Used in cases of controls

A negative answer may be given by those who believe that prepositions can be used in any domain and that the spatial domain has no priority over the other domains. My answer depends on whether space is conceived as an abstract entity described by geometry or topology or as an indispensable component of our experience of the world. We will see that geometric tools such as Cartesian axes and topological notions such as contact and inclusion do not explain accurately the distribution of prepositions.

However, if space is considered as a component of our concrete external experience, as opposed to our internal mental experience, I believe that concrete spatial uses of many prepositions play a determinant role in the elaboration of their total distribution. Geometry and topology describe essentially static situations. Spatial experience, in contrast, is constituted of actions and actions involve movements. The feeling of force is also an important part of our experience. The word dynamic is often used to cover both movements and forces.

Here, I would like to use dynamic exclusively for forces and, for this reason, I will use cinematic or kinetic when I speak of movement. Using forces and movements, I will now try to classify the spatial actions and situations that we meet in our spatial experience. At the first step of my classification, I would like to oppose dynamic to not-dynamic. But one might object that force is always part of movement and that, therefore, dynamic always means kinetic while not-dynamic means static. For this reason, dynamic is often used as the opposite of static.

Yet the contrast dynamic/static cannot replace the contrast dynamic/not dynamic for two reasons:. (1) To show that kinetic is not always equivalent to dynamic, physicists might give a leaden ball in rectilinear uniform movement as a counter-example. Indeed, if one disregards friction, no external force is necessary to keep the movement alive. But the layman perfectly knows that he should worry if a leaden ball rolls over his flowers. Outside the textbooks of physics, it does not matter if the damage is blamed on the force of inertia of the ball or on its kinetic energy.

In any case, we have a feeling of force when a ball is rolling or when a man is running. In order to accommodate this feeling in my classification, I will oppose dynamic cases in which there is exchange of energy to cases in which there is no such exchange. There is no exchange of energy when you walk in the street but there is exchange when you bump into the wall. The first step of the classification, then, will be dynamic exchange vs no dynamic exchange. (2) Against the equivalence of static and not-dynamic, it should be more clear now that static situations may be the result of a dynamic exchange.

Just think of the two pans of a weighting machine: equilibrium occurs when the two weights balance each another. This type of static dynamic situation is not described by a preposition. It is even difficult to represent this spatial situation by a verb: one will say that the apples weight one kilo rather than one weight of one kilo balances the apples. This is so because, in this case, we are more interested in the function of weighting than in the spatial configuration of equilibrium.

However, as we will see later, prepositions in and on are used in cases of controls, that is when a container or a bearer overpowers the potential moves of the content or the burden. Containment and support are two essential static dynamic relationships. From this discussion, it appears that dynamic exchanges as well as non dynamic exchanges can be divided in static and kinetic. I will consider these four cases in turn. Static situations without dynamic exchange: These situations may be described, notably, by projective prepositions, such as on the left and in front in sentences (1) and (2):

(1) The tree is on the left of the house (2) The bird is in front of the house These prepositions are probably the best candidates for the appellation of spatial prepositions in the formal sense of space since they may be related to three axes. The prepositions above/below are related to the vertical axis whereas in front/ behind usually correspond to the frontal orientation of the speaker and to the right/to the left to its lateral orientation. Note that these two egocentric axes already introduce the speaker in the description of space in English.

In the recent years, the existence of absolute languages describing space in terms of geographic landmark has been well documented. These axes, however, determined by the slope of the hill or the direction of the winds, do not bear more resemblance to abstract geometric axes than the frontal and lateral orientations. More importantly, if the function of projective prepositions were the formal description of space relative to Cartesian axes, one would expect converse prepositions in front of and behind to be symmetrical.

Such is the case in sentences (3) and (4) but the converse of sentence (2) looks very odd: (3) The car is in front of the truck (4) The truck is behind the car (5) *The house is behind the bird This is so because projective prepositions are not devoted to a purposeless description of space but are used as instructions in order to find a target one is looking for. In order to guide his addressee, the speaker uses as conspicuous a landmark as possible. Whereas the house in sentence (2) may help someone to find a bird, the bird in sentence (5) cannot, in normal circumstances, help to find an address.

This sentence looks odd because the best candidates to the formal description of space in English, projective prepositions, have a more important function: the localization of a target by a landmark. Kinetic situations without dynamic exchange: Most kinetic situations without dynamic exchange are conveyed by verbs of movement (to come, to go, … ) or of manner of movement (to walk, to drive,… ). The description of these situations may be completed by projective prepositions: (6) John walks in front of the house This means that, in English as in French, projective prepositions can localize a mobile as well as an immobile target.

In contrast to English that marks the contrast between a target in a container and a target moving into it, French uses dans in both cases. Static situations with dynamic exchange: In my classification, I will first distinguish cases of balance, in which equilibrium is the result of two equivalent forces, from cases of control in which the controller overpowers the controlled. As we saw earlier, no preposition is devoted to the relationship of balance. Some symmetrical exchanges of energy may however be conveyed by against or by the verb to touch.

I will come back to these uses later. Asymmetrical relationships of control account for the important prepositions in, on as well as for hanging from. I have extensively studied these relations elsewhere. I argue against the topological definition of a is in b by the inclusion of a in b and against the definition of a is on b by the vertical contact of a with a plane determined by b. Instead, I propose to define in and on by the functional relationships of containment and support respectively and hanging from by the relationship of suspension.

In each case, the landmark controls the target by preventing prospective movements of a fluid target or of a solid target submitted to gravity. In our classification, containment may be distinguished from support and suspension because the container controls the content in more than one direction. In support as in suspension, the controlling entity opposes itself to the weight of the controlled entity along the vertical axis. In suspension, however, control occurs from above whereas in support, the bearer controls the burden from below.