museum have been transferred, while a new Hilton hotel has been built) has been created. Owing to the northerly expansion of the town, the old Uptown Square has become Midtown Square. As it now stands on the corner of Pegasus and Elm, it is curious that the new Civic Center is still called Pegwill: there are inertial phenomena in language (in the same way as today we still apply the name atom to something that has been shown to be divisible). Midtown is now occupied by the artificial Lake Barbarelli, to the delight of the wealthy inhabitants of the new Gaurisander Heights (a series of residential villas that have sprung up on what had previously been open hills). Tully Road stops at the lake, beyond which it appears again as Cicero Road. The old Civic Center now houses the Paradox Arcades: shops and amusements. The new brick houses built along Riverside Drive constitute Venus Village, which for a while was an area whose picturesque bars were frequented by artists, but then was gradually transformed into a red-light district with porn shops and strip clubs. It is now dangerous to walk alone at night in downtown Vanville.
Obviously, the previous interpretations of the Pegwill Center no longer work. Number (2) now defines the Paradox Arcades, while (1) and (3) no longer mean anything.
The two Vanvilles seem to constitute two mutually incommensurable systems, just as is said of languages when the notion of mutual translatability is called into question. How can we translate the sentences pronounced on Vanville 1951 to make them comprehensible (and true) with regard to Vanville 1997? The answer is that we cannot. We are faced with two systems in which the same names refer to different streets (in Vanville 1997, Tully Road means something different from what it meant in Vanville 1951).
The single facts and observation sentences that used to express these names and streets have gradually generated a new system, the Vanville 1997 system, incommensurable with the Vanville 1951 system. We can no longer even consider as equally true the sentence There is a brick house on Elm Street, because, if anything, there is a brick house on East Elm. Besides, that house is no longer close to Uptown Square but to Midtown Square; it is not north of the Pegwill Center but in the Pegwill Center, et cetera, et cetera.
Yet even though the entire system that once defined that brick house has changed, the brick house is still there; anyone can see it, and anyone who saw it in 1951 can
