1. Epistemology of imagination

Intuitively, imagination can be a guide to what is possible. When deciding to move a heavy couch through the door, we might first imagine how to rotate the couch in order to get it through, before coming to believe that it possibly fits. Similarly, when giving feedback to colleagues, I might imagine how my comments would affect their feelings. However, this seems to clash with another intuitive feature of imagination: it is both under our voluntary control and not restricted by what is actually the case. So, how can it be that if we decide what to imagine, that we gain justification from it?

One way out of this problem, researchers agree, is to restrict imagination (cf. Kind Reference Kind, Kind and Kung2016; Kind and Kung Reference Kind and Kung2016; Balcerak Jackson Reference Balcerak Jackson, Macpherson and Dorsch2018). The rough idea is that when we are concerned with epistemically useful imagination (in the sense that it is a guide to what is possible), we focus on the restricted instances, whereas when we want to account for our ability to imagine impossibilities, we consider the unrestricted instances.

Recently, Balcerak Jackson (Reference Balcerak Jackson, Macpherson and Dorsch2018) has forcefully argued that we should focus on a recreativist account of imagination in order to explain the justification we get from imagination.Footnote ³ Imagination, on such a recreativist account, “is a matter of creating or trying to create in one's own mind a selected mental state, or at least a rough facsimile of such a state” (Goldman Reference Goldman and Nichols2006: 42). That is, imagination simulates the having of mental states without the, otherwise needed, external input or stimuli. This means that imagination is inherently restricted by whatever (neuro)physiological (or other) restrictions constrain the ‘online’ cognitive faculty that imagination is recreating.

In this paper, I focus on one particular kind of recreativist account of imagination, namely imagination as the recreation of rational belief revision. This is the kind of imagination that we use when we engage with pretense (e.g., Leslie Reference Leslie1994; Nichols and Stich Reference Nichols and Stich2003; Langland-Hassan Reference Langland-Hassan2012), but also when we engage in planning and risk assessment (e.g., Byrne Reference Byrne2005). Call it pretense imagination.

In what follows, I will first spell out what I take pretense imagination to be (section 2), after which I will present a formal account of it in section 3. This is all meant to give a very general, yet precise account of pretense imagination that we can evaluate for its epistemological merits. As it has been argued recently that one can present an epistemology of modality based on imagination's ability to justify our beliefs in certain conditionals, I will evaluate the claim that this kind of imagination can justify our beliefs in conditionals throughout sections 4–6. Even though pretense imagination can justify our beliefs in certain conditions, I argue in section 7 that it cannot play a foundational role in the epistemology of possibility.

2. Pretense imagination

Consider the following famous example of a pretense tea-party:

Children from a very young age already consistently point to the cup that has been turned upside down when asked to point at the ‘empty cup’ (cf. Leslie Reference Leslie1994; Nichols and Stich Reference Nichols and Stich2003). This indicates that children are able to engage in pretense even if it goes against what they believe the world to actually be like. Yet, they imagine this non-actual scenario in a reality-oriented way. For example, when asked, in the pretense, where there is a puddle of tea after a full cup is held upside-down, we take it to be odd if the subject answers ‘the ceiling’, whereas it seems very natural to answer that there is a puddle on the floor.

This example illustrates that pretense imagination is restricted in important ways by belief: pretense imagination seems to follow belief-like patterns, which explains the rational, reality-oriented behaviour with respect to which cups are full, and background beliefs seem to be imported into the imaginative episode, which explains the beliefs about the workings of gravity in the pretense.Footnote ⁴ Let's elaborate on both these relations between pretense and belief in turn.

The most prominent theories of pretense – e.g., that of Nichols and Stich (Reference Nichols and Stich2003) and Langland-Hassan (Reference Langland-Hassan2012) – suggest that pretense reasoning is a cognitive capacity closely related to rational belief revisions. To capture this in our formalisation, we focus on belief and belief revision, where the latter is of hypothetical nature hinting at real belief changes were the pretend scenario to be actual. In this sense, it is sufficient to use models and operators that describe a situation where the objective facts of the world do not change, but only the belief state of the imagining agent changes. This belief revision process follows, roughly, Ramsey's (Reference Ramsey and Braithwaite1929 [2013]) famous pattern:

Another important factor that restricts pretense imagination is the agent's background beliefs about the actual world. Or, as Williamson notes, “[o]ne's imagination should not be completely independent of one's knowledge of what the world is like” (Reference Williamson, Kind and Kung2016: 114). For example, in the above pretense scenario, the subjects continue the pretense with the imagining that tea falls downwards as opposed to upwards because they import their background beliefs about gravitational forces – that unsupported objects fall towards the centre of the Earth – into the pretense.

In section 3, we will resort to the rich literature in (dynamic) epistemic logic and belief revision theory to model these features.

3. Branching-time belief revision model

As imagination follows ‘belief-like’ inference patterns and develops in stages, we use a simplified version of branching-time belief revision models introduced by Bonanno (Reference Bonanno2007). These models “provide a way of modeling the evolution of an agent's beliefs over time in response to informational inputs” (Bonanno Reference Bonanno2012: 206).

Let Prop = {p ₁, …, p _n} be a finite set of propositional variables and ${\cal L}$ be the language of classical propositional logic defined on Prop. The language ${\cal L}_{{\rm BI}}$ of the logic of belief and imagination is then defined by the grammar:

$$\varphi : = p\vert \neg \varphi \vert \varphi \wedge \varphi \vert B\psi \vert I\psi $$

where p ∈ Prop and $\psi \in {\cal L}$. Read ‘Bφ’ as ‘the agent believes that φ’ and ‘Iφ’ as ‘the agent imagines that φ’. It is important that we allow B and I to range only over Booleans. That is, our language ${\cal L}_{{\rm BI}}$ of belief and imagination follows the cognitive science and philosophy literature on imagination in focusing on first-order attitudes (cf. Nichols and Stich Reference Nichols and Stich2003; Byrne Reference Byrne2005; Williamson Reference Williamson2007; Langland-Hassan Reference Langland-Hassan2012, Reference Langland-Hassan, Kind and Kung2016). We interpret this language on branching-time belief revision models:Footnote ¹¹

Since W is finite, every non-empty subset of W has a minimal element with respect to each ${\rm \preceq }_s$. The set of minimal elements, $Min_{{\rm \preceq }_s}( U ) $, for any U ⊆ W with respect to ${\rm \preceq }_s$, is defined as

$$Min_{{\rm \preceq }_s}( U ) = \{ {w\in U\colon w\;{\rm \preceq }_sv{\rm \;for\;all\;}v\in U} \} $$

So, for each s ∈ S, $( {W, \;{\rm \preceq }_s, \;V} ) $ constitutes a standard plausibility model (cf. Baltag and Smets Reference Baltag, Smets, Bonanno, van der Hoek and Wooldridge2006; van Benthem Reference van Benthem2007), where the order, ${\rm \preceq }_s$, represents the arrangement of worlds to the degree that the agent considers them plausible at stage s (you can read $w\;{\rm \preceq }_sv$ as ‘w is at least as plausible as v at stage s’). This results in a model of the hypothetical beliefs of agents per stage of the branching model, where the stages change over time.

3.1. Histories, upgrades, and semantics

A branching-time belief revision model is intended to represent the evolution of an agent's belief and imagination over time, where imagination can be read off of the actual development of the pretense scenario. This is represented by a finite sequence of linear stages, called history, h (where ‘${\rm \rightarrowtail }$’ denotes the immediate successor relation):

$$h = ( s_0, \;s_1, \;\ldots , \;s_n) \;{\rm such\ that}\;s_i {\rm \rightarrowtail } s_{i + 1}, \;$$

where s ₀ is the root of the underlying next-time branching frame. Let's call s ₀ the initial stage and s_n the current stage. History h thus keeps track of the past stages, but does not tell us anything about the future. For an illustration of a branching-time belief revision model see Figure 1, where the nodes in the figure represent the stages of the imaginative episode with the plausibility ordering of that particular stage – i.e., ${\rm \preceq }_i$ represents the plausibility ordering at stage s _i.

Fig. 1. A toy-example of a branching-time belief revision model: the nodes represent the stages of the imaginative episode with the plausibility ordering of that particular stage.

I suggest that the kind of hypothetical belief revision used by agents in pretense is a lexicographic upgrade, which allows us to explain some of the intuitive features of pretense imagination. This well-known lexicographic upgrade, for example with p, makes all p-worlds more plausible than all ¬p-worlds and keeps the ordering the same within those two zones (cf. van Benthem Reference van Benthem2007: 141).Footnote ¹³ This is the final auxiliary definition in order to define the semantics for ${\cal L}_{{\rm BI}}$.

Definition 2. Upgraded preorder

Given a pre-ordered set $\langle W, \;{\rm \preceq }_s\rangle $ and P ⊆ W, the upgraded pre-order by P is the tuple $\langle W, \;{\rm \preceq }_s^{\Uparrow P} \rangle $, where ${\rm \preceq }_s^{\Uparrow P} $ is the new ordering such that $w\;{\rm \preceq }_s^{\Uparrow P} v$ iff (1) $w\;{\rm \preceq }_sv$ and w ∈ P, or (2) $w\;{\rm \preceq }_sv$ and $v\in W\backslash P$, or (3) ($w\;{\rm \preceq }_sv$ or $v{\rm \preceq }_sw$) and w ∈ P and $v\in W\backslash P$.

In the semantics, formulas of ${\cal L}_{{\rm BI}}$ are evaluated not only with respect to states, but with respect to state-history pairs of the form 〈w, h〉. The intension of φ with respect to h in ${\cal M}$ is $\vert \varphi \vert _{\cal M}^h : = \{ w\in W\colon {\cal M}, \;\langle w, \;h\rangle \,{\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }\varphi \} $.

Definition 3. ${\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }$-Semantics for ${\cal L}_{{\rm BI}}$

Given a model ${\cal M} = \langle S, \;{\rm \rightarrowtail }, \;W, \;{\rm \preceq }, \;V\rangle $ and a world-history pair 〈w, h〉 such that h = (s ₀, s ₁, ….s _n), the semantics for ${\cal L}_{{\rm BI}}$ is defined recursively as follows:

$$\matrix{ {{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }p} \hfill & {{\rm iff}} \hfill & {w\in V( p) } \hfill \cr {{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }\neg \varphi } \hfill & {{\rm iff}} \hfill & {{\rm not}\,{\cal M}{\rm , \;}\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }\varphi } \hfill \cr {{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }\varphi \wedge \psi } \hfill & {{\rm iff}} \hfill & {{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }\varphi \,{\rm and}\,{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }\psi } \hfill \cr {{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\varphi } \hfill & {{\rm iff}} \hfill & {Min_{{\rm \preceq }_sn }( W) \subseteq \vert \varphi \vert _{\cal M}^h } \hfill \cr {{\cal M}, \;\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }I\varphi } \hfill & {{\rm iff}} \hfill & {\exists k < n\left({{\rm \preceq }_{s_{k + 1}} = {\rm \preceq }_{s_k}^\varphi {\rm and\ }{\cal M}{\rm , \;}\langle w, \;h[ k + 1] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\varphi } \right)} \hfill \cr } $$

Imagination, here, is dependent on both w and the whole history h. According to the proposed semantics, an agent imagines φ if they have revised their hypothetical belief state with φ at some stage in the history. In other words, we take what the agent imagines at the current stage to be the collection of propositions by which they have upgraded their pretend belief state at some stage before the current one. So, an appropriate reading of Iφ, then, is that “the agent has taken φ on board at some stage of the imaginative episode”. In this sense, the imagination operator I is a backward looking modality that keeps track of the informational input the agent uses through an imaginative episode. It is important to stress at this point that the belief modality represents the simulated or pretense beliefs of the agent, except when h = (s ₀). The agent's actual beliefs are given by the plausibility model in the initial stage s ₀.Footnote ¹⁴

So, how, if at all, does this model give a formal interpretation of the development of an imaginative episode? Given a history h = (s ₀, …, s _n) and k ≤ n, let h[k] = (s ₀, s ₁, …s _k) be the initial segment of h of length k + 1. We then define the kth imaginative stage i _k, the set of sentences the agent has imagined up to stage k, as

$$i_k = \{ \varphi \in {\cal L}\colon \langle w, \;h[ k] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }I\varphi \}.$$

This way we extract the imaginative stages through the actual history and define the corresponding imaginative episode ${\cal I} = ( i_1, \;\ldots , \;i_n) $ as a sequence of sets of sentences in ${\cal L}$. It is not difficult to see that $i_0 = \emptyset $. An imaginative episode starts with input propositions forming the first imaginative stage i ₁. We can distinguish between stages that follow through internal development and stages that are added through intervention by introducing two distinct operators into our language: I _iφ and I _aφ. The former concerns internally developed stages and the latter concerns added content through intervention.Footnote ¹⁵ We interpret these two modalities as follows:

$$\matrix{ {\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }I_i\varphi } & {{\rm iff}} & {\exists k < n( ( {\rm \preceq }_{s_{k + 1}} = {\rm \preceq }_{s_k}^\varphi \;{\rm and}\;\langle w, \;h[ k + 1] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\varphi ) \;{\rm and}\;\langle w, \;h[ k] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\varphi ) } \cr {\langle w, \;h\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }I_a\varphi } & {{\rm iff}} & {\exists k < n( ( {\rm \preceq }_{s_{k + 1}} = {\rm \preceq }_{s_k}^\varphi \;{\rm and}\;\langle w, \;h[ k + 1] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\varphi ) \;{\rm and}\;\langle w, \;h[ k] \rangle {{\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar\hskip-11pt / }}\,\,B\varphi ) } \cr } $$

Semantically, I _iφ states that “the agent takes φ on board at some stage of the actual history where she already hypothetically believes it”. This is what we take internal development to be: the ordinary development of updating your hypothetical beliefs with what you find most plausible given a particular input. On the other hand, I _aφ says that “the agent takes φ on board at some stage of the actual history and φ was not believed at that stage”. This implies that φ was imagined not as a result of the agent's belief revision process, but added “externally” to the imaginative episode.Footnote ¹⁶

4. Epistemology of pretense imagination

With this formal model of pretense imagination at hand, we now turn to the epistemology thereof. Langland-Hassan (Reference Langland-Hassan, Kind and Kung2016) and Williamson (Reference Williamson2007, Reference Williamson, Kind and Kung2016) both argue that pretense imagination might be central to conditional reasoning and the epistemology of conditionals. However, what we are interested in is the particular use of conditionals to gain knowledge of possibilities and whether pretense imagination plays a crucial role in the epistemology of these particular conditionals (Williamson Reference Williamson2007, Reference Williamson, Kind and Kung2016, Reference Williamson2020). So, we need to evaluate two claims: (i) can pretense imagination provide justification for believing conditionals and (ii) can pretense imagination, in virtue of (i), play a role in the epistemology of possibility?

The model presented in this paper allows us to very precisely evaluate these claims. We saw that imaginative episodes are sequences of imaginative stages; these stages are either explicitly intervened by the agent or developed through hypothetical belief revisions. So, we can evaluate the epistemic usefulness of pretense imagination through an argument by cases. First, I will argue that internally developed imagination cannot be used to gain justification for new beliefs in conditionals, after which I will argue that particular instances of intervened content do give rise to new beliefs in conditionals. Despite this, I will conclude by arguing that these conditionals (and thus pretense imagination) cannot explain our knowledge of non-actual possibilities.

4.1. Beliefs in conditionals and conditional beliefs

The first thing to stress is that I will focus on our beliefs in indicative conditionals (represented with ‘→’).Footnote ¹⁷ However, the logic discussed above does not involve an indicative conditional. In this subsection, I will first argue that we have in fact all we need to evaluate the epistemological question whether pretense imagination can provide us with justification for new beliefs in indicative conditionals.

A venerable tradition of how to determine whether we should believe a conditional has it that we should believe a conditional if we believe the consequent after having (hypothetically) revised our beliefs with the antecedent. This traces back to, at least, Ramsey, who suggested that if we are to determine ‘If φ, then ψ’ and we are uncertain about the antecedent, then we should add φ “hypothetically to [our] stock of knowledge” and then evaluate “on that basis” whether ψ (1929: 247, fn. 1). Stalnaker (Reference Stalnaker, Harper, Stalnaker and Pearce1968) and Williamson (Reference Williamson2007: Ch. 5, Reference Williamson2020: Ch. 2) also suggest epistemologies of conditionals in this vein.Footnote ¹⁸ If such theories are correct, then if the agent has a rational conditional belief, then they are equally in a position to justifiably believe the corresponding conditional.

Even though we do not have an indicative conditional in our semantics, we do have everything we need to define conditional beliefs in our model. Given Definitions 1 and 2, we can define conditional beliefs in our models as follows:

Definition 4. Conditional belief

$${\cal M},\langle w,h\rangle ||\joinrel\joinrel\relbar }B^\varphi \psi \;{\rm iff}\; Min\;{\rm \preceq }_{s_n}^\varphi (W)\subseteq |\psi |_{\cal M}^h, {\rm where} \;h = (s_0, \ldots,s_n)$$

‘B ^φψ’ is a conditional belief: the agent believes ψ given (or conditional on) φ. Epistemologically speaking, if something like the Ramsey test is a correct epistemology of conditionals, a conditional belief is similar enough to a belief in the corresponding conditional for our purposes.Footnote ¹⁹

5. Epistemic usefulness of internal development

Both Langland-Hassan (Reference Langland-Hassan, Kind and Kung2016) and Williamson (Reference Williamson, Kind and Kung2016) defend the idea that after an imaginative episode with explicit input φ, if at some point you end up imagining ψ, the knowledge that you gain is of the (indicative) conditional φ → ψ (see also Nichols and Stich Reference Nichols and Stich2003; Byrne Reference Byrne2005; and a lot of the suppositional reasoning literature following the Ramsey test). “[T]he inferences drawn in imagination are imported back into one's beliefs as consequents to a newly believed conditional” (Langland-Hassan, Reference Langland-Hassan, Kind and Kung2016: 68, emphasis added). In this section, I will argue that internally developed conditionals that one might import back into one's beliefs are not newly believed conditionals.

It is important to stress that at this point in the argument by cases, we focus only on internal development: an imaginative episode where we only rely on hypothetical belief revision with (hypothetically) believed propositions. That is, for any world-history pair that we consider here, the history, h = (s ₀, …, s _n), is such that for any $i < n, \;{\rm \preceq }_{s_{i + 1}} = {\rm \preceq }_{s_i}^\varphi $, for some $\varphi \in {\cal L}$ such that $\langle w, \;h[ i] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\varphi $. Let us call such a history an internally developed history.

The claim that the internal development of pretense imagination can provide us with justification for new conditional beliefs is as follows: it is possible to come to have a conditional belief somewhere in an internally developed history such that the agent does not have that conditional belief at the root stage – i.e., the conditional belief is new. For if revising one's beliefs with the antecedent results in believing the consequent and the conditional was not yet believed in the original state of the imaginer, then it can be said that the imaginative episode provided the justification for a new belief in the conditional. Call this the target claim.

I will argue that this is false – i.e., I will argue that the beliefs that are the result of such imaginative episodes are not new beliefs. To show that the target claim is false, I will prove that for any internally developed history, if there is a stage where revising one's beliefs at that stage with φ results in believing ψ at the next stage, then the agent already had a conditional belief in ψ given φ in the root stage – i.e., the conditional belief is not new.

Show: For all internally developed histories, h = (s ₀, ….s _n), and all formulas φ and ψ, if there is an i < n such that ${\rm \preceq }_{s_{i + 1}} = {\rm \preceq }_{s_i}^\varphi $ and $\langle w, \;h[ i + 1] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\psi $, then $\langle w, \;s_0\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B^\varphi \psi $.

The first step is to note a consequence of our belief revision policy and the effects this has for an internally developed history. Remember that when we revise our beliefs with φ, the plausibility ordering amongst all the φ-worlds remains the same (see condition (1) of Definition 2).Footnote ²⁵ Thus, upgrading our beliefs with a believed proposition – i.e., a proposition such that it is true at all the most plausible worlds – does not alter the set of most plausible worlds. Given that an internally developed history only involves updates with believed propositions, it follows that the set of most plausible worlds is the same at all stages of an internally developed history. That is, $Min\;{\rm \preceq }_{s_0}( W) $ is identical to that of any state s _i in h = (s ₀, …, s _n) (of an internally developed history) – i.e., $Min\;{\rm \preceq }_{s_i}( W) = Min\;{\rm \preceq }_{s_0}( W) $ for any i ≤ n. Let us call this ‘(NCP)’, for No Change in most Plausible worlds.

Given that the set of most plausible worlds is constant for an internally developed history (NCP), it follows that all beliefs and conditional beliefs, which are based on revisions with believed propositions (see footnote 25), of the agent are also constant at all stages. This suggests that the target claim has to be false. To see this, take an arbitrary s _i, where i < n, from an internally developed history h = (s ₀, …, s _n), such that (i) ${\rm \preceq }_{s_{i + 1}} = {\rm \preceq }_{s_i}^\varphi $ and (ii) $\langle w, \;h[ i + 1] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\psi $. Because we focus on internally developed histories, all belief revisions are with believed propositions. So, we can conclude from (i), plus Definition 2 and (NCP), that φ is true in all the most plausible worlds of the agent at all stages of the internally developed history. From (ii), plus Definition 3 and (NCP), it follows that ψ is true in all the most plausible worlds of the agent at all stages of the internally developed history. From this it follows that ${\rm \preceq }_{s_1} = {\rm \preceq }_{s_0}^\varphi $ and $\langle w, \;h[ 1] \rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B\psi $. So, by Definition 4, $\langle w, \;s_0\rangle {\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar }B^\varphi \psi $. Thus, the target claim is false.Footnote ²⁶

This suggests that the internal development of pretense imagination cannot provide justification for new beliefs in conditionals. Any conditional that might be imported back into our actual beliefs was already believed, for otherwise the internal development would never result in the consequent given the antecedent.

The above argument, one might worry, seems to assume that indicative conditionals express propositions, whereas not everyone might agree with this (e.g., Edgington Reference Edgington1986; Levi Reference Levi1988; see Leitgeb Reference Leitgeb2007 for a clear discussion on these and related views). If you think that conditionals do not express propositions, they cannot, strictly speaking, be believed. As Leitgeb points out, “conditionals [on such a view are] accepted by the agent without being believed” (Reference Leitgeb2007: 119). For these theorists, ‘beliefs in conditionals’ simply are conditional beliefs (or degrees of belief in the consequent conditional on the antecedent). Note that the argument against the epistemic usefulness of the internal development of pretense imagination was phrased completely in terms of conditional beliefs. So, the conclusion holds even for those who think that indicative conditionals do not express propositions.

To sum up, despite the fact that it might seem as though our imaginative episode makes us believe certain conditionals, it is not the internal development of the imagination that provides the justification for the beliefs in these conditionals.

6. Epistemic usefulness of intervened content

When focusing on internally developed histories, we saw that we cannot gain knowledge of any new conditionals. Williamson (Reference Williamson2020) points out that this is because we usually rely on conditionals prospectively: “[w]e need ‘if A, C’ most when we do not now that A” (p. 17, original emphasis). Correspondingly, the idea is that pretense imagination really comes into its own when we intervene some content and then look at the resulting hypothetical belief revisions. As we will see, it is indeed the case that we can come to gain conditional beliefs that we did not have at the root stage when we have actively intervened content in the imaginative episode.

To show this, let's construct a model where there is a conditional belief at a stage of the imaginative episode and that conditional belief is not true at s ₀ – i.e., it is a new conditional belief. Consider a model such that W = {w ₁, w ₂, w ₃}, V(p) = {w ₂, w ₃}, V(q) = {w ₁, w ₃}, and the plausibility orderings per stage are as represented in Figure 2 – i.e., ${\rm \preceq }_{s_{12}} = {\rm \preceq }_{s_0}^p $ and ${\rm \preceq }_{s_{21}} = {\rm \preceq }_{s_{12}}^q $ (only part of the model is represented). We take the actual history to be h = (s ₀, s ₁₂, s ₂₁). Note that both developments are intervened content, as we assume that the explicit input is also intentionally added. For our argument, we focus on the second intervention (i.e., the one within the imaginative episode, not the one that starts it).Footnote ²⁷ After the upgrade with q, the agent hypothetically believes p; that is, at stage s ₁₂ the agent has a conditional belief: they believe p conditional on q. However, it is easy to see that this is not the case at the initial stage: $\langle w, \;s_0\rangle {{\rm \mathrel\vert \,\joinrel\mathrel\vert \joinrel\relbar\hskip-11pt / }}\,\,B^q \; p$. So, it seems that we are able to gain new beliefs in conditionals by upgrading our (hypothetical) beliefs with intervened content. In our toy example, we gain justification for the belief in q → p, which we didn't believe before we engaged in the imaginative episode (i.e., at s ₀).Footnote ²⁸

Fig. 2. New conditional beliefs from intervened content.

7. Pretense imagination and the epistemology of possibility

Section 5 showed that if the antecedent is already believed, we gain no new conditional beliefs, which is in line with Williamson's (Reference Williamson2020: 17) comments on prospectivity. In section 6 we say that an imaginative episode with an intentionally intervened (believed to be) false proposition might indeed result in justification for a belief in a conditional. So, pretense imagination can justify us in believing prospective conditionals: conditionals of which we do not (yet) know whether the antecedent is true. The question thus becomes whether we can use this in a conditional-based epistemology of possibility. When considering the epistemological role of conditionals in the epistemology of possibility, we see that researchers often focus on providing us with justification for believing the possibility of the consequent.Footnote ²⁹ How do pretense imagination and prospective conditionals help us in determining the modal status of the consequent? That is, can they, and if so how do they, play a role in a conditional-based epistemology of possibility?

Given that we do not believe the antecedent to be true, there are two prominent options: the antecedent is ‘merely actually false’ (i.e., false in the actual world, though possibly true) or ‘necessarily false’ (i.e., impossible). This difference has a significant effect with regards to the role the conditionals in question play in an epistemology of possibility. Consider the following pairs of conditionals to see this:

1. (1) If Amy squared the circle, she becomes a famous logician. (Ripley Reference Ripley2012)

2. (2) If Lamyae works in her office, she is sitting in a comfortable chair.

Let's assume that we justifiably believe both conditionals based on our pretense imagination and we believe both antecedents to be false. If we are unaware of the modal status of the antecedents, what good does knowledge of these conditionals do us in the epistemology of possibility? So, the crucial issue is how we determine that the relevant hypothetical situation (i.e., the antecedent) is possible.

The fact that the antecedent is intervened does not help us here. Intervened content is just content transferred from the intention (to imagine something) to actually imagining it. Correspondingly, merely being the input for an imaginative episode does not allow us to distinguish between merely false or impossible antecedents: there are virtually no constraints on what we use as intervened content and we can intervene content that is true, false, impossible, etc.Footnote ³⁰

Considering the way most conditional-based epistemologies of possibility work, we can see that, in general, they rely on the transfer of possibility from the antecedent to the consequent. That is, they rely on the antecedent being known to be possible and the conditional being believed to be true, in order for you to be justified to believe that the consequent is possible (e.g., Williamson Reference Williamson2007: 156; Kment Reference Kment2014: 4). This shows that in order for the beliefs in the conditional to be useful as a tool for the epistemology of possibility, we need to have prior knowledge of the modal status of the antecedent.

So, once we have independent evidence for the possibility of the input proposition, we might use indicative conditionals (and the corresponding imaginative exercises) to extend our knowledge or beliefs in possibilities. But, prior knowledge of the modal status of the antecedent is crucial; without it pretense imagination is of no help in the epistemology of possibility.