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The Logical Development of Pretense Imagination


We propose a logic of imagination, based on simulated belief revision, that intends to uncover the logical patterns governing the development of imagination in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises (1) the algorithm that specifies what goes on in between receiving a certain input for an imaginative episode and what is imagined in the resulting imagination, as well as (2) the goal-orientedness of imagination, by allowing the context to determine, what we call, the overall topic of the imaginative episode. To achieve this, we employ well-developed tools and techniques from dynamic epistemic logic and belief revision theory, enriched with a topicality component which has been exploited in the recent literature. As a result, our logic models a great number of cognitive theories of pretense and imagination [cf. Currie and Ravenscroft (Recreative minds, Oxford University Press, Oxford, 2002); Nichols and Stich (Mindreading: an integrated account of pretence, self-awareness, and understanding other minds, Oxford University Press, Oxford, 2003); Byrne (The rational imagination, The MIT Press, London, 2005); Williamson (The philosophy of philosophy, Blackwell Publishing, Oxford, 2007); Langland-Hassan (Philos Stud 159:155–179, 2012, in: Kind and Kung (eds) Knowledge through imaginaion, Oxford University Press, Oxford, 2016].

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  1. It is an interesting question whether this kind of imagination also features in other cognitive activities besides pretense, such as future planning, decision making, and risk assessment. We believe that it does but neither the conceptual arguments nor the adequacy of the formal model presented in this paper hinges on this view (we will get back to this point in our concluding remarks).

  2. Note that one can imagine recalcitrant situations with respect to both of these restrictions if the agent explicitly intervenes. We will set this complication aside for now and address the details of this in the next section, when we elaborate on the theory of imagination at play here.

  3. In the literature concerning pretense and the relevant imagination involved, there is a debate between those claiming that there is nothing over and above the cognitive attitudes belief and desire that is needed to account for what is going on during pretend play (the use of ‘desire’ here is meant in a non-technical, pre-theoretical sense) and those claiming that there is a specific cognitive capacity, distinct from belief and desire, that is involved (a pretense- or imagination-attitude). The former support the Single Attitude (SA) account and the latter support the Distinct Cognitive Attitude (DCA) account. Ultimately, the models of this paper can be interpreted in line with either theory.

  4. Some problems remain open, one of which we raise below and aim to address in our model.

  5. In both scenarios it is stipulated that a tornado is highly probable but not absolutely certain. This is to make sure that the cognitive exercise at play here is pretense imagination and not mere belief revision, as the agent might not actually believe that there will be a tornado. We thank an anonymous reviewer for pointing this out.

  6. This is inspired by an objection raised against Berto’s work by Timothy Williamson when the former presented some of his work at the ‘Philosophy of Imagination’ conference at the Ruhr Universität Bochum in March 2018.

  7. The particular form of our models is not essential to this enrichment. The same solution could also be implemented in Berto’s (2018, 2021) models of imagination.

  8. See Nichols and Stich (2003, pp. 23–24) for empirical evidence that people do make such choices in pretense.

  9. Though most of what is said here is taken from the work of Langland-Hassan (2012, 2016), the resulting general picture (and thus our model thereof) captures most theories of pretense (e.g., that of Currie and Ravenscroft 2002; Nichols and Stich 2003) and is compatible with particular theories of imagination (e.g., that of Byrne 2005; Williamson 2007; Berto 2021).

  10. For those who worry about phenomenology of an imaginative episode and the lack of ‘active choice’ that seems to be involved, note that most of this intervening happens sub- or unconsciously. “What we might pre-theoretically think of as a single imaginative episode could in fact involve many such top-down ‘interventions.’ These interventions would allow for the overall imagining to proceed in ways that stray from what would be generated if one never so intervened” (Langland-Hassan 2016, pp. 74–75).

  11. ‘Pretense’ is usually used to denote the imaginative episode in combination with the appropriate physical actions. So, in the case of the tea-party, when one moves their arm in the motion as if sipping tea from an empty cut, this is part of (and often the defining part of) the pretense episode. However, for our purposes, we ignore this part and only focus on the imagination that is involved in such pretense.

  12. This is not to say that there is no imagery involved in pretense, what we mean is that the kind of imagination that allows us to explain the pretense behaviour is propositional imagination.

  13. There is a very interesting and intricate relationship between ROI and RAT. For our purposes, focusing on ‘tea-party-like’ examples of pretense imagination, the distinction is relatively intuitive. However, when one considers cases of pretense imagination involving more ‘exotic’ cases (e.g., ‘imagine there is a monster under the bed’ or ‘imagine that I am Luke Skywalker’) more needs to be said. We thank an anonymous reviewer for pressing us on this issue. We will return to it in the conclusion of this paper.

  14. Every well-preorder \({\preceq _s}\subseteq W\times W\) is a total order: either \(w\preceq _sv\) or \(v\preceq _sw\) for all \(w, v\in W\).

  15. This condition guarantees that the agent never believes a blatant contradiction and, in turn, never imagines a blatant contradiction such as \(\bot\). Note, however, that we think that inconsistent pretence is possible in principle. It is just that the current framework cannot deal with it in a completely satisfactory way. One way to do so, would be to add impossible worlds or states to the models (see for example, respectively, Berto 2017; Saint-Germier 2021). See below for more about imagining contradictory propositions within a single imaginative episode. Thanks to an anonymous reviewer for urging us to stress this point.

  16. If we eliminate the downward closed-ness condition of Q in Definition 4.2.3, the agent in principle can follow a belief revision policy such that after revision by a consistent proposition P, some of the initially less plausible P-worlds become the most plausible ones. In this case \(\mu\) violates the minimality constraints of the classical AGM belief revision theory (AGM3 and AGM7) as well as principles of informational economy under consistent revision (AGM4 and AGM8) (see Bonanno 2012, Section 3 for a similar comparison). We leave the investigations of the conceptual underpinnings of different belief revision policies involved in imagination to future work and here adopt the AGM-like policy \(\mu\) as a first pass.

  17. The agent is said to have successfully revised their beliefs by \(\varphi\) at some stage s in the given history if they believe \(\varphi\) in the next stage, after revision by \(\varphi\). This corresponds to the Success Postulate of the AGM belief revision theory (Alchourrón et al. 1985) and, as \(B\) ranges only over Booleans, our framework is not subject to problems concerning higher-order beliefs such as the Moorean phenomena (cf. Holliday and Icard 2010). Due to the second conjunct in the semantic clause of \(I\varphi\) in Definition 4.3 (that is, \(\mathcal {M}, \langle w, h[k+1]\rangle \Vdash B \varphi\)), our imagination operator is always concerned with the so-called successful revisions (for the sake of brevity, we usually drop the phrase “successful”). In fact, as stated above, the simulated revision function \(\mu\) by definition always leads to successful revisions as long as the intension of the new informational input is nonempty. Since \(Min_{\preceq _{s}}(W)\not =\emptyset\) for all s in every model, both \(\lnot B_@\bot\) and \(\lnot B\bot\) are validities with respect to the proposed semantics. This means that the agent never believes (actually or in pretense) nor imagines blatant contradictions (where the latter is guaranteed by the above mentioned component in the semantic clause of \(I\varphi\)).

  18. It is easy to see that the second conjunct in the semantic clause of \(I_i\varphi\) is redundant: \(\langle w,h[k]\rangle \Vdash B\varphi\) (or \(\langle w,h[k+1]\rangle \Vdash B_@\varphi\), if \(k=0\)) guarantees that \(|\varphi |_\mathcal {M}\not =\emptyset\), thus, \(\preceq _{s_{k+1}} = \preceq _{s_{k}}^{\varphi }\) implies that \(\langle w,h[k+1]\rangle \Vdash B\varphi\) since \(\mu\) leads to successful revision by \(\varphi\) as long as \(|\varphi |_\mathcal {M}\not =\emptyset\).

  19. If the stage after which \(\varphi\) is taken on board is the initial stage (i.e., \(k=0\)), “believe” in the reading of \(I_i\) refers to the agent’s actual beliefs. Otherwise, it is the agent’s simulated beliefs at stage k. The same applies to \(I_a\).

  20. Note that, in theory, an agent might ‘intervene’ content that they already believe in the pretense. Such ‘interventions’ are not captured by our semantic clause of \(I_{a}\) and our model would label such a transition between two stages as internally developed. This might seem like a flaw in the definition, yet we would argue that this is in fact as it should be. The interventions that make pretense imagination have CHO—the fact that an agent can make choices in pretense imagination—as a characteristic feature are not ‘interventions’ with something the agent already believes (in the pretense). These latter instances of ‘intervening’ are neither philosophically interesting nor the kind of interventions that authors discussing CHO seem to have in mind (e.g., Nichols and Stich 2003).

  21. The lexicographic upgrade of a preorder \(\preceq \subseteq W\times W\) by a subset \(P\subseteq W\) makes all P-worlds strictly more plausible than all \(W\backslash P\)-worlds and keeps the ordering the same within those two zones. Our simulated belief revision function \(\mu\) is the lexicographic upgrade when \(P=Q\) in Definition 4.2.3. Even though the lexicographic upgrade does not play an essential role in our conceptual arguments, for the sake of simplicity, we take \(\mu\) to be a lexicographic upgrade operator in all our (counter)examples.

  22. Note that this straightforwardly generalises to other two-place connectives.

  23. The definitions of internally developed imaginative stages and intervened imaginative stages can be made topic-sensitive in a similar manner.

  24. See also Olkhovikov and Wansing (2018, 2019).

  25. Thanks to an anonymous reviewer for pushing us to think about this and for this particular example.

  26. For example, suggesting that imagination is a recreative capacity might involve the claim that imagination can simulate perceptual experiences as well as belief revision (see, for example, Currie and Ravenscroft 2002; Williamson 2007).


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Much of this work was conducted when the authors were employed by the ILLC, University of Amsterdam and affiliated with Arché Research Centre, University of St. Andrews through the project 'The Logic of Conceivability'. We thank our reviewers for exceptionally stimulating and helpful feedback. A version of this paper was presented at the Fiction and Imagination Workshop at the University of Turin in June 2019. Thanks to the audience for their valuable feedback. Special thanks to Francesco Berto, for his detailed comments on an earlier draft which allowed us greatly improve the paper. Also thanks to Ilaria Canavotto, who read a version of (parts of) this paper. Finally, thanks for the input of the Logic of Conceivability team: Francesco Berto, Peter Hawke, Karolina Krzyżanowska, and Anthi Solaki. This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council (ERC CoG), Grant Number 681404.

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Özgün, A., Schoonen, T. The Logical Development of Pretense Imagination. Erkenn (2022).

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