A Common Frame for Formal Imagination

In relation to Van Leeuwen (2013), we can say that our interest lies in constructive imagining.

It is worth noting how, on page 127, the authors explain that, without taking action into account, their theory of pretense can be understood as a theory of imagination, which is in fact where our interest lies in this work.

It is worth noting that, as argued in Spaulding (2016), Williamson uses the term “imagination” in a broad sense, which includes supposition, the evaluation of conjunctive conditionals, and so on.

As the author points out in Balcerak-Jackson (2016), succeeding in such voluntary action may vary depending on whether we are supposing, imagining or conceiving.

Note that, if possible worlds are used as formal models, imaginary worlds will then be required to be formally consistent. Nevertheless, different authors, such as Priest (2016), Berto (2017), or even Nichols and Stich in Nichols and Stich (2003) argue that one can also imagine impossible scenarios. If we wanted to allow for paraconsistent imaginings, our approach could be adapted to accommodate the use of impossible worlds in the way they are used, for instance, in Berto (2017).

In the formal definition, we use the expression “\(p_{j}\) is accounted for in \(\varphi\)” to express the fact that the truth conditions for the formula \(\varphi\) determine the truth-value of the atomic formula \(p_{j}\) by requiring it to be either true or false in the state of affairs described by \(\varphi\).

For a comprehensive introduction to propositional logic, see Hodges (2001), for instance.

Particularly, on page 118 of Nichols and Stich (2000), they identify both processes as the inferential elaboration, without distinguishing between their static or dynamic character.

It is important to note that Fig. 5 is not meant to be a Kripke model, but rather just a schematic representation of the process. As such, and in order to stress out the fact that this process elaborates on the details of the same imaginary world, we represent believed factual rules using standard propositional logic and without any kind of modal operator. Figure 5, then, aims to represent how the world on the left changes into the world on the right, rather than representing that both worlds are different, in terms of possible-worlds semantics. For more details on modal logic, see Blackburn et al. (2010).

Note that, although this kind of expressions can be mapped into Lewis’ account of counterfactuals in Lewis (1973), the way they are used in our approach is different. Whereas Lewis’ approach of such expression would “move” the point of evaluation to a different world where both antecedent and consequent are the case, our approach “breaks down” the evaluation in two different steps. First, it checks whether the antecedent is already the case in the current world and, if so, then creates a new world, which represents a refinement of the current one, and in which the consequent also holds. The notion of “refinement” can be, in fact, a bit controversial when thinking about possible worlds; after all, possible worlds are maximally consistent sets of formulas in which each and every atomic formula is already assigned a truth-value. We use the term “refinement” is a more informal or intuitive way. Even if the truth-value of all atomic formulas needs to be set in our imaginary worlds, their truth-value may be the result of importing it from the world of reference, instead of determining what is should be by looking at how the imagining develops. In this sense, and even if the technical apparatus behind a classical approach requires all atomic formulas to have a truth-value, by “refining” the world we mean that, by pulling onto certain factual beliefs, the agent “realizes” that the truth-value of certain atomic formulas should change in the imagining, with respect to what they were before. In this sense, “refining” a world could be understood as “updating” the truth-values of certain atomic formulas step-by-step, given the factual rules believed by the agent. Those “refinement” steps could be seen as specific executions of some of the broader sets of inferential mechanisms identified by previous authors.

In Funkhouser and Spaulding (2009), the authors use the term “script” to refer to something that can be imitated or enacted, and that can guide action without the need of being backed up by beliefs or knowledge. Our use of the term differs from theirs in the sense that, in our account, scripts are not meant to guide an actual action, but rather to set, according to the current state of the imaginary scenario, which actions or events could take place in there. In particular, our scripts encode something like “in a situation in which such and such was the case, executing action \(\alpha\) could lead to this set of outcomes”. Scripts, then, are neither guides to enact an action, nor a way to assign a tendency to certain actions to happen in an imaginary scenario, but rather a way of determining what an action could bring about, given the conditions of such scenario. Therefore, although both our and their use of the term “script” has some similarities, as in both cases it concerns actions that could happen in an imaginary scenario, in our setting scripts are just meant to open new modal paths opened up by certain actions or events.

It could be argued that, in fact, scripts do provide some information regarding what actions are most likely to occur in a certain scenario. Nevertheless, the structures we use to define our approach do not allow to capture, at least not explicitly, this notion of “typicality”, or “likeliness” for an action to happen in a given scenario. Instead, our approach assumes that the agent already has scripts about every possible action available; what makes an action “executable” in a certain scenario, then, is determined by the conditions that the script should fulfill in order to bring about its consequences. More intuitively, the action “pour tea into a cup” would only have an actual effect in those scenarios in which, for instance, there is a cup and a tea pot, but it will not affect, say, a scenario where there are only apples and oranges on a table. Even though our approach, as it is, cannot yet account for updating the likeliness of certain actions to be imagined in particular scenarios, it could be extended by including a kind of “sorted preference list” over scripts for the imagining being entertained. The list would have to be ordered in such a way that, the closer the current imagining is to the preconditions of a particular script, the more relevant this script becomes in the list, and thus the more likely it is to be selected by the agent.

In Fact, Langland-Hassan argues that these kind of additions, which Nichols and Stich attribute to their opaque Script Elaborator, are nothing more than new premises that the agent clamps to the imaginary scenario.

It is only fair to note how, considering the way the Description algorithm works, it still creates a new state of affairs related via an accessibility relation. Nevertheless, and conversely to what happens with the Default Evolution, this transition is purely meant to capture a refinement of a static scenario, rather than an actual event occurring in the scenario being represented. In other words, these refinements can be interpreted as small “reasoning steps” similar to those that appear in Velazquez Quesada (2011). If a formal layer for time was to be added to our approach, only those transitions labeled with an action would represent an actual change in time, whereas those transitions resulting from an execution of the Description would still represent a scenario at the same time instant.

When considering other, more specific kinds of imagination acts, it could be necessary to add additional vertex to the rhombus. For instance, a vertex accounting for actions, in the case of pretense, or another one accounting for emotions, in the case of empathy.

In paradigmatic cases of fiction, such as medieval fantasy stories, this set of reality-oriented rules and facts is not only formed by those rules the agent believes about the real, actual world, but also by those rules that usually apply to the fictional setting being depicted. This latter kinds of rules correspond to Genre Truths, as identified in Funkhouser and Spaulding (2009). Additionally, but still related to this kind of paradigmatic rules, Lewis (1978) offers an account on how to assess truth in fiction.