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Interpreting enthymematic arguments using belief revision

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Abstract

This paper is about the situation in which an author (writer or speaker) presents a deductively invalid argument, but the addressee aims at a charitable interpretation and has reason to assume that the author intends to present a valid argument. How can he go about interpreting the author’s reasoning as enthymematically valid? We suggest replacing the usual find-the-missing-premise approaches by an approach based on systematic efforts to ascribe a belief state to the author against the background of which the argument has to be evaluated. The suggested procedure includes rules for recording whether the author in fact accepts or denies the premises and the conclusion, as well as tests for enthymematic validity and strategies for revising belief state ascriptions. Different degrees of interpretive charity can be exercised. This is one reason why the interpretation or reconstruction of an enthymematic argument typically does not result in a unique outcome.

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Notes

  1. Throughout this paper, we refer to authors by female pronouns and to interpreters by male pronouns.

  2. This does not commit us to deductivism, the claim that all arguments “really” are deductive, nor to heuristic deductivism (Ennis 1982, pp. 74–76, 86), the strategy of reconstructing arguments as deductively valid as a means for determining “missing” premises. For the sake of simplicity, we will assume that the author and the interpreter do not reason differently in that they acknowledge different logical rules and axioms as valid. Those who think that different logics are in use need to incorporate this variable in their theories of interpretation.

  3. This includes arguments that are presented just for the sake of argument. See Sect. 5.

  4. In the literature, interpretation is sometimes contrasted with reconstruction as follows: Interpretation is associated with what ordinary language users actually do in dealing with arguments presented by an author, whereas reconstruction is an activity guided by theoretical considerations, standards of evaluation and techniques of argument analysis (cf. van Rees 2001). In this terminology, we deal with reconstruction rather than interpretation.

  5. Paglieri and Castelfranchi (2006) propose to use a belief revision framework for analysing how arguments may effect (or fail to effect) belief changes in an addressee in an attempt to persuade him.

  6. As Jacquette (1996) argues, adding premises is not always the best strategy for reconstructing an argument as valid. Sometimes it may be more charitable to alter the given argument by strengthening its premises or weakening its conclusion.

  7. In practice, interpreters also frequently come across arguments that are incomplete because they lack an explicit conclusion. We neglect such cases, following a common practice in the literature on enthymemes (for an exception see Walton and Macagno 2009).

  8. Since working with belief states implies that premises and conclusions are something that one actually can believe, our approach is not applicable to schematic arguments, which contain schematic letters instead of natural language expressions. This is not a serious limitation. Schematic arguments are the province of logicians, and they can be expected to present their schematic arguments non-enthymematically. The literature on enthymemes thus generally does not deal with schematic arguments (but see Paglieri and Woods 2011).

  9. We are using the derivability symbol \(\vdash \) in a slightly unconventional way, with a belief state rather than a set of sentences to the left of it. (1) means that the set of beliefs supported by, or accepted in, the belief state \(\mathbf{B} \otimes P\) entails \(c.\) We trust that this notational convention will not cause any confusion (cf. also Sect. 4).

  10. A similar point could be made with alternative readings, such as “Having an immortal human soul is a necessary condition for thinking.” This interpretation is less charitable. It renders the second “theological” premise superfluous, as we may assume that the author of the argument believes that only men and women can have human souls.

  11. In general, argument reconstruction involves four types of operations: deleting irrelevant elements, adding, reformulating and reordering premises and conclusion. In the present context, we assume that reconstruction does not include “completing” enthymemes by adding premises.

  12. For a more extensive discussion of these points see Brun (2004, 2008) and Brun and Hirsch Hadorn (2009).

  13. We are aware of the fact that there may not be a unique understanding of conditionals in natural language. We do not want to take a stand here on the question whether the conditional \(>\) should be read in the indicative or the subjunctive mood. In any case, \(>\) is supposed to be a Ramsey test conditional in the sense explained below.

  14. For overviews of belief revision theory see Gärdenfors (1988), Gärdenfors and Rott (1995), Rott (2008).

  15. The classical references are Ramsey (1931, p. 247, footnote), Stalnaker (1968, p. 102) and Gärdenfors (1979). For information about the problems of the Ramsey test and some ideas how to solve them, see Gärdenfors (1986), Lindström and Rabinowicz (1998), Nute and Cross (2001), Leitgeb (2010) and Rott (2011).

  16. This use of the term “hypothetical” must not be confused with the more traditional terminology that labels any argument with an if-then premise a “hypothetical argument”.

  17. Notice that (\(\mathbf{B} \div p_{1}) \div p_{2}\) is in general different from (\(\mathbf{B} \div p_{2}) \div p_{1},\) and this effect may not be welcome. Simultaneous belief change with respect to two beliefs does not offer a general way out. Simply contracting with the conjunction \(p_{1} \wedge p_{2}\) or the disjunction \(p_{1} \vee p_{2}\) does not help, since the former will not necessarily eliminate both conjuncts from \(\mathbf{B}\) while the latter will not only eliminate the disjuncts but also the disjunctive belief \(p _{1} \vee p_{2}.\)

  18. Arguments involving a “mixed” acceptance status of premises and conclusion are more difficult to deal with because standard belief revision theories can only handle one belief state manipulation at a time. Combining a revision with a contraction may be a problem, because the contraction operation \(\mathbf{B} \div p_{i}\) removes not only \(p_{i}\) from the belief set supported by \(\mathbf{B}\) but also enough of the remaining part of \(\mathbf{B}\) to guarantee that \(\mathbf{B}\) no longer supports \(p_{i}.\) Thus when we want to combine a revision with a contraction, the second operation may partly undo the first. For example, contracting with \(p_{2}\) will possibly eliminate \(p_{1}\) if we perform (\(\mathbf{B} * p_{1}) \div p _{2}.\)

  19. This can of course be disputed, as the order of processing the statement of premises and conclusion and the transition from the former to the latter does not appear to be fixed. We do not have strong reasons why an interpreter should account for the acceptance/rejection of premises and conclusion before evaluating the enthymematic validity of the argument. But our suggestion has at least the advantage of being the simplest solution.

  20. We thank Eduardo Fermé for coming up with the following variant of this example. Someone says: “\(y\) is odd. Therefore the sum of \(x\) and \(y\) is odd, too”. Every charitable interpreter will construe this as an enthymeme, assuming that the author somehow believes or knows that \(x\) is even.

  21. We thank Ralf Busse for coming up with this example. It originates with Sellars (1953, p. 323).

  22. If the author presents the argument to a child, she may think that (Law) is unknown to him.

  23. We thank an anonymous reviewer of this journal for raising this point.

  24. Revising by the material conditional \(p \rightarrow c\) would not suffice. For instance, a revision by \(p \rightarrow c\) has no effect if B already supports \(\lnot p,\) so this method cannot be used for JFTSOA-arguments. However, revising a belief state by the (stronger) conditional \(p > c\) is not an easy task. In the theory of belief revision, research on this problem has begun in the 1990s (Boutilier and Goldszmidt 1995; Nayak et al. 1996; Kern-Isberner 1999). The revision by the conditional \(p > q\) is guaranteed to effect a restructuring of a belief state within the \(p\)-worlds, and thus has far-reaching consequences in the “dispositional” part of the belief state. The only thing we need here is the idea that after a revision by \(p > c,\) the possible worlds satisfying \(p \wedge \lnot c\) are set back in terms of doxastic plausibility. But the details of all this are dependent on the specific method used for revisions by conditionals.

  25. See Katsuno and Mendelzon (1991), Hansson (1992), Peppas et al. (2000), Lehmann et al. (2001), Konieczny and Pino-Pérez (2002) and Arieli et al. (2007). Thanks to one of our reviewers for pressing us to be explicit in acknowledging the fundamental role that the similarity of belief states plays in our proposal.

  26. Here we refer to the axioms introduced by Alchourrón, Gärdenfors and Makinson (see the references given in footnote 14 above). However, the axiom most relevant in the present context, “recovery”, is very controversial. Note that in ordinary belief revision theory, belief states are identified with belief sets.

  27. A much easier solution would be to take simply \(\mathbf{B} * (p > c)\) rather than \((\mathbf{B} \div c) * (p > c)+c\) as the charitably ascribed belief state. But it is not clear, for instance, whether \(\mathbf{B} ^{-} := (\mathbf{B }* (p > c)) \div c\) would validate \(\mathbf{B}^{-}\!+p\vdash {c}.\) It would be interesting to study the connection between \(\mathbf{B} * (p > c)\) and \((\mathbf{B } \div c) * (p > c)+c\) more closely, but this is a complex task and cannot be done here.

  28. We could express distances if we used Spohn’s (1988, 2012) model based on ranking functions. This would give us much more powerful tools for constructing contractions, but this model does not only take propositions as inputs, but also needs numbers qualifying the inputs, and such numbers are not provided in spoken or written arguments.

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Acknowledgments

We would like to thank audiences in Constance, Lund, Prague, Regensburg, Salzburg and Stockholm, and in particular Gregor Betz, Ralf Busse, John Cantwell, Eduardo Fermé, Sven Ove Hansson, Eva-Maria Konrad, Christoph Lumer, Jaroslav Peregrin, Friedrich Reinmuth, Vladimir Svoboda as well as two anonymous referees of this journal for numerous critical comments on earlier versions of this paper. They have been very helpful.

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  1. ETH Zürich, CHN H 73.1, Universitätstrasse 16, 8092 , Zürich, Switzerland

    Georg Brun

  2. Department of Philosophy, Universität Regensburg, 93040 , Regensburg, Germany

    Hans Rott

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Brun, G., Rott, H. Interpreting enthymematic arguments using belief revision. Synthese 190, 4041–4063 (2013). https://doi.org/10.1007/s11229-013-0248-6

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