Abstract
The main goal of this paper is to investigate what explanatory resources Robert Brandom’s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. One such case in particular is the preface paradox, which will receive an extensive treatment. As we shall see, the problem of logical omniscience not only arises within theories based on deductive logic; but also within the recent paradigm shift in psychology of reasoning. So dealing with this problem is important not only for philosophical purposes but also from a psychological perspective.
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Notes
Predecessors: in a way Levi (1991, Chap. 2; 1997, Chap. 1) was the first to emphasize that one could make progress with respect to the problem of logical omniscience by thinking of it in terms of commitments rather than in terms of belief. Subsequently, Milne (2009) has gone down a similar path. What the present investigation adds is giving it a more Brandomian spin (which was already implicit in Milne 2009) and by formulating bridge principles that are capable of dealing with the constraints presented in MacFarlane (manuscript). After writing this paper, I discovered that Dutilh Novaes (forthcoming) has a very similar agenda, and it seems that the two papers complement each other very well.
Explication of the framing effect: it has been shown that different ways of presenting the same information will give rise to different emotions, which in turn affects our judgments and decision making. Accordingly, the statement ‘the chance of survival one month after surgery are 90 %’ will be found more reassuring than the equivalent statement ‘mortality within one month of surgery is 10 %’ (Kahneman 2012, p. 88). As a result, participants will respond differently to these two statements in spite of their logical equivalence.
See also Pfeifer and Kleiter (2007).
Qualification: however, as one of the reviewers points out, one can find quotes in Oaksford and Chater (2009, pp. 107–108) foreshadowing the observations Evans (2012) makes in the quote below. And indeed the same holds for Pfeifer and Kleiter (2007, p. 24). The point is just that the implications that such observations have for issues such as the problem of logical omniscience have not made their way into the general awareness of the psychological literature.
On Brandom’s notion of material inferences: it should be noted that material inferences are used as a generic notion for content-based inferences in the writings of Brandom. To be sure, Brandom does not accept the analytic/synthetic distinction for familiar Quinean reasons. But his notion of material inferences covers what would have traditionally been thought of as falling in both of these categories. In his writings one thus not only finds examples of material inferences that sound like analytical inferences, like the example in the text, but also examples like inferring that a banana is ripe from its being yellow (Brandom 2010, p. 104), which sounds like synthetic judgments with an inductive basis.
A more adequate ranking-theoretic explication is offered in Skovgaard-Olsen (draft).
Refinement through J-conditionalization: to allow for cases of entitlement to \(\Gamma \) where \(\hbox {P}(\Gamma ) < 1\), the second condition could be replaced by Jeffrey conditionalization as follows: \(\mathop \sum \nolimits _{i=1}^n \left[ {\hbox {P}_{\textit{initial}} (q|{\upgamma }_{\mathrm{i}} )\cdot \hbox {P}_{\textit{new}} \left( {{\upgamma }_{\mathrm{i}}} \right) } \right] \) > b, for \(\hbox {P}_{\textit{initial}} \left( {{\upgamma }_{\mathrm{i}}} \right) \) > 0 and \(\mathop \sum \nolimits _{i=1}^n P_{\textit{new}} \left( {{\upgamma }_{\mathrm{i}}} \right) > b\). Notice moreover that entitlement is specified w.r.t. the probability distribution at the context of assessment. See Skovgaard-Olsen (draft) for details.
Inferentialism as a probabilistic reason relation semantics: by exploiting the idea from Spohn (2012, Chap. 6) that p is a reason for q whenever \(\mathrm{P}(q{\vert } p) > \mathrm{P}(q{\vert }\lnot p)\), and that p is a reason against q whenever \(\mathrm{P}(q{\vert }p) < \mathrm{P}(q{\vert }\lnot p)\), the weak and the strong notions of incompatibility are treated as cases of when p is an inductive or a deductive reason against q, and entitlement preservation and commitment preservation are treated as cases, where the set \(\Gamma \) counts as an inductive or a deductive reason for q. This explication treats inferentialism as a probabilistic reason-relations semantics, and it is in general agreement with Dorn’s (2005) account of the strength of arguments. However, this explication can only be partial, because it needs to be supplemented by Brandom’s pragmatic account of the conditions under which the scorekeeper should add and subtract commitments and entitlements from the speaker’s score, which Kibble (2005, 2006a, b), Piwek (2011, 2014), and Skovgaard-Olsen (draft) have begun to formalize. See also Walton and Krabbe (1996).
Clarification on assertion: actually on Brandom’s view, making an assertion is to be viewed as putting forward a claim as something that the hearer can use as a premise in his/her own reasoning and not: putting it forward as an uncontroversial starting point for further inquiry. The reason why the latter formulation is preferred here is to bracket the issue of reductios. The point is that while reductios use the speaker’s assertions as premises in one’s own reasoning, the premises in reductios cannot be thought of as uncontroversial starting points for further inquiry. Rather I take it that reductios can be seen as a dialectical tool that scorekeepers use to show that there is a problem with the speaker’s constellation of commitments. (I thank Michael De for forcing me to clarify this point.)
Dispositional Beliefs vs. Occurrent Beliefs: actually a case could be made that this problem could be set aside as a misunderstanding. The reason is that the problem of cluttering up our minds with logical consequences seems to concern beliefs understood as occurrent beliefs, whereas formal epistemology is usually taken to model dispositional beliefs.
Separating a weak and a strong version: notice that it would also be possible to hold the view that the deontic score built up in the course of a conversation would be completely ruined by an inconsistency. Instead, a weaker version was put forward here, according to which entitlement is only withheld with respect to the assertions producing the inconsistency (e.g. p and q, where q entails non-p) and not with respect to the whole deontic score. However, repeated instances of such failures can diminish one’s trust in the agent, which is why the idea of blacklisting recurrent sinners is introduced below.
Potential objection: here Paul Piwek (p.c.) raises the reasonable objection that the most sensible thing to do in cases where agents are confronted with paradoxical requirements may simply be to refrain from undertaking any public commitments at all and stick to their private beliefs. While this is a good point in general, I think it loses its intuitive force when applied to the preface paradox. Surely, we should not encourage authors not to write books or refrain from expressing a recognition of their own fallibility when doing so.
Explication of the liar paradox: one version of the liar paradox runs as follows. The second sentence in this endnote is not true. Suppose the second sentence is true, then it is true that the second sentence is not true, and so the second sentence must not be true. Suppose it is not true, then things are as the second sentence says they are, and so it must be true.
Moreover, after writing this paper, I discovered that a similar response is suggested already in Walton and Krabbe (1996, p. 60).
Thanks to one of the reviewers for pointing out this further possibility of a de re and de dicto ambiguity in the interaction between the Bruja and the scorekeeper.
Qualification: as one of the reviewers pointed out this may in fact be an idealization, because surely cases can arise, where there is some difference between the views of the author expressed in the book and the views of the author when writing the preface simply due to a temporal delay. In response, I would point out that the problems associated with acting as a scorekeeper on one’s own views do not arise for cases, where one is dealing with the past self. Accordingly, the points made in the main text deal exclusively with the paradigmatic case, where an author corrects any claim that he deems to be false prior to the publication so that the views articulated in the book actually express the claims the author wants to commit himself to at the time of publication.
Parallel to Moore’s paradox: in exhibiting this difficulty in asserting something about one’s own doxastic perspective that one would be able to assert about a foreign doxastic perspective, the preface paradox bears some resemblance to Moore’s paradox. Moore’s paradox consists in that we cannot assert sentences such as ‘p, but I do not believe that p’ or ‘p, but I believe that non-p’ without it sounding paradoxical—in spite of the fact that it is perfectly possible for any agent that p is the case and that this agent either believes that non-p or fails to believe that p (cf. Brandom 1994, p. 605). In both cases we seem to be faced with things that we know hold with respect to any other doxastic perspective (and a fortiori with respect to our own), which, however, we cannot assert directly about our own (present) doxastic perspective. Perhaps the best that the author can do is to restrict himself to counterfactuals about how he would have acted as a scorekeeper if the book had been written by someone else.
I thank Paul Piwek for pointing out the need to introduce a qualification here.
Qualification: as pointed out by one of the reviewers, I may actually be weakening Brandom’s position at this point, since he has quotes indicating that every committive-inferential consequence of an acknowledged commitment should be added to the deontic score (cf. Brandom 1994, p. 190). However, in that case, I would hold that the present version of the position constitutes an improvement, insofar as it allows us better to deal with problem 4 for the scorekeeping perspective.
I thank Michael De for helping me to clarify this point.
On commitments without an expiration date: as the practice of defending the works of deceased philosophers shows, the deontic score of an agent can outlive his/her biological time in virtue of other agents stepping in and administering the commitments of a deceased agent either as he/she would have been disposed to or in the way that would have been most optimal.
Explication of the Wason selection task: in this task, the participants are presented with four cards, which have D, K, 3, and 7 respectively faced up and given the conditional rule ‘If there is a D on one side of any card, then there is a 3 on its other side’. The task then consists in determining which cards to turn over to decide, whether the rule is true or false. To check for its falsity, the participants would have to select the D and the 7 card. Yet, most tend to select D and 3 (Manktelow 2012, Chap. 3).
Evans and Over (2004, p. 74).
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Acknowledgments
This paper profited greatly from discussions with Wolfgang Spohn, Michael De, Lars Dänzer, Eric Raidl, and the other members of a reading group on The Laws of Belief at the University of Konstanz. I would also like to thank the participants at Thomas Müller’s colloquium, Keith Stenning, Paul Piwek, the reviewers of Synthese, Hans Rott, and the audience at AISB50 for insightful discussions.
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Skovgaard-Olsen, N. The problem of logical omniscience, the preface paradox, and doxastic commitments. Synthese 194, 917–939 (2017). https://doi.org/10.1007/s11229-015-0979-7
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DOI: https://doi.org/10.1007/s11229-015-0979-7