Beall-ing O

Jeremiah Joven Joaquin



In “A neglected reply to Prior’s dilemma” Beall [2012] presents a Weak Kleene framework where Prior’s dilemma for Hume’s no-ought-fromis thesis fails. It fails in the framework because addition, the inference rule that one of its horns relies on, is invalid. In this paper, we show that a more general result is necessary for the viability of Beall’s proposal –  a result, which implies that Hume’s thesis holds in the proposed framework. We prove this result and thus show that Beall’s proposal is indeed viable.


Beall; Hume’s Thesis; Prior’s Dilemma; Weak Kleene

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Beall, Jc, 2012, “A neglected reply to Prior’s dilemma”, pages 203–208 in J. Maclaurin (ed.), Rationis Defensor: Essays in Honour of Colin Cheyne, Studies in History and Philosophy of Science, vol 28, Springer, Dordrecht. DOI:

Beall, Jc, , 2016, “Off-topic: A new interpretation of Weak Kleene logic”, Australasian Journal of Logic 13 (6). DOI:

Bochvar, Dmitri A., and Merrie Bergmann, 1981, “On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus”, History and Philosophy of Logic 2 (1–2): 87–112. DOI:

Francez, Nissim, 2019, “On Beall’s new interpretation of WK3”, Journal of Logic, Language and Information 28 (1): 1–7. DOI:

Pigden, Charles (ed.), 2010, Hume on Is and Ought, Palgrave-Macmillan. DOI:

Prior, A.N., 1960, “The autonomy of ethics”, Australasian Journal of Philosophy, 38 (3): 199–206. DOI:

Russell, Gillian, and Greg Restall, 2010, “Barriers to implication”, in [Pigden, 2010].

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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