Abstract
The new paradigm in the psychology of reasoning draws on Bayesian formal frameworks, and some advocates of the new paradigm think of these formal frameworks as providing a computational-level theory of rational human inference. I argue that Bayesian theories should not be seen as providing a computational-level theory of rational human inference, where by “Bayesian theories” I mean theories that claim that all rational credal states are probabilistically coherent and that rational adjustments of degrees of belief in the light of new evidence must be in accordance with some sort of conditionalization. The problems with the view I am criticizing can best be seen when we look at chains of inferences, rather than single-step inferences. Chains of inferences have been neglected almost entirely within the new paradigm.
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Notes
I will sometimes also use the terms “subjective probabilities,” “degrees of belief,” or “credences” for these attitudes.
To get a first idea of what I have in mind, notice that the epistemological literature on subjective Bayesianism does not address the question what role, if any, partial beliefs play in human reasoning (see Staffel 2013, p. 3536). Consequently, it is not clear what, if anything, Bayesian epistemology can tell us about reasoning.
One might think that if that is right, then this is a problem for Bayesianism — and not only for the new paradigm psychology of reasoning. Suppose, for example, that we should “avoid talk about knowledge and acceptance of hypotheses, trying to make do with graded belief” (Jeffrey 1970, p. 183; see also Maher 1993, pp. 152–55) — as some Bayesian epistemologists claim we should. Then we would need an account of the rationality of reasoning with partial beliefs, if we want an account of rational reasoning at all. As John Broome has recently put it: “Bayesians owe us an account of the active reasoning processes by which you can bring yourself to satisfy Bayesian requirements” (Broome 2013, p. 208). However, I want to put the question whether it is a problem for Bayesianism that it has little to say about reasoning to one side. Whether or not it is a problem for Bayesianism, it surely is a problem for the new paradigm in the psychology of reasoning.
Here is an example of the task: Four cards are lying in front of you. Printed on them you see “A”, “K”, “2”, and “7”, respectively. Each card has a letter on one side and a number on the other. You are then given the statement “If there is a vowel on one side, then there is an even number on the other side”; you must then select those cards that you must turn over to determine whether the statement is true of false.
Thanks to an anonymous referee for alerting me to this work.
I am not sure whether a process by which an entire credal state changes at once should be called “inference.” Be that as it may, we can reason by forming chains of inferences. And it is easy to find examples that concern empirical, non-necessary facts that can only be known a posteriori.
Note that I am not interested in reasoning with outright beliefs about probabilities; I am only concerned with reasoning in which the involved attitudes are degrees of belief.
Note that accounts of reasoning with outright beliefs do not have these problems. Regarding the first, their rules typically require less information as input. Regarding the second problem, we can say — just to give a toy example of how such a theory can deal with the problem — that an ideal agent, who is not subject to computational limitations, keeps all her beliefs that are not changed by any possible chain of correct inferences starting (inter alia) with the new information. The resulting belief-state (if there is a stable one) is necessarily coherent if the agent can, e.g., use a rule like reductio ad absurdum and she eliminates a belief when she adopts a belief in the negation of the original belief. After all, if the resulting belief-state were incoherent, the agent could get rid of one of the beliefs by deriving the negation of the content of the belief by reductio. Of course, it is not a trivial matter to give rules for rational reasoning with outright beliefs. As is well known, we cannot simply take the rules of classical logic (see Harman 1986). And the problems I am pointing out in this paper apply with equal force to AGM-style theories (Alchourrón, Gärdenfors, and Makinson 1985) if one tries to use them as computational-level theories of (rational) inferences. At least, the same problems arise as long as updating and revising are conceived as global operations on belief-states. However, some promising work has been done in this area (see, e.g., Jago 2009). In any event, I am not trying to provide such a theory here.
For a response to Elga see (Chandler 2014). I think that Elga’s claim can be defended against Chandler’s critique, but that would lead us too far afield. Note that in the context of trying to model rational reasoning, i.e., a diachronic phenomenon, it is not an option to respond to Elga by defending so called “time-slice rationality,” as is sometimes done in the recent literature (Moss forthcoming; Hedden forthcoming, Chap. 8).
I use the variables as in rule (7).
It is also worth noticing that p-validity defines a monotonic consequence relation. Adams was explicit about this, and Over (2009, p. 437) pointed it out again in a discussion of the new paradigm.
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Acknowledgments
Thanks to Michael Caie, Adam Marushak, Robert Brandom, Karl Schafer and an anonymous referee for this journal for their insightful comments.
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Hlobil, U. Chains of Inferences and the New Paradigm in the Psychology of Reasoning. Rev.Phil.Psych. 7, 1–16 (2016). https://doi.org/10.1007/s13164-015-0230-y
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DOI: https://doi.org/10.1007/s13164-015-0230-y