Abstract
What I will call “the deviant logician objection” [DLO] is one line of attack against the common and compelling tenet that our justification for logical truths is grounded in our understanding of their constituent concepts. This objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic (and also beyond), between understanding and justification. I will consider varieties of the deviant logician objection developed by Horwich (2000, 2006) and by Williamson (2006, 2008). My thesis is that while the deviant logician objection falls short of proving that this traditional tenet must be rejected, nonetheless it serves to bolster some important refinements.
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Notes
Not to mention some other good old Quinean virtues like elegance and fecundity!
Williamson’s version of what I am calling [UJLT corollary] is: if something is a logical truth, then assenting to it is a necessary condition for understanding it.
Actually, the ambiguity option might have some real purchase in this case. One could argue that “~Φ” or “Φ v Ψ” literally means something different for an intuitionist, as opposed to a classical logician. (Thanks to Wayne Myrvold for pressing this case in the discussion period after I gave a version of this talk.) To the extent that this is so, then this points to a rather clear difference between the DLOs of Horwich and of Williamson. This would undermine the promise of Horwich’s DLO to support any drastic conclusions about [UJ] connections.
As Flanagan (2013: 346–7) documents, multiple authors have tried to answer Williamson’s challenge in one (or both) of these ways, but in Flanagan’s (and my) assessment, that will not do. As Williamson (2009: 135; 2011: 499) insists, this is a case of “theoretical disagreement,” not equivocation or incompetence.
As for [&E], Williamson (2008: 95) concedes that it may “have the best chance” as far as candidates for [UJ] connections go, but argues that even it is subject to competent, unequivocal dissent. However, his putative counterexamples (p.96) are relatively weak and problematic. (Cf. Boghossian (2011), Peacocke (2011) for discussion.) In my opinion, he does a much better job of motivating counter-instances for “All As are As,” and they are enough to force a challenge to [UJLT].
This is based on an example discussed by Railton (2000: 178).
The influence here of Wittgenstein (1921) is palpable. Consider 5.473 “… In a certain sense, we cannot make mistakes in logic”, 5.4731: “… What makes logic a priori is the impossibility of illogical thought”. Some things have the status of conditions for the possibility of intelligible discourse; to change them is to change the framework of discourse itself. (Alternatively, compare what it would be like to reject the following two claims:
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[1]
Squares have four sides.
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[2]
Neptune has four moons.
The latter would be easy and relatively inconsequential, but the former would involve a change of framework. The meaning of “Neptune” would preserve unscathed, but not so for “square”!)
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[1]
Here, compare Peacocke’s (2000, 2004) notion that certain beliefs are meaning-constituting. The cases under discussion of all squares having fours sides and all conjunctions entailing their conjuncts are good examples. (Compare, for example, the remarks about the meanings of “square” vs. “Neptune” in note 9.) I will come back to this notion of “meaning-constituting” again below, closely related as it is to our ongoing notion of [UJ] connections.
Indeed, within propositional logic, one might take the LEM and LNC to implicitly define the term “proposition.” (The price of that move is that “There will be a sea battle tomorrow” or “Erin is tall” might fail to express a proposition.)
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Acknowledgments
This research is supported by a Standard Research Grant from the Social Sciences and Humanities Research Council of Canada, whose support I gratefully acknowledge. Versions of this paper were presented to the Memorial University Philosophy Colloquium, the Canadian Philosophical Association, and Logic & the Philosophy of Science III in Bogota, Columbia. I thank the participants in those sessions for their helpful feedback.
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Sullivan, A. What Do Deviant Logians Show About the Epistemology of Logic?. Acta Anal 30, 179–191 (2015). https://doi.org/10.1007/s12136-014-0241-9
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DOI: https://doi.org/10.1007/s12136-014-0241-9