# Précis of Thinking in Images

Let me start with a couple of examples. Look at the night sky and try to find the Big Dipper. At first, you see an unordered magnitude of astronomical objects. A star chart can guide you in your task. The chart helps you to localize objects in the night sky.

Next, suppose you want to demonstrate that a triangle can be constructed from three straight lines with specific lengths. You cannot deduce the task’s solution from the triangle definition. You have to construct the triangle diagram.

Last, let us compare two geometrical three-dimensional objects in different spatial orientations and determine whether they are congruent. One can imagine a spatial rotation of these objects to solve this task.

The examples above are instantiations of imagistic thinking. Other examples are easy to list. Engineers, biologists, and chemists use diagrams in their scientific practices (e.g., Rheingold, 1991; Earnshaw and Watson, 1993; Nersessian, 2008; Tufte, 1997). Scientists think with diagrams (e.g., Ferguson, 1992; Gooding, 2010; Mößner, 2018; Sheredos et al., 2013; Shin, 2015; Sloman, 2002). Finally (and obviously), auditory and visual images are essential for art (e.g., Carvalho, 2019).

However, listing examples of imagistic thinking is a relatively easy task. The difficult task is to say exactly what thinking with images is. Imagistic thinking is commonly contrasted with thinking with words and propositions (e.g., Slezak, 2002; Zhao et al., 2020), for, as is commonly held, not everything that is depicted or represented in an image can be described in language-like and propositional form. However, that is only a negative description of the phenomenon.

The main difficulty in describing imagistic thinking stems from the fact that thinking with images is not a case of trying to solve a clear-cut problem where we need answers to some ready-made questions. It is the opposite. The fact that we think with images is intuitive but poorly understood. This book is just about that. It is aimed at making our thoughts about imagistic thinking more clear.

In Thinking in Images, I argue that explaining the nature of imagistic thinking requires considering two sets of desiderata. The first set includes the requirements for any theory of imagistic thinking. It consists of the so-called Irreducibility Thesis and Translatability Thesis. According to the Irreducibility Thesis, images are metaphysically necessary for the existence of some thoughts. Images can be bearers of thoughts and express non-propositional content and knowledge. According to the Translatability Thesis, some imagistic thoughts can be translated into propositional ones, i.e., some imagistic information can be expressed by propositional representations, and some imagistic knowledge can be expressed by propositional knowledge. For instance, a picture of a cat and the proposition ‘it is a cat’ seem to be mutually translatable. Any proper explanation of imagistic thinking involves demonstrating how it is possible to conjoin both theses.

The second set of desiderata includes the requirements for any compelling theory of thought. First, any theory of thought should be able to deliver a theory of knowledge, for knowledge is a structure based on thoughts. Second, a theory of thought should be able to deliver a theory of content, for we want to know how to determine what we think of. Third, it should be able to deliver a theory of thoughts’ compositional and systematic nature. These three requirements challenge any attempt to formulate a compelling theory of imagistic thinking.

The skepticism (e.g., Bennett and Hacker, 2003; Pylyshyn, 2002) concerning the concept of imagistic thinking is based on the belief that images, taken traditionally as resembling represented objects, do not have epistemological, semantic, and metaphysical features that we are willing to ascribe to thinking. According to the sceptical line of reasoning, images can accompany our thoughts. However, they cannot be the bearers of thoughts.

In the book, I present the argument from the best explanation of the following kind. I argue that if images were to be able to meet these two sets of requirements, they should be taken as measurement devices comparable to rulers and balances. According to the measurement-theoretic account of images (and the so-called two-dimensional model of iconic reference), images refer to their target in two ways. First, they denote their objects. Second, they exemplify construction rules to identify these objects in some logical or physical space. Just like rulers, images determine the properties of some space in order to localize certain objects or features.

Thinking with images is a rule-governed manipulation of construction rules revealing how something can be perceived in a measurement set-up, for instance, thinking about how an object would look if parameters, such as height or orientation, were different. In short, thinking with images is a skill in using construction rules, comparable to using rulers.

To explicate the measurement-theoretic account of images, I introduce two technical terms. First, the concept of construction refers to the ways of localizing the target by determining the parameters of some space. Respectively, construction rules are the functions that establish the correct ways of determining these parameters. Second, the concept of recognition-based identification refers to the way we identify objects as belonging to the same kind based on identifying the invariant properties of constructions and construction rules.

To illustrate it, let us go back to the opening examples. We use a star chart to localize the Big Dipper. The map determines the properties of the night sky to localize the specific astral pattern. Does the map resemble a night sky? In a general sense, it does. However, it is not to say as if some astral structures were floating in the sky just to be copied into the map. Moreover, there is no principled way to determine this space’s properties. For instance, there is no point in asking why the Big Dipper is represented canonically and not as it is depicted in the figure below.

According to the measurement-theoretic approach, the map imposes an order on the manifold of astronomical objects to identify the structure. The map determines the construction parameters of the astronomical space to localize the Big Dipper. The canonical representation of the Big Dipper is a matter of construction rules we follow. They preserve certain invariants, such as the geometrical relations, which serve to identify the celestial pattern.

The same observations apply to triangle diagrams. The construction rules order the way the lines have to be connected. Identifying the construction invariants, such as the number of angles, serves to recognize triangles. The diagram exemplifies this construction.

Last but not least, mental manipulation of the construction parameters, such as the orientation of the three-dimensional figures, can help solve mental rotation tasks. Knowing that the same construction properties are preserved, one can determine whether some geometrical figures are congruent.

How does the measurement-theoretic account of thinking in images address the two sets of desiderata mentioned above? First, it allows us to acknowledge the irreducible role of images in thinking. Images serve the function of localizing objects of our beliefs and theories. At the same time, imagistic and propositional representations are bound together. Although images can localize objects, enabling their recognition-based identification, they cannot describe them. We need propositional structures to make images meaningful, i.e., to place them within our beliefs and theories.

Second, the measurement-theoretic account addresses the epistemological, semantical, and metaphysical conditions. Images are a source of understanding since they localize objects of our beliefs and theories in some logical or physical space. They possess iconic content by exemplifying the measures by which we recognize objects, properties, and events. Finally, images are systematic and decomposable as they exemplify the rules of construction, which identify construction parameters and invariants.

I want to finish with a general statement. One of the consequences of the ideas presented in the book is that knowledge is more than propositional knowledge and thinking is much more than the Fregean game in truth. In contrast to Frege, I hold that thinking involves much more than truth-evaluable operations. What this ‘something more’ is should be a philosophical topic, just as truth is. Even if this book does not succeed in presenting a coherent theory of non-propositional thinking, I hope that it presents the need for such a theory. I am convinced that the philosophy of images can play the same role in our understanding of the mind as the philosophy of language has played.

Literature

Bennett, M., Hacker, P. (2003). Philosophical Foundations of Neuroscience. Oxford: Blackwell.

Carvalho, J. M. (2019). Thinking with Images. An Enactivist Aesthetics. New York, London: Routledge.

Earnshaw, R. A., Watson, D. (Eds.) (1993). Animation and Scientific Visualization: Tools and Applications. London: Academic Press.

Ferguson, E. S. (1992). Engineering and the Mind’s Eye. Cambridge, MA: MIT Press.

Gooding, D. C. (2010). Visualizing scientific inference. Topics in Cognitive Science, 2, 15-35.

Mößner, N. (2018). Visual Representations in Science. Concept and Epistemology. London, New York: Routledge.

Nersessian, N. (2008). Creating scientific concepts. Cambridge, MA: MIT Press.

Pylyshyn, Z. W. (2002). Mental Imagery: In search of a theory. Behavioral and Brain Sciences, 25, 157-182.

Rheingold, H. R. (1991). Virtual Reality. London: Secker and Warburg.

Sheredos, B., Burnston, D., Abrahamsen A., Bechtel, W. (2013). Why Do Biologists Use So Many Diagrams? Philosophy of Science, 80 (5), 931-944.

Shin, S.-J.(2015). The Mystery of Deduction and Diagrammatic Aspects of Representation. Review of Philosophy and Psychology, 6 (1), 49-67.

Slezak, P. (2002). Thinking about thinking: language, thought and introspection. Language & Communication, 22, 353-373.

Sloman, A. (1978). The Computer Revolution in Philosophy: Philosophy, Science, and Models of Mind. New Jersey: Humanities Press.

Tufte, E. R. (1997). Visual Explanations. Images and Quantities, Evidence and Narrative. Cheshire, CN: Graphics Press.

Zhao, F., Schnotz, W., Wagner, I., Gaschler, R. (2020). Texts and pictures serve different functions in conjoint mental model construction and adaptation. Memory and Cognition, 48 (1), 69-82.