Chris studied philosophy and logic in Hamburg and Amsterdam. After obtaining his PhD in philosophy from the Ruhr University Bochum, he is now working as a consultant in the strategy department of Hamburg University. He still likes to think about and discuss philosophical issues surrounding imagination and logic.
A post by Chris Badura & Tom Schoonen
The debate on the epistemic value of imagination is maturing (cf. Badura & Kind 2021). Here, questions about whether and how imagination has justificatory force have taken center stage. Discussions often focus on whether imagination justifies beliefs in modal statements, conditional statements, and even whether imagination provides us with justified beliefs about actuality. While these are all interesting and important questions, we think that one important question has not (yet) received the attention it deserves: can we imagine disjunctions?
Tom is a Junior Fellow at the Center for Advanced Studies in Humanities "Human Abilities", where he is working on the epistemology of human abilities and thinking about potential epistemic uses of (embodied) imagination. Before this, he finished his PhD at the Institute for Logic, Language and Computation (University of Amsterdam) on (imagination-based) epistemologies of possibility.
To see why it is interesting to look at disjunctions and imagination, let us consider one area where they cross paths: decision-making. Based on empirical data and conceptual arguments, Nanay (2016) has forcefully argued that we rely on imagination when we are making decisions. When faced with a decision, we have several options to decide between, which (together) can be expressed by a disjunction. For example, when standing in front of the breakfast buffet at a conference hotel, we can choose between having an apple or having a Nutella toast for breakfast. That is, we could have an apple for breakfast or a Nutella toast for breakfast. In contemplating what to choose, it seems that we do not, however, imagine that we have an apple for breakfast or a Nutella toast for breakfast, i.e., we do not imagine a disjunction. Instead, “when we decide between two possible actions, we imagine ourselves in the situation that we imagine to be the outcome of these two actions and then compare these two imaginings” (Nanay 2016, p. 134, emphasis added). This suggests that when we are facing a decision between n options, we engage in (at least) n imaginative episodes, each of which has one of the options (disjuncts) as initial input.
This suggests that in decision-making, we do not imagine disjunctions. Let us now consider a more general case in which we are explicitly requested to imagine a disjunction. What does it take to comply with such a request? Consider the situation in the hotel again and we now explicitly ask you:
(D) Imagine that you are having an apple or a Nutella toast for breakfast.
We think that, as in the decision-making case, we can comply with this request, but, interestingly, not by imagining a disjunction. In fact, we think we can’t imagine disjunctions, strictly speaking. For consider some intuitive responses. If we imagine a “witness” of the disjunction (in one imaginative episode), we do not imagine a disjunction. This has to do with the aboutness of imagination. Request (D) involves an imagining that is, in a sense, about having an apple for breakfast and about having a Nutella toast for breakfast (for aboutness in imagination, see, e.g., Berto 2018). Imagining one witness of the disjunction does not suffice; if we ignored one option that we are requested to imagine about, we would be ignoring one of the options the requested imagining is about. On the other hand, if we imagine both disjuncts in the same imaginative episode, the imagining would be no different from imagining the corresponding conjunction. This also does not seem to be what (D) is asking of us. So it seems that to comply with the request we engage in two distinct imaginative episodes: one for each of the disjuncts -- just as Nanay argued in the case of decisions. We imagine that we are having the apple, which unfolds to imagining feeling good about ourselves for being healthy. We imagine that we are having Nutella toast, which unfolds to imagining feeling guilty about giving in to our sweet desires.[1] Although in both imaginative episodes we imagine “a witness” of the disjunction as the initial input of the episode, we do not imagine the disjunction (as the input of the episode).
This is not just some esoteric interest of ours, but in fact relevant to a number of discussions surrounding the philosophy of imagination. For example, (i) in the literature concerned with the logic of imagination (Berto 2018, McHugh 2018), it is taken for granted that we sometimes imagine disjunctions;[2] (ii) when discussing the inputs to imaginative episodes, there is almost no mention of restricting such inputs (e.g., ruling out disjunctions) (Williamson 2007, Langland-Hassan 2016); and (iii) in debates about what we cannot imagine (e.g., cases of imaginative resistance), disjunctions are -- to the best of our knowledge -- rarely if ever considered (cf. Gendler 2000). In this post, we would like to push imagining disjunctions as a research topic and suggest that we actually rarely, probably never, imagine disjunctions. Instead, when we are confronted with disjunctions, we imagine each disjunct separately and evaluate their consequences.
We will discuss two kinds of distinctions between types of disjunctions that we think are of interest here: (i) the distinction between disjunctions with mutually exclusive disjuncts and disjunctions with compatible disjuncts; (ii) the distinction between, what we will call, explicit and implicit disjunctions.[3] Our (in)ability and/or the difficulty to imagine these different kinds of disjunctions might differ significantly. We will discuss these in turn.
Mutually exclusive versus compatible disjuncts
Consider the example of imagining taking a new job or staying at one’s present job and compare it with an imagining of having an apple or a Nutella toast for breakfast. These two examples point to an interesting distinction: while one typically (or, for the sake of this argument) can’t stay in one’s present job and pursue a new one at the same time, one can have an apple and a Nutella toast for breakfast. We call the former ‘disjunctions with mutually exclusive disjuncts’ (‘DMD’) and the latter ‘disjunctions with compatible disjuncts’ (‘DCD’). Perhaps, one might think, it is not so controversial that we don’t imagine DMDs, but have distinct imaginative episodes for the relevant disjuncts in the case where these are mutually exclusive. However, there seem to be reasons to think that we have distinct imaginative episodes for the disjuncts, even when we are asked to imagine DCDs.
Consider the following situation (depicted in the figure above, (Ciardelli et al. 2018, p. 578)):
A particular light is linked to two light-switches and the light is on when both switches are in the same position (either both up or both down). Starting with both the switches up, Ciardelli et al. asked participants to consider the following two sentences:
● If switch A or switch B was down, the light would be off.
● If switch A and switch B were not both up, the light would be off.
Interestingly, 69% of the people (of over a 1000 participants) judged the former to be true, whereas only 22% judged the latter to be true. Of course, the antecedents are logically (classically) equivalent. Now, given the figure, we know that if A and B are in the same position, then the light is on. So, to judge the former as true, one basically has to ignore the possibility that A and B are both not up (for that would be the situation in which the sentence would be false). As Ciardelli et al. note “it seems that most participants interpreted A∨B >off by considering one switch at a time, while ignoring the option that both switches might be toggled simultaneously” (2018, p. 591, emphasis added). Some have taken this to suggest that the disjunction in imagination should be exclusive (McHugh 2018). However, we suggest that we should take the evidence at face value, as telling us something about the way we imagine disjunctions. In particular, this evidence seems to suggest that we imagine disjunctions (even with mutually compatible disjuncts) by cases. So, it seems that regardless of the relation between the disjuncts, there is evidence that we imagine disjunctions by cases, rather than as a disjunction.
Explicit versus Implicit Disjunctions
Now consider the distinction between, what we will call, implicit and explicit disjunctions. This distinction is best brought out by considering the following two sentences:
● Imagine marrying Sam or Quinn.
● Imagine marrying someone.
The former is what we will call an explicit disjunction, something of the explicit logical form: AvB. The latter, on the other hand, is an instance of an implicit disjunction, it doesn’t wear its disjunctive-ness on its sleeve, but is in a sense still disjunctive. As there are only finitely many people one could marry, “someone” can be translated into a finite disjunction. So far, what we have said concerns explicit disjunctions. What about implicit disjunctions? Here, it might be much less obvious that we are unable to imagine such things; we, seemingly, easily imagine being married to someone.
We suggest that what happens in these cases, focusing particularly on existentially quantified versions of implicit disjunctions, is that if it is indeed the case that we can imagine marrying someone, it is because we do so by imagining the situation as determinate without determinately imagining it (Yablo, 1993). This means, following Yablo, that we imagine the situation “as possessing the higher-order [properties], that of possessing a determinate property for each of its determinables[, without] specifying in each case what the underlying determinate is'' (idem, p. 28). This seems to be sufficient when complying with an existentially quantified implicit disjunction; the goal might be to get one to imagine the consequences of being married, regardless of to whom we imagine being married. It is much less clear, we suggest, that this can also be said in the case of explicit disjunctions, without thereby not collapsing into ‘merely’ imagining the existentially quantified claim. If this is true, we suggest, then it is not the case that in these instances we have actually imagined a disjunction.
To conclude, if what we have said above is right, then we might not be able to imagine disjunctions. When we think we comply with a request to imagine such a disjunction, we would either imagine an existentially quantified sentence (or something like it) as determinate or we would imagine each case separately. Interestingly, these findings might have important consequences for what role one assigns to a logic of imagination: is the logic modelling how we should imagine or is its aim to describe how we imagine? People like Berto and ourselves have taken the latter route. Consequently, when we formalise sentences like “they imagine eating an apple or a Nutella toast for breakfast”, we should not represent this as “they imagine that A or B” but rather as “they imagine that A, and/or they imagine that B”.
Notes
[1]Of course, it might be pointed out to one that the disjunctions are compatible. One might say: “You know, you could have an apple and a Nutella toast for breakfast”. However, it seems plausible to say that in that case, you are asked to (or you do) imagine a conjunction, rather than a disjunction.
[2] Even though, e.g., Berto (2018) explicitly rejects the inference ‘A |= A v B’ for imagination, he does so because of the fact that B might be about something completely different than A is. Not because of some principled objection against imagining disjunctions. In fact, if B is on topic with A, the inference does hold on Berto’s theory.
[3] We set aside so-called ‘Hurford disjunctions’, where one of the disjuncts entails the other. E.g., “I live in Berlin or I live in Germany”.
References
Badura, C. & Kind, A. (eds.) (2021). Epistemic Uses of Imagination. Routledge.
Berto, F. (2018). Aboutness in Imagination. Philosophical Studies, 175, 1871-1886.
Ciardelli, I., Zhang, L., & Champollion, L. (2018). Two switches in the theory of counterfactuals. Linguistics and Philosophy, 41, 577-621.
Gendler, T. S. (2000). The puzzle of imaginative resistance. Journal of Philosophy, 97(2), 55-81.
Langland-Hassan, P. (2016). On Choosing What to Imagine. In A. Kind & P. Kung (eds.) Knowledge Through Imagination, (pp. 61-84). Oxford University Press.
McHugh, D. (2018). Counterfactuals and the Logic of Imaginative Content. MSc Logic Thesis, Institute for Logic, Language, and Computation, University of Amsterdam.
Nanay, B. (2016). The Role of Imagination in Decision-Making. Mind & Language, 31(1), 127-143.
Williamson, T. (2007). The Philosophy of Philosophy. Blackwell Publishing.
Yablo, S. (1993). Is Conceivability a Guide to Possibility? Philosophy and Phenomenological Research, 53(1), 1-42.