A second way in which targets could be ontologically different to natural systems is if they are thought of as fictions or imaginary systems that are described by idealized models. Scientists sometimes construct models of systems that do not exist. In fact, they sometimes construct models of systems that
could not possibly exist (Weisberg 2013).4 For example, the exponential growth model (equation 3.1)
represents how a population would grow if it were not checked by density effects. There is no population on Earth which is not subject to density effects, as there is no environment which can support an exponentially growing population indefinitely. The main difference between the exponential growth model and the logistic growth model is that the latter takes resource scarcity into account and therefore can be said to represent actual populations in actual environments. Consequently, its target systems are aspects of the world. Then, the question to ask is: what are the targets of the exponential growth model?
One option is to say that the target systems of the exponential growth model are hypothetical systems of populations in environments with unlimited resources, whose populations are infinitely large. Of course, it is impossible to have an environment without scarcity or an infinite population in the actual world. This means that these hypothetical targets cannot, strictly speaking, be thought of as aspects of the world. If this is the case, then we need to have an account for how the imaginary system relates to the actual system. In more general terms, models are supposed to tell us about real world phenomena, but if they represent imaginary systems, then there is an extra step to account for, namely how the imaginary systems relate to real-world phenomena.
The Exponential Growth Equation
One way to account for this is through the notion idealization (McMullin, 1985; Weisberg, 2007a). The exponential growth model is idealized because it represents an environment without resource
dN
dt
=
rN
1.4
28
4 Another group of models which can be claimed to have hypothetical targets are generalized models (Weisberg 2013). These are
hypothetical targets of generalized phenomena. For example, a general model of sexual reproduction “isn’t supposed to be about kangaroo sex or fungi sex, but about sex itself” (Weisberg 2013 116). According to Weisberg, the target of a general model of sex will also be general, without the particulars associated with any particular population. However, just because the model is general, does not mean that it must apply to a single generalized target. In fact, a model can be considered general when it applies to many targets, hence the model of sex is about kangaroo sex and fungi sex and tasmanian devil sex etc. In fact, Weisberg agrees that so called generalized targets are actually constructed out of actual targets in the world, hence his view is compatible with my own. While I would resist referring to the generalized system as a ‘target system’, the important point for my argument is that ultimately these general models represent real-world target systems.
limitations and populations as infinite. One could argue, therefore, that the model contains the same idealizations as the target it represents, and it is the target which is idealized with respect to the system in the world. While this is a possible solution, it makes the target system redundant. In the standard account of modeling practice, idealization occurs in the construction of the model. If the target system is also idealized, then it will be identical to the model. This would add an extra step to the process of modeling without conferring any benefits. We would still have an incomplete account of model-world relations because we would not know how the idealized model and target related to the non-idealized phenomenon in the real world.
On the other hand, if we restrict idealization to the model, and maintain that the target system is part of the world, the inclusion of the target adds something important. Specifying a target system allows us to give a full account of model-world relations, given that we now have an account of how the target relates to the world. On this view, the targets of the exponential growth model are very similar to the targets of the logistic growth model. For example, if the exponential model were to be applied to the population of marmots outlined in the introduction, the target would be comprised of the marmots and some of their properties. The difference between exponential growth target and the logistic growth target of the marmot population, is that the latter includes the maximum number of marmots supported by the ecosystem. Hence, both models are idealized, yet both targets are merely abstract when compared to the entire ecosystem. Unlike the view of targets as imaginary systems, my view of targets provides a clear distinction between model and target, but also reflects the importance of target systems in scientific practice.