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Formal Epistemology and the New Paradigm Psychology of Reasoning

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Abstract

This position paper advocates combining formal epistemology and the new paradigm psychology of reasoning in the studies of conditionals and reasoning with uncertainty. The new paradigm psychology of reasoning is characterized by the use of probability theory as a rationality framework instead of classical logic, used by more traditional approaches to the psychology of reasoning. This paper presents a new interdisciplinary research program which involves both formal and experimental work. To illustrate the program, the paper discusses recent work on the paradoxes of the material conditional, nonmonotonic reasoning, and Adams’ Thesis. It also identifies the issue of updating on conditionals as an area which seems to call for a combined formal and empirical approach.

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Notes

  1. Thus, we do not accept Kauppinen’s negative experimentalism thesis—which allegedly is accepted by some experimental philosophers—according to which “armchair reflection and informal dialogue are not reliable sources of evidence for (philosophically relevant) claims about folk concepts” (Kauppinen 2007, p. 97).

  2. As an anonymous referee noted, the logical empiricists may have believed their verification theory of meaning, according to which a sentence is meaningful only if it is verifiable, to eliminate the possibility that philosophers were really writing fiction. But that theory was soon found to be untenable, if only because it does not live up to its own standards of meaningfulness.

  3. Callebaut (1993) gives an excellent overview of the naturalization program in philosophy up to the 1980s.

  4. Specifically, a bit more than half of the participants interpret the conditional as a conditional probability and a sizable proportion of participants interpret it as a conjunction in the beginning of these experiments. This replicates a robust finding in traditional probabilistic truth table tasks (Evans et al. 2003; Oberauer and Wilhelm 2003). However, in the end of the experiment, more than 80 % of the responses were consistent with the conditional probability interpretation. In these tasks inter-individual differences do not imply different reasoning/interpretation strategies but rather reflect how fast participants are able to adopt the competence interpretation. Although we doubt that the iterative presentation of the same task will resolve all aspects related to the deep problem of individual differences, we believe that it helps resolve at least some of them.

  5. An example of the latter kind is the distinction between reasoning to an interpretation and reasoning from an interpretation, where the former involves interpreting the meaning of the task material, while the latter begins only after the interpretation of the task material has been fixed by the participant and he or she starts to solve the task. We like to think that it is not coincidental that this distinction is due to recent joint work by a psychologist (or at least cognitive scientist) and a philosopher, to wit, Keith Stenning and Michiel van Lambalgen (Stenning and van Lambalgen 2008).

  6. For more on what formal epistemology is and how it differs from mainstream epistemology as well as from the probabilist underground epistemology that van Fraassen refers to, see (Douven 2013c).

  7. For an overview, see Bennett (2003).

  8. “All” here includes the special case where Pr(B) = 1. Bonnefon and Politzer correctly point out that in this case “ ‘If x, y’ must also be certain, and the inference is valid” (Bonnefon and Politzer 2011, p. 154). This is true for the standard approach to probability, which defines the conditional probability Pr(B | A) by the fraction of the joint and the marginal probability, Pr(A ∧ B) / Pr(A) (provided Pr(A) > 0, otherwise Pr(B | A) is undefined). In the framework of coherence-based probability theory, however, Pr(B | A) is not necessarily certain if Pr(B) = 1. As Pr(A) may be equal to 0, it follows that Pr(B | A) may also be equal to 0, and therefore 0 ≤ Pr(B | A) ≤ 1 is coherent (Pfeifer 2013a).

  9. An anonymous referee noted that it is not clear whether the observed response—that nothing follows—fully accounts for a “subjective feeling of oddity”, which emerges from some instantiations of the paradoxes of the material conditional. The tasks used in Pfeifer and Kleiter (2011) were formulated by neutral instantiations of A and B (i.e., in terms of colors and figures), which means that a feeling of oddity—if it occurred—was based on the formal structure of the paradoxes only.

  10. An argument form is probabilistically non-informative iff the tightest coherent probability bounds on the conclusion are zero and one, respectively, under all possible probability values of the premises (Pfeifer and Kleiter 2009).

  11. We observe that this argument form is a special case of the cautious monotonicity rule of System P. (Compare the probability propagation rules in Gilio (2002)).

  12. From “If A, then B” and “If B, then C” infer “If A, then C”.

  13. This argument form corresponds to the cut rule of System P (Gilio 2002). Moreover, it can be interpreted as a conditional version of modus ponens: each premise and the conclusion conditionalize on A, if A is dropped, the modus ponens remains.

  14. If conditionals do not express propositions, they cannot occur in ordinary conjunctions. They can occur in what Adams calls “quasi-conjunctions” (Adams 1975, p. 46 f). By Adams’ own admission, however, quasi-conjunctions lack some important logical features of conjunctions.

  15. Note that, in view of the experiments on the probabilities of conditionals mentioned in the text, Douven and Verbrugge’s results also show that the probability of a conditional is not the same as the degree of acceptability of a conditional, pace Adams.

  16. An anonymous referee noticed that the fact that we seem to learn something in such cases puts pressure on Adams’ non-propositional view of conditionals. We agree, albeit only insofar as Adams’ view rules out the seemingly most straightforward type of proposal for modelling conditional updates, to wit, those proposals that model such updates as the accommodation, in some way, of the proposition (putatively) expressed by the conditional. But there are other forms that updating on a conditional might take; see Douven and Romeijn (2011) and Douven (2012).

  17. For an important different approach to modelling updates on conditionals, see Hartmann and Rafiee Rad (2012).

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Acknowledgments

The authors thank two anonymous reviewers and Paul Égré for useful comments. This work is supported by the FWF project P20209 and the DFG grant PF 740/2-1 (project leader: Niki Pfeifer; project within the DFG Priority Program SPP 1516 “New Frameworks of Rationality”). Niki Pfeifer is supported by the Alexander von Humboldt Foundation.

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  1. Munich Center for Mathematical Philosophy, LMU Munich, Munich, Germany

    Niki Pfeifer

  2. Faculty of Philosophy, University of Groningen, Groningen, The Netherlands

    Igor Douven

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Pfeifer, N., Douven, I. Formal Epistemology and the New Paradigm Psychology of Reasoning. Rev.Phil.Psych. 5, 199–221 (2014). https://doi.org/10.1007/s13164-013-0165-0

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