I've recently finished the first draft of a paper on disagreement about logic. I'll put a version here when I've had time to take into account some of the comments I got at the PhD seminar. Unfortunately, I have another deadline creeping up for a paper on proof-
theoretic harmony, so I'll have to let it wait for a couple of weeks. For now I just want to air one or two ideas discussed in the paper.
Broadly speaking, the paper deals with disagreement about logic under an
inferentialist assumption - that is, roughly the assumption that the logical rules (properly constrained) of a logical constant determine its meaning. A problem for
inferentialism is that it threatens to reduce all 'genuine' disagreement about logic (say, between the intuitionist, the classicist, the
relevantist, and the
dialethist) to mere verbal disputes. For, if we assume that the natural deduction rules specify the meaning of the logical constants, it seems that any disagreement about which inferences are valid, will ultimately turn on disagreement about the correct meaning of the involved logical constants. A typical diagnosis along these lines is that, for example, the law of excluded middle is ambiguous between the law with IL-constants and the law with CL-constants (see Hellman '
Never Say “
Never”! On the Communication Problem between
Intuitionism and Classicism' (1989)).
The first part of my paper offers a criticism of some
inferentialist attempts at
accommodating this worry. The first, due to
Dummett and
Prawitz, grants that the rivals are in fact talking at cross purpose (i.e., there is a terminological disagreement), but denies that this should lead us to conclude that there is no genuine disagreement. Rather,
Dummett and
Prawitz argues that there can still be a fact of the matter to base a genuine disagreement on. A disagreement about logic is grounded in an underlying disagreement about meaning-theory, and by checking if a logic complies to certain meaning-theoretic principles (such as
harmony, formally interpreted as conservativeness), a verdict of correctness is possible - genuine disagreement is reinstated. One worry discussed in my paper is whether the details of the
Dummett-
Prawitz approach hinges on a particular formal framework for disagreement, one which, moreover, cannot be generalized.
The second attempt that I discuss is outlined in Stephen Read's forthcoming paper 'Harmony and Modality', presented at
UNILOG 2005. The approach attempts to avoid the concession that the disagreement is terminological by introducing a distinction between meaning-conferring rules and non-meaning-conferring rules. The idea is that whereas disagreement about the latter rules is genuine, disagreement about the former is only verbal. Of course, the challenge is to find a stable and well-motivated distinction between these two types of rules. My criticism has two parts: one which deals directly with the Read's suggestion of basing the dichotomy on a distinction between structural and operational rules, and one which more generally argues against the possibility of separating out which rules pertain to the meaning and which do not.
Lastly, my paper explores what sense can be made of a more pessimistic
inferentialist approach, namely
Quine's theory of
logic in translation. Quine famously claimed that 'change of logic, is change of subject', arguing that rival
logics ought to be translated away by imposing the translator's logic on the
translatee's (the
native's). Now, Quine took this to mean that deviant
logics ought to be put into line with classical logic, but, as pointed out by Graham Priest (2006), there is no reason to believe that this point is not perfectly symmetric: the deviant translator imposes her deviant logic on the classical native. The upshot of the Quinean approach is that disagreement about logic can always be translated away. My paper follows
Pelletier and Urquhart (2003) in exploring whether or not the theory can be given a formal framework through the technical notion of
interpretability (or
embeddability). I won't go into any more details now - I'll leave some suspense for the actual paper.
While working with formal translations between logics, I came across some very interesting papers by Lloyd Humberstone,
'Béziau’s translation paradox' (2005) and '
Logical Discrimination' (2005). In general, I'm interested in literature dealing with the relationship between mutual interpretability, the deductive power of a logic, and the discriminatory power of a logic. Recommendations are welcomed.
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