and
Achille C. Varzi (Columbia University, New York)
One can conceive of philosophy of geography as a new branch of applied philosophy, similar in some respects to applied ethics. There is within it an interesting metaphysical side. Some discussions in ethics are metaphysical: one might want to have a nice definition or an understanding or a rough characterization of what a person or personal identity is for various purposes (persons, as opposed to non-persons, are the bearers of a whole class of rights and duties). Not that everything is settled by having defined entities. In the delicate issue of abortion, it does not seem that drawing a line at some point in the life of a foetus resolves the issue of the right or wrong of abortion; for it might be that even killing a person in some circumstances is not wrong (consider cases of legitimate defense), let alone that killing a non-person could be as wrong, in some circumstance, as killing a person (consider killing your dog for sport). Now there are empirical issues in geography, but there are conceptual, broadly structural issues too. Is a nation to be associated with a definite region of space? Can it survive without space or without definite boundaries? Are there clear-cut identity criteria for nations? If geographic units are collections of individuals, how do they change? And again, not everything is settled once we define concepts such as nation's boundaries or identities. Very different moral and political agendae can be pursued on the basis of an agreement on the metaphysical terms of the issue.
Our concern here is with the metaphysical part of philosophy of geography and its epistemological consequences. We shall first situate geographical representation within the more general frame of spatial representation. Then we shall present some of the basic issues in spatial representation related to the composition problem., which has an exact analogon in geography: what counts as an unit when this is said to have parts? What is for a geographic unit to be composed of other units? Mereology, topology and the theory of localization are the main tools of formal spatial representation, and their relevance to geographic representation is to be assessed. We finally raise the question of non-standard geographies, that might be associated to a classical conception of geography in the same sense in which non-standard logics are associated with classical logic.
Spatial representation
We take geographical representation to be a special province of spatial representation, and we think that it inherits some of the broad conceptual issues linked to spatial representation. Spatial representation has become a major focus of research in cognitive science and related areas. This includes logic as well as psychology, brain science, linguistics, and those branches of computer science involved in the construction of machines capable of autonomous interaction with the environment. There are two main senses of the term "spatial representation":
(i) a theory of the way an organism--a brain, a mind, but also a cognitive sub-system, such as a language or a fragment of a language--represents its spatial environment (this representation serving the twofold purpose of organizing perceptual inputs and providing sufficiently articulated grounds for behavioral outputs);
(ii) a formal theory of the geometric representation of space capable of accounting for certain typical inferences of spatial reasoning ("the fly is inside the glass; hence it is not behind it"; "the book is on the table; hence the table is under the book").
With some approximation, these two options may be said to reflect the concerns of psychology and artificial intelligence, respectively, and are relatively independent from each other. A formal theory in the sense of (ii) does not presuppose, and is not presupposed by, a psychological theory in the sense of (i): one can reason about space in a totally abstract fashion, without any intuitive representation of it (and the purpose of a type (ii) theory is, ideally, to provide a system of axioms and rules of inference whose execution does not depend on their intended interpretation). On the other hand, it seems highly plausible that not only lower animals, but also primates and humans possess a system of spatial representation that does not require the execution of inferential procedures in the sense of (ii). Thus, one may have a type (i) theory without having a type (ii) theory, and vice versa. Even so, this relative independence does not rule out the possibility that the study of spatial representation in either sense will be useful for the study of spatial representation in the other sense. After all, the abstract concepts employed by a geometer come from the unsophisticated (or seemingly unsophisticated) notions of common sense--'plane', 'vertex', 'point', 'concavity', 'inclusion'--and these latter exhibit features that can be reasonably ascribed to the functioning of the cognitive system dedicated to the representation of space.
The following questions lie in a region partly overlapping theories of type (i) as well as theories of type (ii). Both kinds of theory speak of spatial entities and spatial environments.
--What sort of entities are spatial entities? What is a region of space?
--What is the relation between space and its inhabitants--people, material objects, events? Is the former somehow dependent on the latter?
--What does it mean to occupy space, as opposed to simply being located in space?
--Are there things that consist merely of space?
--What is a point, a line, a surface?
--What are the connections between truly spatial relations--such as "contained in", or "located between"--and purely mereological (part-whole) relations? What notions can be assumed as primitives in either case?
These questions delineate some basic issues and require specific theoretical tools.
Basic Issues
Regions of space and things in space. Common sense distinguishes between an object and the region of space in which the object is located. This, however, dramatically increases the number of primitive entities in the system. The quesion arises as to whether it is possible to do either without objects or without regions. This is related to the choice between
Absolutis vs relational theories of space. A more general question can be raised not only in relation to a single region of space, but to space in its entirety. Does it exist as an independent individual over and above all possible objects and spatial relations between objects, or are those relations the only facts of the matter concerning space?
Ontological dependence and ontological priority. Purely ontological issues become important here. An overall ontological framework (in which to express the more general facts about the objects in the representational system) is required at this stage. If space is ontologically independent from material objects, then spatial relations between objects are to be reconstructed in terms of spatial relations between the regions at which the objects are located. (In the geographic domain, one might wonder whether - and how - the existence of regions of space or of boundaries depends upon that of socio-economic units, which in turn seem to depend upon individuals and relations between individuals.)
Things and events. There are important asymmetries as to the relations different types of entities bear to space (for instance, objects and events are differentially related to the regions at which they are located) and a complete descriptive account should address these asymmetries (Again, in the geographic domain this has relatively at hand examples, such as the location of changes in socio-economic units.)
Boundaries and vagueness. Possession of a boundary is a mark of objecthood; but boundaries can be difficult to individuate. At this stage a general theory of vagueness is required. It turns out that the theory is sensitive to the context (spatio, temporal or spatiotemporal) in which it is applied.
Theoretical tools
Mereology. A major, fundamental portion of our reasoning about space involves mereological thinking, that is, reasoning in terms of the part relation. A mereological theory is first and foremost an attempt to explicate the meaning of the word 'part' and to set out the principles underlying its correct use (and that of kindred notions). For instance, virtually every mereological theory agrees on treating parthood as a partial ordering, which in a way reflects some very basic meaning postulates for 'part'. Here, however, we are interested in a stronger interpretation, according to which mereology may provide a fundamental framework for the task of spatial representation. Mereology tells us how the world is structured. In this sense not just any partial ordering will qualify as a part-relation, and the question of what additional principles are involved becomes a fundamental (as opposed to merely terminological) question. It is worth recalling that this view has sometimes been associated with a nominalistic stand, and mereology has been presented as a parsimonious alternative to set theory, dispensing with abstract entities or, better, treating all entities as individuals. One can appreciate this stand when one cansiders identity criteria for geographic entities. Imagine a situation in which Italy sells Sicily to the USA. Is Italy the same state after the sale? If countries are mathematically construed ad sets of regions, say, then one is forced to talk of two different countries, for sets are the same if and only if they have exactly the same elements. If, on the other hand, countries are mereological aggregates, then the looser identity criteria for aggregates (which allow for partial identities) would let one accept the existence of a shrunk Italian area.
Mereology can be credited a fundamental role whether or not we take the entire universe to be describable in terms of parthood relationships. The recent ascent of mereology in artificial intelligence and the cognitive sciences can be seen in this light. The question is, rather, how far one can go with it--how much of the universe can be grasped and described by means of purely mereological notions.
Topology. Independently of how exactly the question above is answered, it is apparent that a mereological prospect need be supplemented with topological concepts and principles. For instance, mereologically there is no way to distinguish between a self-connected whole, such as a stone or a rope, and a scattered entity made up of several disconnected parts, such as a broken glass or an archipelago. It is impossible to account for the difference between a scattered country such as the United States and a self-connected country such as Switzerland in a purely merelogical frame: both turn out to be made out of their parts. Moreover, mereology alone cannot account for some very basic spatio-temporal relations among the entities of ordinary discourse, such as the relationship between an object and its surface, or the relation of continuity between two adjacent objects, or the relation of something being inside, abutting, or surrounding something else. All of these are phenomena that go beyond plain part-whole relations, and their systematic account requires a topological machinery of some sort. These motivations (at times combined with others, e.g., semantic transparency or computational efficiency) have led to the development of theories in which both mereological and topological notions play a pivotal role. How exactly these notions are related, however, and how the underlying principles should interact with one another, is still a rather unexplored issue. One can see mereology and topology as two independent chapters; or one may grant priority to topology and characterize mereology derivatively, defining parthood in terms of connection; or, again, one may privilege mereology and explain connection in terms of parthood and other predicates or relations. It is also possible, on some assumptions, to develop a unified framework based on a single mereotopological primitive of connected parthood.
Theory of location
The introduction of a theory of localization permits the investigation of the relation between an object and its region (which appears to be non-reducible to a purely topological notion: an object is not connected to its region - at least, not in the same sense in which two adjacent regions can be connected to one another). If Italy is different from a certain region (which fact we should accept: for Italy can change its shape, but a region cannot), then what exactly is the relationship between Italy (at a certain time) and the region it is located at? Moreover, there are different though interrelated types of localization: People in Sardinia are in Italy in a sense, and Sardinia is in Italy in another sense.
Morphology and kinematics. From the standpoint of spatial representation, topology and the theory of location are thus necessary steps after mereology. However, there is much more to topology than connection and one-piecehood. The point is that there are many important topological notions that cannot be captured by any of the systems mentioned above and which nevertheless play a very basic role in our everyday reasoning about space. For instance, how can systems for spatial representation distinguish between things with holes and things without holes -- between a sphere and a torus? We need an additional predicate of "simple connectedness", or some means to distinguish surfaces of different genus. How can we account for such basic spatial relations as being inside or outside a given object (or region) when this is not a matter of pure topological closure? For instance, what sort of formal theory do we need to say whether an object is inside or outside a container? We need, some authors have suggested, an additional topological operation capturing some notion of "convex hull", not definable in terms of "connection" and the like. Whether or not such additions yield an adequate treatment of the examples mentioned is of course a complex matter. However, from this point of view one can hardly feel satisfied with simply expanding a mereological framework with a notion of connectedness. One needs much more just to accomplish some very basic pieces of topological reasoning. More importantly, even if a satisfactory amount of topological reasoning could be regained, we would need to move into other provinces to account for equally basic commonsensical intuitions concerning, for instance, movement of parts or interactions among wholes. After all the bounds of topology are pretty narrow too. The world of topology is initially a world of spheres and toruses and little else, and we need to step into morphology--the theory of qualitative discontinuities--just to account for certain basic differences in shape; we need to step into kinematics just to account for certain basic differences of behavior. (One can set here some general axioms for changes: for instance, that although the same result can be produced by different changes, it is not the case that same changes can produce different results; or that change can take place only where there is identity of the thing that changes).
Geographical metaphysics
Things. Over and above the general issues listed above, there are some metaphysical problems that arise specifically in the geographical domain. A general question concerns the nature of the entities geographers deal with. Common-sense recognizes paradigmatically entities such as material objects, artifacts and people. Geographers talk of units (things you can at least count), which are of a more abstract kind. The basic metaphysical question concerns the status of these units. Are there geographical things? What kinds of geographical things are there?
An extreme position would be strong methodological individualism: there are - say - only people and stones and quantities of water, and no socio-economic units. This position is liable to uselesness: if the proper representation of geographical fact requires details at the scale of people, then most maps would be impossible to draw. A more reasonable position is weak methodological individualism: if socio-economic units exist, they depend upon or are supervenient upon individuals. Finally, extreme metaphysical tolerance is associated with no individualism (geographic realism): socio-economic units exist over and above the individuals that they appear to be related to. If you accept some form of methodological individualism, then units are seen as carriers of data about individuals.
This question (a metaphysical question) should be kept separate from the epistemological problem of the alleged nonexistence of socio-economic units (they would not exist because they are artifacts of classification). All the same, often one is tempted to reify abstract entities.
More detailed questions here are: what processes produce socio-economic units? What ontology should we use for them? (what is a town square?). How do they live? Can they move? Shrink? Disappear? Have intermittent existence? Resuscitate? Can socio-economic units be not regions or not associated with regions? If they are regions, could they be arbitrary n-dimensional?
Places. Why do we need places in addition to real things (i.e. things that can move and things that cannot move)? What are places? Why do we need to refer to places? When no clear identity criteria for an entity over time are specified or specifiable, reference to some portion for space may be involved. We can think of the following example: Imagine a square divided into the two rectangles Left and Right by a vertical line in the middle. John owns Left and Mary owns Right. Now for some reason John and Mary agree on changing the way to divide the square; they draw a horizontal line in the middle, and now John owns North and Mary owns South. The identity graph of the area is Left-North and Right-South. Could you describe this without talking of regions?
Classical and non-classical geographies
These were the questions. We shall now tentatively suggest a possible enrichment of the logical space of geographical tools. An analogy coud help to fix ideas here. In the nineteenth century a number of non-classical (non-Euclidean) geometries have been put forward by accepting some of the axioms of Euclidian geometry and rejecting the axiom concerning parallelism. In the field of logic there has been a proliferation of non-classical logics that reject some of the principles of classical propositional calculus (such as that of the excluded middle, or of the double negation). One might consider the possibility of setting a classical geographical frame against some non-classical geographies. As we do not know at this stage what classical geography is, we shall proceed by putting forward some informal axioms that seem to be plausible for a minimal characterization of geographic representation, and which are such that violations to these axioms produce intuitively "incomplete" representations. The consistency and the completeness of these axioms has not been tested - this is a rough proposal and the suggestion of a line of research.
Principles of classical geography
The partition axiom: every area of a geographic domain is assigned to a definite geographic unit (there are no no-man's lands).
The location principle: every geographic unit has a location (the converse of the partition axiom).
The sharp map axiom: no two distinct units of the same status overlap. It does not imply, but is implied by, partitioning.
The unit axiom: partitions are unit-relative.
The sharp boundary axiom: every unit has has a sharp boundary.
The two-sidedness axiom: every boundary has two sides (i.e., it separates two units).
The metric axiom: every unit should have a non-zero side.
The mereological-localization axiom. Every region which is within the boundaries of a unit is part of the unit.
The connection axiom: Every unit is self-connected (there are no scattered units).
Varieties of non-standard geographies
Consider some ways of violating these axioms. Units could have no clear-cut boundaries, or they could overlap. Units could have no boundaries at all: we would have a boundariless geography. Placeless countries could be allowed (Poland at some stages, or Austria between 1938-1944). Scattered countries could be allowed (United States). How small can an unit be? Limit case: Members of an ecological movement buy very little fragments of land bordering the track of a projected railway in order to slow down the construction by multiplying the legal difficulties of expropriation. But if countries are so finely individuated as to be where their citizen's are, do countries interpenetrate by the sheer fact that people live abroad? And suppose all Italians move into France and all French move into Italy - did Italy and France themselves changed places? One can further tolerate no man's lands. Or countries made up of sums of heterogeneous entities. Or different criteria for country-drawing (as now we have different criteria for citizenship).
Non-classical geographies could help giving flexible classificatory tools. Non-standard geographies could enhance our dealing with political problems. There is a very widespread and oversimplified picture of boundaries, that we might label the island paradigm. According to the island paradigm, people live in geographic units (nations, regions, preserves) which are ideally like islands in sea. The border is extremely salient. Crossing the border of the unit must be a physically engaging activity. Those who enter the island have to be learly identified as they approach, etc. The paradigm shows an obsession with self-connectedness, and with exhaustion: all points in a map must be in some unit.
Whatever the applicative agenda here, the metaphysical work to be pursued is not to be seen as just a collection of difficult cases for standard geography, but more as a collection of different ways of treating geographical structures. However, the study of bizarre, limit cases is useful for understanding ordinary cases. We think that pursuing the analysis of the basic structures in space representation could be seen as a first fundamental step towards a satisfactory understanding of geographical representation.