Abstract
The problem of closure for the traditional unstructured possible worlds model of attitudinal content is that it treats belief and other cognitive states as closed under entailment, despite apparent counterexamples showing that this is not a necessary property of such states. One solution to this problem, which has been proposed recently by several authors (Schaffer in: Hawthorne and Gendler (eds) Oxford studies in epistemology, Oxford University Press, Oxford, pp 235–271, 2005; Yalcin in Philos Phenomenol Res 97(1):23–47, 2018; Hoek in: Kindermann (ed) Unstructured content, Oxford University Press, Oxford, forthcoming), is to restrict closure in an unstructured setting by treating propositional attitudes as question-sensitive. Here I argue that this line of response is unsatisfying as it stands because the problem of closure is more general than is typically discussed. A version of the problem recurs for attitudes like wondering, entertaining, considering, and so on, which are directed at questions rather than propositions. For such questioning attitudes, the appeal to question-sensitivity is much less convincing as a solution to the problem of closure.
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Notes
There are, in fact, multiple “problems of closure”, e.g. the problem of closure under necessary equivalence, closure under conjunction, and closure under believed/known/desired implication. Here I stick with closure under entailment, though the points I make apply mutatis mutandis to other forms. See Yalcin (2018), pp. 4–5 for an overview of these problems.
Note that logical omniscience implies that every epistemic agent knows all logical truths. For a survey of logical omniscience and various responses to it see ch. 9 of Fagin et al. (1995).
As well as the logic of some modalities, e.g. deontic modality. A classic version of the problem as it arises for the logic of obligation is Ross’s paradox (Ross, 1941): if you ought to post the letter then you ought to post it or burn it.
Stalnaker himself is openly ambivalent about this example, however (locus cit.). This is, I take it, because his dispositional conception of propositional attitudes calls the problematic status of closure itself into question.
It is beyond the scope of this paper to discuss these; the literature on the issue is large. A useful starting point is Stalnaker (1984, ch. 2), which explores the benefits of the unstructured approach in part by contrasting it with the drawbacks of a more structured approach, specifically a linguistically structured approach of the sort discussed in Field (1978). Yalcin (2018, p. 3) also discusses the advantages of the unstructured approach in capturing holism about attitudinal content. Fodor and Lepore (1992) is a classic examination and criticism of holism, though see (Perry, 1993) for a rebuttal.
While the partition approach goes back to Groenendijk and Stokhof (1984), Lewis (1988) also models questions in this way. Those interested in relevant applications can explore Yalcin (2018) or Hoek (forthcoming) both of whom take a similarly unstructured approach to questions; though whether they wish to identify these unstructured entities as the contents of questioning attitudes is unclear. Another central theory comes from Ciardelli et al. (2019) who develop a theory of issues covering both informative and inquisitive content. On this latter account, attitudinal contents are modeled as downward closed sets of information states (coarse-grained propositions), allowing that the same information state may constitute a different content depending on which issue/question it resolves.
A partial answer can thus be modeled as a union of complete answers.
In linguistic circles, there is a classification of attitude verbs as being rogative, anti-rogative, or responsive depending on whether they license interrogative complements only, prohibit interrogative complements altogether, or allow either interrogative or non-interrogative complements, respectively (see for instance Lahiri (2001)). For example ‘wonder’ is rogative, ‘believe’ is anti-rogative, and ‘know’ is responsive; one can say, e.g., ‘I know that it’s raining’ as well as ‘I know whether it’s raining’. Since I take knowledge to be a propositional attitude however, it is not clear that these syntactic categories perfectly match the distinction between propositional and questioning attitudes.
Indeed, as with propositions, there are various logics (plural) of questions that have been extensively explored. See Hamami and Roelofsen (2015) for an overview.
Hintikka’s (1981, 1999, 2007) work on his interrogative model of inquiry, which describes inquiry as an essentially questioning activity (e.g. a question-and-answer game between an inquirer and nature) is a leading example of this perspective. In some places (e.g. 2007, pp. 24–28), Hintikka explicitly characterizes questions in terms of the attitude of desiring to know their answers. Within inquiry, then, Hintikka’s view is that a question is determined by a pair, consisting of a presupposition and a desideratum, with the latter being the state of knowledge that the agent posing the question thereby desires to be in.
Recall that a complete answer to a question rules out all possible answers incompatible with it, and so all other possible complete answers
Or, if we insist that the contents of propositional attitudes shouldn’t simply be identified with propositions, we can think of this as a set of propositional attitude contents rather than a set of propositions. Thanks to an anonymous reviewer for Synthese for encouraging me to emphasize this distinction.
For wondering, it might also be important to include that the agent does not knowQ, where this means that there is no complete answer to Q that s knows. Whether and in what sense one can wonder about what one knows is an interesting issue (See Archer 2018). Ciardelli and Roelofsen (2015. pp. 1659–1660) build an ignorance component into their analysis of wondering. But for simplicity I ignore this complication as it will not bear significantly upon my arguments.
Cf. Ciardelli and Roelofsen (2015, pp. 1648–1660) for similar analyses of entertaining and wondering.
The proof of this is immediate and trivial given the analysis of wonder reports, UW, and the definition of q-entailment. Suppose s wonders Q, where Q q-entails \(Q^\prime \). Then it follows from UW that any proposition that constitutes a complete answer to what s wonders about also constitutes a complete answer to Q. But, since Q q-entails \(Q^\prime \), it follows that any proposition that constitutes a complete answer to Q also constitutes a complete answer to \(Q^\prime \). Thus it follows from UW that s wonders \(Q^\prime \).
Ciardelli and Roelofsen (2015, p. 1654) propose an unstructured analysis of this sort for entertaining a question.
Indeed, it is enough that the account of questioning attitude contents at work in question-sensitive epistemology be coarse-grained [as is assumed by Schaffer (2004, 2006), Yalcin (2018), Ciardelli and Roelofsen (2015), and Hoek (forthcoming)], the restriction to partitions specifically, rather than sets of overlapping unstructured propositional attitude contents, isn’t essential.
cf. Yalcin’s (2018 p. 19) ‘closure under visible consequence’ and Hoek’s (forthcoming) (p.16) ‘closure under parthood’. Hawke (2016, pp. 2778–2881) proposes restrictions on closure based on subject matters determined by atomic predications occurring within sentences. But I think this approach to subject matters can be re-interpreted in terms of question-based restrictions too, albeit on an slightly more syntactic modelo of questions.
More abstractly, thinking of concepts as sets of entities to which they apply, and letting \(C_W\) denote the intersection of William’s ‘war concepts’ (e.g. NAVAL WAR) he is wondering a question of the form: for which values of x \(\in C_W\) is x a war that England can avoid?
See Yalcin ibid p. 12.
Yalcin (ibid., p. 13) also notes this fact about the detective, but leaves it unexplored as to the precise sense in which the detective’s cognitive state is sensitive to the overlooked question.
Stalnaker and Yalcin both explicitly present the absent minded detective as failing to consider the chauffeur in this way. I take it we can read this as a failure to consider, entertain, or wonder about the question of whether the chauffeur is the murderer. i.e. as a failure to close one’s questioning attitudes under q-entailment.
My thanks to two anonymous reviewers for Synthese for pushing me to consider this approach further.
See (Aloni, 2008).
Or suppose someone is wondering what the square root of 324 is, relative to the conceptual cover of natural numbers. This person need not be wondering whether 18 is the square root of 324; if they were they’d presumably answer their question much more quickly. Another worry with reltivizing interrogative interpretations to contextually supplied conceptual covers is what to say about cases of conceptual poverty and conceptual change. Regarding conceptual change, if the detective happens to learn that the butler and the valet are actually the same person, would this mean that now, having revised her conceptual cover, she is wondering about a different question when she continues to wonder who the murderer is? I think this is unclear. Regarding conceptual poverty, it is plausible that, for example, Aristotle might have wondered what the origin of the universe is without having the concepts to consider a possible answer in terms of quantum mechanics. But would that mean that such an answer, if true, would not have answered the question posed by the Stagirite? I think that is also unclear. My thanks to an anonymous reviewer for Synthese for prompting me to address this.
And if there are content-bearing attitudes in addition to propositional and questioning attitudes, it may very well recur for those attitudes too, assuming that their contents have a logic of their own as questions do.
More formally: she might know the answer to the question: for which x is it the case that 5 + 3 = x, without knowing the answer to:for which x is it the case that x + 3 = 8.
Indeed, arguably all logical and mathematical questions correspond to this partition.
Formally, in the apparatus of answers as ordered pairs of coarse-grained propositions and partitions, she knows the answer \(\langle {\mathcal {W}}, \lbrace {\mathcal {W}} \rbrace \rangle \).
Friedman (2013, pp. 167–168) also suggests a more structured account on the basis of what she calls ‘the possibility of radical ignorance in inquiry’. This is a putative scenario in which an agent who is unaware of any possible answer to a question can nevertheless wonder about, consider, or entertain that question. Personally, I am skeptical about the possibility of such total answer ignorance, in the sense of an inability to imaginatively generate any possible (even partial) answer to the questions one wonders about. But this is not the place to explore that skepticism.
Sincere thanks to Hüseyin Güngör, Robert Rynasiewicz, and especially Justin Bledin for many hours of helpful discussion. My thanks also to the bright minds of the Hammond Society at Johns Hopkins University for their helpful feedback on earlier versions of this paper.
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Teague, R. The problem of closure and questioning attitudes. Synthese 200, 345 (2022). https://doi.org/10.1007/s11229-022-03826-4
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DOI: https://doi.org/10.1007/s11229-022-03826-4