A post by Fiora Salis.

Scientific models crucially involve imagination. But what sort of imagination is this? Answering this question is crucial to an understanding of the ways in which scientists construct and develop models in order to learn about reality. Philosophers of science do not offer explicit analyses of imagination but they commonly associate it with mental imagery. Some authors see the imagistic character of imagination as an asset in explaining how scientific models work, but most scientists and philosophers dismiss the imagination as soon as it is linked to mental imagery. I share this scepticism and I offer reasons for it toward the end of this post. But one cannot see the imagination as being crucial to scientific models and also dismiss it because of its allegedly imagistic character. The solution I have offered to this apparent puzzle consists in arguing that the sort of imagination that is really crucial to scientific models is propositional imagination of the make-believe variety (Salis 2016, Salis and Frigg forthcoming). Here I will briefly state the main argument in support of this idea. 

Propositional imagination can be characterised as a relation to some particular proposition (or propositions), which can but does not need involve any mental images. Three main features of propositional imagination emerge from the current literature in cognitive science and philosophy of mind: freedom, mirroring, and quarantining. Propositional imagination manifests freedom to the extent that we can (propositionally) imagine whatever we want. It manifests mirroring to the extent that it carries inferential commitments that are similar to those carried by belief. And it manifests quarantining to the extent that it does not have effects outside of an imagined episode. Different varieties of propositional imagination, including supposition, counterfactual reasoning, dreaming, daydreaming and make-believe, can be distinguished by the further conditions they satisfy.

Kendall Walton (1990) originally identifies make-believe as a social imaginative activity involving props that convey a normative and objective aspect to its content. Anything that can affect our senses can become a prop in virtue of there being a prescription to imagine something, i.e. a social convention explicitly stipulated or implicitly understood as being in force within a certain game of make-believe. Props generate fictional truths, where fictional truth is a property of those propositions that are among the prescriptions to imagine of a certain game. Thus, the statement “it is fictional that p” (where “p” is a proposition) is to be understood as “it is to be imagined that p”, independently of whether one actually imagines p. Fictional truths divide into primary truths and implied truths, where the former are generated directly from the props while the latter are generated indirectly via general principles and standard rules of inference. These are called principles of generation. Sometimes implicit fictional truths are generated according to the so-called reality principle, which keeps the world of the fiction as close as possible to the real world. Some other times they can be generated according to the mutual belief principle, which is directed towards the mutual beliefs of the members of the community in which the story originated.

Let me illustrate how these ideas help us understand one paradigmatic example of scientific models, Newton’s model of the sun-earth system. Our problem is that of determining the orbit of the earth moving around the sun. Solving this problem requires turning to Newtonian mechanics, and in particular to his second principle, also known as Newton’s equation of motion (see figure 1).

To apply this principle to the movement of the earth around the sun we need to build a model of the earth-sun system.

The linguistic, mathematical, and graphic descriptions Newton used in the development of the model are props that prescribe imagining certain propositions that are fictionally true or true in a model. Newton prescribes imagining that the force acting between the sun and the earth is gravity and that its magnitude is given by Newton’s law of gravity (see figure 2). 

Applying this law requires making a number of idealising assumptions. Newton prescribes imagining that gravity is the only force relevant to the earth’s motion and that the earth doesn’t have any gravitational interaction with anything else. He further prescribes imagining that the sun and the earth have a homogenous mass distribution, which allows him to treat their gravitational interaction as if their masses were concentrated in the centre of the sun and the centre of the earth, respectively. Furthermore, the mass of the sun is larger than the mass of the earth, so he further prescribes imagining that the sun is at rest and the planet orbits around it (so we only need to consider the mass of the earth and its acceleration). Of course all of these assumptions are false. The earth gravitationally interacts with several objects, including the sun, the moon, asteroids and other planets. The sun and the earth do not have a homogenous mass distribution and their individual masses are not concentrated in the centre of each object. And the sun is not at rest. Newton therefore prescribes imaginings about a fictional scenario wherein the sun and the earth are imagined as being different from the way they really are. Now Newton can insert his force law in his equation of motion to obtain a differential equation describing the earth's trajectory in the model (see figure 3).

This equation can be solved and we find that, at least in the model, the earth moves on an elliptic orbit around the sun.

To use the model properly we must conform to the original prescriptions to imagine and derive the outcomes from the initial assumptions and the relevant principles of generation. We could imagine that the sun and the earth are cubes with inhomogeneous mass distribution, but this is a violation of Newton’s prescriptions to imagine. Different principles of generation may be needed in specific domains of scientific enquiry, and neither the reality principle nor the mutual belief principle have any special relevance in the development of a model. It is an advantage of the framework of make-believe that it has the flexibility to accommodate context-specific principles of generation, which are usually general theoretical principles and mathematical principles like Newton’s laws of motion and his law of gravity. This also provides an epistemology for fictional truths: we investigate a scientific model by finding out what follows from the primary truths and the principles of generation. Eventually, this leads to the generation of hypotheses about the real world that can be tested for genuine truth or falsity. We find out that in Newton’s model the earth moves on an elliptic orbit.

Imagery is neither sufficient nor necessary for the development of scientific models. It is not sufficient because not all factors that matter to the derivation of a model outcome have sensory-like correlates. When considering Newton’s model of the earth-sun system we do not have a mental image of the concept of force. What we have is a theoretical definition given in linguistic and formulaic symbols. Furthermore, deriving the model outcome requires general theoretical principles and laws, mathematical laws and logical inferential abilities. Imagery is also not necessary because one can develop the scientific model simply by understanding the propositional content of the model description and by deploying the mathematical and theoretical notions that are relevant for its specific domain of enquiry.

Thus, propositional imagination is really crucial to the development of the model. But this is still one step away from learning about reality. Exporting what we have learned about the model into knowledge of reality requires formulating two main kinds of theoretical hypotheses, model-world comparisons and direct attributions. The first involve comparisons between features of the model and features of reality. The second involve the identification of a relevant feature of the model and its attribution to the target. For example, we test whether the earth really moves on an elliptical orbit around the sun through a series of observations of the real earth’s movement around the sun.

References

• Salis, Fiora and Frigg, Roman (forthcoming). Capturing the scientific imagination. In Peter Godfrey-Smith and Arnon Levy (Eds.), The Scientific Imagination, Oxford University Press.
• Salis, Fiora (2016). The nature of model-world comparisons. The Monist 99(3): 243-259. DOI: 10.1093/monist/onw003.
• Walton, Kendall L. (1990). Mimesis as Make-Believe: On the Foundations of the Representational Arts. Harvard University Press.