Tom Schoonen is an assistant professor of philosophy at the Institute for Logic, Language and Computation and the Department of Philosophy at the University of Amsterdam. His research interests lie in the intersection of epistemology and philosophy of cognition. He is currently editing a volume on the epistemology of ability together with Barbara Vetter.
A post by Tom Schoonen
It's been almost ten years since a great burst of logics of imagination appeared (depending on when you start counting, of course). The idea behind these formalisations is that, although “imagination will take you anywhere,” it will not take you anywhere. That is, there is some method to the madness and the aim is to capture this in a logical framework. (Note that most logics of imagination focus mainly on reality-oriented imagination, I will follow suit here.) Theorists working on the logic of imagination try to strike a balance: we can imagine things we believe, or know, to be false (“imagination will take you anywhere”), though in most instances of imagination it does not seem to be the case that anything goes (“well…, not anywhere”). In this post, I want to highlight a worry for a branch of the most popular logics of imagination, based on joint work with Aybüke Özgün and Tianyi Chu.
A very prominent approach to the logic of imagination is that of Franz Berto and colleagues, called two-component semantics (Berto 2018, 2022, 2024, Hawke et al., 2024). Formally, this approach sees imagination as a variably strict operator combined with a topic filter (i.e., two-components). The rough idea is that in the act of imagining φ, you also imagine ψ if and only if (i) all the (relevant) φ-worlds are also ψ-worlds and (ii) ψ is about the same things as φ. This nicely seems to account for the fact that we can imagine things that we do not believe (e.g., we can imagine that it is raining and, thereby, imagine the streets getting wet, even if we are looking at bright blue skies) and it also explains that not anything goes (e.g., when imagining that it is raining, we will not automatically imagine the square root of 4624, as this is not within the topic of our imaginative episode). For more formal details, see any of the cited papers.
The main novelty of the two-component semantics, is the topicality (or aboutness) component. And, as these things go, in response some have come up with problems for it. In particular, some have pointed out that the topic inclusion-condition is too strict – i.e., it rules out developments of imaginative episodes that seem perfectly fine. Roughly, the worry is that there might be ψ’s, such that they are a perfectly natural development of the imaginative episode starting with φ and that are ‘on topic’ in an intuitive sense, yet that do not satisfy the topic-inclusion condition of Berto’s semantics. This means that, according to Berto’s account, these situations are ruled out. This has been the main (technical) discussion of the two-component semantics and researchers have developed sophisticated formal frameworks of topics (e.g., by developing first-order topics or more complex mereo-topological relations between topics; cf. Badura 2021, Özgün & Schoonen 2024, Özgün & Cotnoir 2025). However, I want to raise a different worry for the two-component semantics, one that does not focus on the aboutness component, but that focuses on the (good old) truth-conditional component.
In order to raise the problem, let’s spell out the motivation for adding a topic-filter in a bit more, informal, detail. The rough idea is this, given that we imagine φ, one naïve suggestion would be that we imagine anything that is true in all the relevant φ-worlds. This would be a simple variably strict interpretation of the imagination-operator. However, if we only work with possible worlds in our semantics, this over-generates. Since, the fact that 68 is the square root of 4624 is a necessary truth, this also true in all φ-worlds for any arbitrary φ. But, it seems that in many instances of imagining something, we don’t imagine that 68 is the square root of 4624. This is where the topic filters of Berto's two-component semantics come in. We look at everything that is true in all the relevant φ-worlds and then kick out everything that is not on topic -- i.e., we filter the result for the relevant topic.
Thus, the topic filter addresses the issue of, amongst others, truths in all the relevant φ-worlds that we do not (necessarily) imagine. Note, however, that the opposite also seems to occur regularly. That is, there seem to be plenty of propositions that, though (i) not true at all the relevant φ-worlds, are (ii) natural developments of an imaginative episode starting from φ. Consider the following example (adapted from Boardman & Schoonen forthcoming):
You have to catch a train from Amsterdam to Berlin and your plan was to take your bike to get to the train station. However, getting to your bike, you see that it has a flat tire. You want to know whether it is possible that you still make your train. You imagine various situations. You imagine hailing a taxi, running, and so on. In imagining running to the train station, you imagine that you won't make it on time to catch the train, while in the imaginative episode where you hail a taxi, you imagine that you do make your train.
Now, in both cases, the imagination develops in a perfectly respectable, reality-oriented manner. Yet, in neither case is the development true in all the relevant input-worlds. So, whereas the topic filter accounted for situations that are true at all relevant input-worlds, but are not (likely) to be imagined; the problem that we are interested in are cases that are (likely) to be imagined, yet that are not true at all the relevant input-worlds. This raises the question of whether the truth-conditional component of Berto's two-component semantics also needs relaxing.
We argue that it does and note that some intuitive weakenings do not work. Consider another main example used in the literature on reality-oriented imagination:
You bought a new couch at IKEA and before carrying it up the stairs, you imagine whether or not it fits through the door.
Both this and the previous case, are paradigm examples of reality-oriented imagination that may (or may not) involve some kind of simulation. As such, they all fall within the purview of Berto's theory. Assuming that we can account for the topic relation in these imaginative episodes, it seems clear that in none of these cases, the resulting imaginative state is true in all the relevant input-worlds. That is, the truth-conditional component of the semantics would rule out these cases as reality-oriented imaginings, which seems false. So, in order to ‘accommodate’ these imaginative episodes, we need to weaken the truth-conditional component of the two-component semantics.
Here’s a very intuitive suggestion of weakening that condition. The truth-conditional clause from Berto's semantics has it that imagination is a variably strict operator, meaning that it is, in a sense, a necessity that varies with the input. E.g., given that we imagine φ, ψ is necessarily also imagined. So, ψ is true in all the relevant φ-worlds. One natural suggestion of weakening this, would be to suggest that ψ is true in at least one of the φ-worlds. This would come down to mere compatibility/compossibility of φ and ψ.
Though an intuitive weakening, it is clearly not the right solution for reality-oriented imaginings. For example, note that seeing your bike has a flat tire and running faster than the speed of sound to the station are (logically) compatible, but clearly this is not reality-oriented development of your imaginative episode. There could be ways to find a middle way between the variably strict and compatibility models (e.g., a proportion-based models; cf. Jaster’s 2020 account of ability modals), however, we will focus on finding a way to restrict the relevant φ-worlds further and then base our semantics on this.
One (natural) suggestion of restricting the relevant φ-worlds would be not to look at all logically possible φ-worlds, but only at the (relevant) φ-worlds that are in line with our laws of nature -- i.e., the nomologically possible φ-worlds. This seems to be in line with what some philosophers of imagination suggest (e.g., Nichols 2006, Kind 2016, Williamson 2016). Ultimately, we don't think that this suggestion works, for similar reasons as those discussed above. There simply seem to be prima facie respectable developments of imaginative episodes, that would not even be true in all nomologically possible worlds. There are quantum possibilities that are nomologically possible, but that are simply not relevant for reality-oriented imagination (cf. Clavel Vázquez & Clavel-Vázquez 2023, Jones & Schoonen 2024, Boardman and Schoonen forthcoming).
So, what to do? Currently, we are looking into various ways of how to apply a more subjective constraint to restrict the relevant φ-worlds. This will be something along the lines of what the agent takes to be likely or plausible. A formal development on this way out of these problems is very much work in progress. However, on the conceptual-side, we think there are good reasons to think that the truth-conditional condition of Berto’s two-component semantics can be challenged and thus deserves more attention. The logic of imagination, we suggest, should not be all about aboutness.
References:
Badura, C. (2021). More Aboutness in Imagination. Journal of Philosophical Logic, 50, 523-547.
Berto, F. (2018). Aboutness in imagination. Philosophical Studies, 175, 1871-1886.
Berto, F. (2022). Topics of Thought: The Logic of Knowledge, Belief, Imagination. Oxford University Press.
Berto, F. (2024). Logic will get you from A to B, imagination will take you anywhere. Noûs, 58, 717-729.
Boardman, S. & Schoonen, T. (forthcoming). Core Imagination. Philosophers’ Imprint, 1-30.
Clavel Vázquez, M. J. & Clavel-Vázquez, A. (2023). Robustly embodied imagination and the limits of perspective-taking. Philosophical Studies, 180, 1395-1420.
Hawke, P., Hornischer, L. & Berto, F. (2024). Truth, topicality, and transparency: one-component versus two-component semantics. Linguistics and Philosophy, 47(3), 481-503.
Jaster, R. (2020). Agents' Abilities. De Gruyter.
Jones, M. & Schoonen, T. (2024). Embodied Simluation and Knowledge of Possibilities. Philosophical Psychology, 1-25. https://doi.org/10.1080/09515089.2024.2417990
Kind, A. (2016). Imagining Under Constraints. In Kind, A. & Kung, P. (Eds.) Knowledge Through Imagination (pp. 145-159), Oxford University Press.
Nichols, S. (2006). Imaginative Blocks and Impossibility: An Essay in Modal Psychology. In Nichols, S. (Ed.) The Architecture of the Imagination (pp. 237-255), Oxford University Press.
Özgün, A. & Cotnoir, A.J. (2025). Imagination, Mereotopology, and Topic Expansion. The Review of Symbolic Logic, 18(1), 28-51.
Özgün, A. & Schoonen, T. (2024). The Logical Development of Pretense Imagination Erkenntnis, 89, 2121-2147.
Williamson, T. (2016). Knowing by Imagining. In Kind, A. & Kung, P. (Eds.) Knowledge Through Imagination (pp. 113-123), Oxford University Press.