Abstract
This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.
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Notes
This formulation of an inference in Modus Ponens is grammatically problematic, since ‘P’ and ‘Q’ occur both as noun-phrases (when standing alone) and as sentences (in ‘if P, then Q’), and ‘’if P, then Q’ occurs as a noun-phrase. I keep this formulation for convenience. But a final characterization should avoid the use of noun-phrases and, perhaps, be given in terms of the inference pattern:
\( {\frac{{\begin{array}{*{20}c} {\text{P}} \\ {\text{Q}} \\ \end{array} }}{{ {\text{If P}},{\text{ then Q}}}}} \)
As Harman stresses (1986, p. 1), pieces of reasoning such as (Ice-Cream) have two features: one theoretical and one practical. They are theoretical in that they affect one’s beliefs (e.g., you give up the belief that you will buy an ice-cream), and they are practical in that they affect one’s intentions (e.g., you give up the intention to buy an ice-cream). I shall only be concerned with the theoretical aspect of change in view, and shall not discuss its practical aspect.
Here I frame the issue in terms of the way in which logical knowledge interacts with ordinary reasoning rather than in terms of the way logical principles interact with principles of ordinary reasoning (whatever they might be). It is really the epistemological question that interests me, not the foundational one.
This is not meant as a definition of reasoned change in view, but merely an initial characterisation to fix ideas.
Harman’s claim that ordinary reasoning is reasoned change in view is widely accepted (but see Knorpp 1997 for arguments against this claim). However, some have argued against Harman that that doesn’t mean that there is no relation between logic and reasoning or that we never reason deductively. One focus has been the question of whether there is a normative connection between logic and reasoning—whether logic provides norms for reasoning, even if the contents of logical principles are not explicitly normative. On this matter, see for instance Field 2009 (and Harman’s replied to Field in his 2009) and MacFarlane (unpublished).
I do not go into the details of what exactly makes a logical rule meaning-constituting according to him here. But see Boghossian 1996.
Many other arguments have been put forward against the propositional account. One has to do with Carroll’s regress argument in his 1895, which many take to show that knowledge of logical principles cannot be propositional and must be dispositional. See Besson 2010 for arguments that Carroll’s regress does not provide support for dispositional accounts. Ryle 1949, also famously argued that knowing a logical principle is having a bit of knowledge-how, which is in turn analysed in terms of dispositions. Field (2009 and in conversation) has also suggested that Curry’s paradox provides some motivation for dispositional accounts.
See here Rumfitt 2000 for arguments that rejecting P does not amount to accepting not-P.
This distinction is due to Ryle in his 1949, chap. 5, p. 114. Some philosophers argue that fundamentally there aren’t really multi-track dispositions but only single-track ones. Others argue that many apparently single-track dispositions are really multi-track. Consider fragility again: although it is usually stated as a single-track disposition, it could be stated as a multi-track one, with different types of stimuli (stressing, dropping, smashing, etc.) and different types of outcome for each of the types of stimuli (breaking into pieces, cracking, tearing, etc.).Whether a disposition ultimately comes out single- or multi-track will largely depends on how types of stimuli and types of manifestations are individuated (i.e., finely or coarsely). I cannot discuss these issues here. See Bird 2007 for a useful discussion.
See Harman (1986, p. 19). Harman does not give any detail as to how these dispositions that can be overridden ought to be characterized (although it is clear that he would not go for anything like (DTR) for the reasons outlined in sect. 3 (i)–(ii)). The dispositionalist accounts discussed below can be seen as attempts to characterize the relevant dispositions in a way that makes them apt to be overridden.
These are of course not synonyms. They are all qualifications used in discussions of (different sorts of) dispositions. In what follows I will mainly use the qualification ‘normal’. However, choosing any other qualification would not alter the discussion in any substantive way.
This objection is not specific to (ST1*). It points to a general difficulty in handling cases of masks or antidotes by including restrictions in the statement of the conditions of manifestation of the disposition. A dispositionalist could say here that, since it is just part of the way dispositions work that the restrictions in the conditions of manifestations need not be finitely specifiable, this fact should not count against an account of a particular disposition such as (ST1*).
Here my account of dispositions as habituals follows Fara’s in his 2005.
Notice here that not all generic sentences state dispositions; for instance ‘Alice holidays in Scotland’ does not seem to state a disposition: it does not seem right to paraphrase it as ‘Alice has a disposition to holiday in Scotland’. Also, it is unclear that all dispositions can adequately be stated as habituals. For instance, fragility is arguably not a disposition that can be stated using a generic sentence: fragile objects are not in the habit of breaking—they only break once. (I’ll come back to this issue shortly). But see Fara (2005, pp. 72ff.) for arguments that dispositions of this sort can be adequately stated using generic sentences.
The connection between dispositions, habituals and generics is complex. I cannot do justice here to its intricacy, which would deserve another paper.
For instance, the same problems would arise if the weaker dispositions were framed in probabilistic terms, where a disposition would not necessitate the manifestation of the disposition given the right condition of manifestation but merely raise the chance of its manifestation. So for instance the disposition to infer according to MP would be such that believing P and believing if P, then Q, would raise the chance of believing Q as a result. However, it is again possible that this would not generally be the case.
Notice here that this sort of reasoning might in some sense mimic a proof of not-P in natural deduction from the assumption that if P, then Q. In that case, one would assume P, derive a contradiction (Q and not-Q) and then conclude not-P.
This need not be thought of as a final characterisation of the proposition that is the object of propositional knowledge of MP. But it seems to be the simplest way to state it. One issue with it is that it is really a schema, and so not quite a full-fledged proposition. I do not pursue this interesting issue, which is worthy of discussion, here.
You might perhaps object to this that ‘imply’ is modal, but ‘if, then’ is not; and so argue that in this respect the former is harder to understand than the latter. However, note first it is not obvious that ‘imply’ is modal, and second that this aspect of meaning might not need to be appreciated to count as understanding ‘imply’, as the remarks below about the division of linguistic labour suggest. See Tarski 1936 for a non-modal account of logical implication.
Obviously this cannot be a final diagnosis. Much depends on what sort of account of knowledge one is working with. On some accounts (e.g., where knowledge of logical rules is non-defeasible), the case could not be described as a case of destroyed knowledge; for that would be impossible.
Such reasons are typically referred to as ‘pro-tanto’ reasons. See Kagan 1989, pp. 17ff. for an excellent discussion of pro-tanto reasons. I remain tentative on the connection between propositional knowledge and reasons. Although I believe it gives us the right picture of the way logical knowledge connects to reasoning, the topic of reasons is far too intricate to be addressed thoroughly here. For instance one looming problem here would be some kind of bootstrapping problem—if we took P and if, P then Q to automatically give you a reason to infer Q. See Bratman 1999, pp. 23–27, and Broome 2001, for classic discussions of reasons and bootstrapping.
The way I see it, your knowledge of MP gives you a reason to infer according to MP in certain circumstances—e.g., when you believe both P and if P, then Q. It does not give you in general a reason to infer according to MP—or to promote such inferences.
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Acknowlegments
Thanks to Brian Ball, Hartry Field, Jane Friedman, Andrew Hudson, Hemdat Lerman, Adrian Moore, and Barbara Vetter for helpful discussions on the topic of this paper. Thanks also to audiences in Stockholm, Dubrovnik, and East Anglia for useful feedback. Special thanks to a discussion group in Oxford, Timothy Williamson, and a referee for this journal for very helpful comments on a complete draft of this paper.
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Besson, C. Logical knowledge and ordinary reasoning. Philos Stud 158, 59–82 (2012). https://doi.org/10.1007/s11098-010-9672-3
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DOI: https://doi.org/10.1007/s11098-010-9672-3