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Belief and cognitive limitations

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A number of philosophers have argued that it is hard for finite agents like us to reason and make decisions relying solely on our credences and preferences. They hold that for us to cope with our cognitive limitations, we need binary beliefs as well. For they think that such beliefs, by disposing us to treat certain propositions as true, help us cut down on the number of possibilities we need to consider when we reason. But using Ross and Schroeder (Philos Phenomenol Res, doi:10.1111/j.1933-1592.2011.00552.x, 2012) as my stalking horse, I argue that such an appeal to binary beliefs does not work. I begin by explaining why there’s supposedly a problem for an account of reasoning that invokes only credences and preferences. I then argue that Ross and Schroeder’s account of belief—as well as other similar accounts—does not help solve the problem. Finally, I consider an alternative approach to solving the problem. This approach, unlike the accounts I criticise, does not hold that having a disposition to treat a proposition as true is necessary for believing it.

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  1. Ross and Schroeder (2012) think that we need beliefs to guide us not only in practical reasoning, but in theoretical reasoning as well (p. 8). For simplicity, I’ll focus on practical reasoning. Nothing of importance will hinge on this.

  2. For reasoning about whether to treat a proposition as true is itself a decision problem and will involve treating other propositions as true (Ross and Schroeder 2012, p. 9).

  3. Cohen (1989) distinguishes between belief and acceptance, and holds that the latter ‘implies commitment to a policy of premissing that p’ (368). He also offers arguments for why acceptance does not entail belief. For instance, he thinks that one can’t choose to believe at will, but one may choose to accept a proposition and employ it as a premise in one’s reasoning (369–370). Now, there’s a question whether having an automatic disposition to treat p as true in one’s reasoning is the same as being committed to employing p as a premise. But Cohen’s point can be used to support the claim that the former isn’t sufficient for belief. Our engineer may have an automatic disposition to treat Newton’s Second Law as true in her reasoning. But she may choose to stop treating it as true, in which case she’ll lose her automatic disposition to treat it as true. However, if she believes that Newton’s Second Law is true, she can’t simply choose to stop believing it.

    At any rate, while Ross and Schroeder hold that having an automatic disposition to treat p as true is necessary for believing that p, they don’t hold that it is sufficient. (See the comments section at

  4. It’s worth noting that Ross and Schroeder (2012) argue explicitly that, given RDA, binary beliefs are irreducible to one’s credences or to one’s credences and preferences. For they hold that a belief that p essentially involves a defeasible disposition to treat p as true, but for any credence less than 1, an agent may have that credence in p, together with whatever preferences she may have, and yet not be disposed to treat p as true—at most, she may be disposed to treat p as very highly probable (pp. 12–13). And if believing that p requires having a credence of 1 in p, then an agent who believes that p will have an indefeasible, rather than a defeasible, disposition to treat p as true.

    I’ll not attempt to evaluate whether RDA really entails that binary beliefs are irreducible to credences and preferences. But it’s clear that Ross and Schroeder lose a reason for subscribing to the latter view if they lose support for RDA.

  5. This is neither to argue that there are no binary beliefs nor to take a stand on whether binary beliefs are reducible to credences.

  6. Ross and Schroeder (2012) distinguish between occurrent and non-occurrent beliefs but give no indication that RDA applies only to the former (p. 13).

  7. In a later paper, Wedgwood posits two kinds of credences—theoretical credences, which ‘represent the way in which the agent registers, or keeps track of, the amount of justification that she has in favour of the relevant propositions’, and practical credences, ‘on the basis of which the agent maintains and revises her intentions about how to act’ (Wedgwood 2012, p. 319). And he maintains that to have a binary belief that p is to be in a ‘state of being stably disposed to have a practical credence of 1 in p, for at least all normal practical purposes’ (ibid., p. 321; Wedgwood’s emphases). Now, Wedgwood seems to think that to be disposed to have a practical credence of 1 in p is to be disposed to take p for granted or to treat it as true. In fact, he continues to hold in the later paper that if we believe p, then we’re disposed to take p for granted in reasoning (ibid., p. 313). But then, the worry I’ll raise for the above accounts of belief will pose a problem for Wedgwood’s later account too.

  8. Examples of some heuristics include the availability heuristic and the representativeness heuristic. See, for instance, Schwarz and Vaughn (2002) and Kahneman and Frederick (2002).

  9. Shafer (2007) discusses Cournot’s Principle in some detail.

  10. For a discussion on why Cournot’s Principle seems false, see Hájek (2007).

  11. How close to 1 or 0 must a probability value be for us to reason as if it’s 1 or 0? There may be no precise threshold—what counts as close may be vague and vary with different agents.

  12. According to the threshold view of belief, binary beliefs are reducible to credences that meet a sufficiently high threshold. Though it’ll take me beyond the scope of this paper to discuss the view in depth, it’s worth noting (as I did in footnote 4) that Ross and Schroeder (2012) maintain that binary beliefs are not reducible to credences and hence, not reducible to credences that meet a certain threshold (pp. 12–13). Furthermore, Holton (2008), Wedgwood (2008) and Smithies (2012) also find the threshold view of belief problematic and reject it explicitly (p. 34; 3–4; 279).

  13. Thanks to an anonymous reviewer for raising this worry.

  14. Heuristics may be employed at a reflective or non-reflective level. Those employed automatically or at a non-reflective level may sometimes be overridden by cognitive processes that take place at the reflective and deliberative level (Kahneman and Frederick 2002, pp. 51–60).


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Many thanks to Jens Christian Bjerring, Ben Blumson, Mark D’Cruz, Ole Koksvik, and an anonymous reviewer for valuable comments. I’m especially indebted to Mark D’Cruz for providing very useful feedback on more than one draft of the paper.

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Correspondence to Weng Hong Tang.

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Tang, W.H. Belief and cognitive limitations. Philos Stud 172, 249–260 (2015).

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