TERRITORIO, BARRIO Y COMUNIDAD

The first possibility is if the target system is thought of as a type of model, which is itself represented by the mathematical model. An example of a system which is represented by a model but which is itself a representation of a system in the world, is Suppes’s notion of models of data (Suppes, 1969). A model of data is an intermediate step between the model of the experiment and the experimental design. The experiment yields a set of raw data which the scientist can observe. She then proceeds to make sense of this data by eliminating any errors (outliers) and presents it in a comprehensible way, for example by fitting a curve to the set of data points (Frigg & Hartmann, 2009). As models of data involve distorting the raw data by presenting it in a ‘neat’ way, they constitute idealized models.

Models of data are supposed to circumvent a criticism of the isomorphism view of model-world relations. The criticism is that real world phenomena do not have the kind of structures which can be

typical model in ecology (which I mentioned in chapter 1), is used to measure how the growth rate of a population N is limited by the density of the population itself (see equation 1.1 p. xx). The important component for this discussion is r, the intrinsic rate of increase. This is the growth rate of the population independent of resource limitations, competition, or predation. In other words, it is the average number of offspring that an individual has, when the population is at low density. The question is how can r be isomorphic to a structure in the real world system?

The short answer is that it cannot, because there is nothing in a real-world system which is

structurally similar to r. A growth rate is not a property of an actual population, but a statistical variable

derived from data collected from parts of the system in the world. As stated previously, organisms are born, have offspring and die. Ecologists collect data on the number of births and deaths of the population within a specified timeframe. Then they construct a life table, a tabular summary of the birth rates, fecundity and death rates of a population, divided into age groups (Ricklefs & Miller 2000). The values from the life table are then used to calculate the intrinsic growth rate of the population. However, the actual birth and death events of the population do not have the same structure (or even a similar structure) to the mathematical notion of a growth rate.

The model of the data helps to circumvent the criticism because it is an ‘empirical model’ which has the necessary structures and can be isomorphic to the mathematical model. However, as it stands, the isomorphism account does not give a full picture of model-world relations. It may be true that the model of the data is somewhat ‘closer’ to the real-world phenomenon, yet it is still an idealized and manipulated model.

Suppes’s account includes two additional steps which are meant to show how the model of data relates to the phenomenon in the world. Working downwards from the model of data, we arrive at the stage that deals with the problems associated with ‘experimental design’. For example, it involves a formalized way of randomly assigning subjects into groups. This is the preliminary step for the experiment which yields the raw data. The issues that are ironed out at this level are usually determined by the lowest level, that is the determination of ‘ceteris paribus’ conditions, such as “control of loud noises, bad odors, wrong times of day or season”(Suppes, 1969).

In fact, I think that these other steps are similar to my account of target system specification. For instance, in the determination of ceteris paribus conditions scientists are deciding which of the many factors

which give rise to a particular phenomenon are actually relevant for the study. This looks very similar to my notion of abstraction, as both processes are aimed at identifying the relevant causes of a phenomenon which should be included in the study. In addition, partitioning is already implicit in the determination of the ceteris paribus conditions and the experimental setup, even though Suppes does not identify it as such, as the domain must be partitioned in units such as individuals or groups, whose properties will then be tested in the experiment. Thus, my view of target system specification is compatible with Suppes’s account of model hierarchy, as long as the lower aspects of the hierarchy are seen as the analogues of target systems instead of the models of data.

Of course, it is still possible to designate the model of data as the target system. However, this seems rather arbitrary. Suppes’s account identifies a hierarchy of three kinds of models: linear models, mathematical models and models of data. Given that target systems are defined as what models represent, we would be equally justified in calling the mathematical model a target system (as the linear model represents the mathematical model). This is problematic because it is at odds with what most philosophers of science have in mind when they are thinking of target systems.

An additional issue with this option is that it involves many intermediaries of different kinds. Models of data are empirical models, hence a different type of model to mathematical models. If target systems were to be thought of as models of data we would have three distinct entities, real world systems, target systems and mathematical models. In contrast, on my view, target systems are just parts of the world, hence there are only two entities involved in scientific modeling, models and the world. My view of target systems provides a much simpler and straightforward way to categorize the entities involved in scientific modeling. It also provides a coherent way to distinguish between target systems and models, which can be applied across different studies or disciplines, as target systems are partitioned and abstracted yet models are idealized.