Abstract
This paper argues that representationalism of a Fodorian variety can accommodate the fact that beliefs come in degrees. First, it responds to two key arguments to the contrary. Second, it builds upon these responses and outlines a novel representationalist theory of degrees of beliefs. I call this theory dispositional representationalism, as it involves direct appeal to our dispositions to form representations and propositional attitudes concerning them.
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Notes
Goodman et al. (2015: p. 623) adopt a ‘probabilistic language of thought hypothesis’, according to which mental representations are ‘built from language-like composition of concepts and the content of those representations is a probability distribution on world states’. This is distinct from Fodor’s approach because it doesn’t posit sentence-like representations with propositional content that function as the objects of beliefs (or degrees thereof). Of special significance is that those who wish to avoid or limit appeal to concepts—following Machery (2009)—might prefer a view closer to the Fodorian approach explored here.
Cashing out ‘in normal circumstances’ is harder than it first appears. But the nub of the notion should be evident. The stake should be non-trivial, the bettor should desire to win, and so forth. See Rowbottom (2015, ch. 4) for an extended discussion of measuring degrees of belief.
Recent empirical research indicates that even preverbal infants can make good inferences in some situations involving uncertainty. As Denison and Xu (2019) explain, there is ongoing disagreement, however, concerning how this comes about. Some suggest that heuristics are at play. Others argue that modal inferences—involving, say, rankings of possibilities—are responsible. Still others argue that inferences which are distinctly probabilistic are involved; and Denison and Xu (2012: p. 51) even suggest that: ‘human learners may have an intuitive notion of probability’ and that ‘infants are computing probabilities’. However, one can have cognitive architecture that computes probabilities without having a mental representation of probability (or any close surrogate). Moreover, having such a representation is more difficult than it may first appear. For instance, it’s plausible that probability is not degree of possibility, and hence that beliefs such as ‘p is more possible than q’ do not suffice for capturing some facets of probability. Consider continuous cases, such as picking a point in a circle at random (in connection, perhaps, with Bertrand’s chord paradox); it is possible to pick each point, but the probability of picking any given point is zero. It is also implausible that infants have mental representations of probability under any of the available metaphysical interpretations thereof, which involve partial entailment relations, reference classes, single case propensities, and so forth. See Gillies (2000) and Rowbottom (2015) for an overview. They may have more rudimentary mental representations that are of use in facilitating effective inferences in some cases involving uncertainty.
Aside from in the subjective view discussed hereafter, they feature also in the logical interpretation advocated by Keynes (1921) and Carnap (1950), and the objective Bayesian interpretation advocated by Jaynes (1957) and Williamson (2010). For more details on these interpretations of probability, see Gillies (2000) and Rowbottom (2015).
Some axioms for probability—such as those due to Popper and Rényi—also make conditional probabilities fundamental and define unconditional probabilities in terms of these. The most popular axioms, due to Kolmogorov, do the opposite.
There may be some special cases where we can so distinguish—if we’re told, for example, that the relative frequency of an event is 1/1,000,001 in the only pertinent relevant reference class—but such cases are atypical.
For example, Eriksson and Hájek (2007) do not even mention representationalism in attempting to answer ‘What are degrees of belief?’.
Note that failing to believe that p or disbelieve that p is only a necessary, and not a sufficient, condition for suspending belief in p: someone who doesn’t have the concept ‘God’ cannot be an agnostic.
For a relatively non-technical discussion of this and related issues concerning representing suspension of judgment in terms of subjective probabilities, see Friedman (2013).
Because other kinds of propositional attitudes admit of degree, I do not take degrees of belief to be a ‘special case’, worthy of further discussion, in this regard. So if one takes an (active) degree of belief to involve a representation with two components—e.g., < p, n > for a degree of belief in p of strength n—this presents no unique obstacle. Fears, hopes, and so forth, could involve similar kinds of representation.
‘Assuming/accepting’ is included because we may entertain the possibility of a change in evidence and consider how that would change our active degree of belief in a target proposition. This might be thought to involve mentally forming a conditional degree of belief, without activating it (or mentally forming an equivalent active degree of belief).
One might worry about disjunctive degrees of belief as well as conjunctive ones, and perhaps even negations. However, it should be apparent that these can be handled in a similar way.
For a view of how degrees of belief may feature in self-deception, see Chan and Rowbottom (2019).
I don’t have a strong view because it is an exceptionally difficult empirical question to answer. Consider again, though, the findings of developmental psychologists. Schlottmann (2001: p. 103), for instance, writes that: ‘functional understanding of probability and expected value [is present] in children as young as 5 or 6’. The involvement of a degree of belief formation process would explain how the functional understanding arises, given that children of such ages normally know nothing about the formal theory of probability.
In fact, as Weisberg (2020) notes, it is possible that we can activate beliefs once they are formed without activating degrees of belief, even if we originally formed said beliefs on the basis of degrees of belief. I discuss this idea in greater detail in Sect. 3. If it is correct, then the type-2 belief sufficiency condition should be altered such that ‘has or has had’ replaces ‘has’, and likely also such that b refers to background knowledge employed in the type-2 mental process (i.e., background knowledge that might not be current).
One might restrict this condition to agents with properly functioning mental faculties or to assessments due to type-2 processes, as explained previously. One might also want to allow for forgetfulness. For simplicity’s sake, I won’t revisit such refinements at this juncture.
My thanks to an anonymous referee for pointing out that dispositional representationalism could allow for this possibility, and for directing me to related ideas presented by Weisberg (2020), which I was unaware of before submitting the penultimate version of this paper.
So consider again how the questions mentioned earlier would be answered on this picture. First, it is possible to believe p without having a degree of belief in p. Second, it follows that it is possible to form a mental representation p without forming a degree of belief in p. The only outstanding question is: ‘Is it possible to have a disposition to form a mental representation p without even having any disposition to degree of believe that p?’ I think the answer lies in the negative, provided the representation could be linguistically drawn to one’s attention for conscious consideration. It is possible, however, that some propositions can only be presented in other modes, such as practical modes; see Stanley and Williamson (2001) on know how, for example.
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Rowbottom, D.P. How can representationalism accommodate degrees of belief? A dispositional representationalist proposal. Synthese 199, 8943–8964 (2021). https://doi.org/10.1007/s11229-021-03189-2
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DOI: https://doi.org/10.1007/s11229-021-03189-2