To end up with some closing remarks, I hope Thinking in Images provokes thinking and gives new topics to the discussion (not necessarily in images). That is the only thing a philosopher can wish for.
And yet, although the structural representations framework seems sufficient to explain some mental representations properties, I doubt whether it is sufficient to meet the epistemological, semantical, and metaphysical challenges for the theory of imagistic thoughts. The latter is not reducible to the theory of mental representations.
Burge, T. (2018). Iconic Representation: Maps, Pictures, and Perception. In S. Wuppuluri, F. A. Doria (Eds.), The Map and the Territory. Exploring the Foundations of Science, Thought and Reality (pp. 79-100). Springer.
However, once you recognize John in the picture, you can predicate of John that he is bald. For instance, some language-based systems can use a picture to describe John. In the same way, the indication of the thermometer, such as 20°C, does not predicate the property of being even of the air. It identifies this temperature on a scale. However, once this value is found, we can predicate it of the air, e.g., ‘it is 20°C outside’.
Second, and more importantly, Marcin Milkowski and Mariela Aguilera ask whether the measurement-theoretic approach to imagistic thinking can be extended and unify the explanation of all kinds of thoughts. I find this question very intriguing and hard. On the one hand, I explicitly reject the belief that images can be foundational for propositional representations. Such an approach does not seem convincing. My thought that three is the square root of nine does not involve any images and does not seem to require any of them. That is why I describe imagistic and propositional thoughts as playing different roles in the thinking machinery.
Burge, T. (2010). The Origins of Objectivity. Oxford: Oxford University Press.
There are certain prospects for Vernazzaini’s approach. Foremost, it puts some psychological constraints on our theories of iconic content. Moreover, as Vernazzani rightly suggests, it can strengthen the view I advocate in the book.
Marcin Milkowski raises two points. First, he rightly underlies the similarities between the measurement-theoretic approach and structural representations framework. It is an important point since the necessary condition of every measurement is the structural correspondence between the measurement’s outcome and the measured object. That is why I hold that the measurement-theoretic framework is an extension of the structural-resemblance approach.
Authors love when their books are being read. They love it even more when their books are being discussed. I’ve happily been in this position where the commentators have taken their time and effort to read my book and share their ideas. I am very grateful to Marcin Milkowski, Mariela Aguilera, and Alfredo Vernazzani for their insightful comments and suggestions. I owe you all a debt of gratitude!
In her insightful comment, Mariela Aguilera doubts whether we should reject the traditional and well-grounded division between attributive and singular content. Some passages in my book may suggest that I make such a move. For instance, I hold that images do not describe their objects but identify them. Moreover, I defend the view that iconic content cannot bear predicative functions. Predicates require logical form iconic content lacks.
The idea of measurement predicate is taken from the measurement theory. If I hold that the air temperature is 20°C, I do not hold that the temperature is in some dyadic relation to the number 20. The number 20 does not predicate of this temperature that it has the property of being even or being twice as much as the temperature 10°C. The number 20 is a measurement predicate that represents the way we identify a physical magnitude by finding its place on a scale.
However, I am not convinced that the psychological approach is of enough modal strength to solve the problem of canonical decomposition. It is a metaphysically contingent fact what kind of perceptual capacities we possess. Let us assume that all people went color blind one day. It does not necessarily follow that paintings’ colors stopped being their representational parts. Next, let us assume that one day people will form the capacity to see different shades of black. It does not imply that a black-and-white triangle diagram will start to have more representational parts.
However, I do hold that cognitive systems can use iconic content to describe or attribute properties to some objects. For instance, perceptual systems can use iconic content to identify objects by attributing them properties (Burge, 2010). Language-based systems can use images to describe depicted objects. Yet, I hold that the iconic properties being attributed by the system are measurement predicates. Let me explain it.
In the last comment, Alfredo Vernazzani analyses the problem of canonical decomposition. According to the well-known Fodor’s argument, images lack canonical decomposition since they can be divided arbitrarily into representational parts. Vernazzani holds that this argument is invalid since we can distinguish representational primitives based on our perceptual capacities (see also Burge, 2018). The property of being a picture part piggybacks on our perceptual capacity to recognize what it is a part of.
However, I deeply believe that the measurement-theoretic framework can be extended to give a unified account of thinking. Although it is not the book’s topic, the possibility of such an extension seems very promising. For one thing, there are fruitful attempts to apply the measurement-theoretic framework to the analysis of propositional attitudes (Dresner, 2006; Matthews, 2007). For another, there is a close and natural connection between the measurement-theoretic approach and computational framework (Matthews and Dresner, 2017). Yet, we need a well-conceived division of labor between imagistic and propositional representations within the measurement-theoretic framework. How can such a division look? I do not have an answer, but if I were looking for such, I would probably reread Kant. For him, concepts were measures (rules) taken to identify the world’s states in propositions. Images (schemata) were representations of these measures. For instance, the concept of 5 is a measure of the number of elements in the set. It can be applied in propositions such as ‘there are five apples’. An image of five apples is a representation of such a measure. It is a diagram of the number 5. And while I am not saying it is a correct answer, I hold that it offers a possibility to think about such an answer.
Matthews, R. J., Dresner, E. (2017). Measurement and Computational Skepticism. Noûs, 51 (4), 832-854.
Matthews, R. J. (2007). The Measure of Mind. Propositional Attitudes and their Attribution. Oxford: Oxford University Press.
Dresner, E. (2006). A Measurement Theoretic Account of Propositions. Synthese, 153, 1-22.
Does it mean that the psychological interpretation is wrong? No, it does not! It suggests, however, that some other constraints should supplement it.
Let us take an image of John representing him as bald. According to the measurement-theoretic framework, an image of John being bald represents the way of identifying John. The property of John being bald is the measurement predicate used to identify John. It does not predicate anything of John, as if there were some relation between these properties and their object seen in the picture, i.e., something we predicate of and a predication. A portrait of John localizes John by determining the properties that serve to recognize him. For instance, it represents the property of being bald, a measurement predicate used to identify John.

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