Thought ISSN 2161-2234
Currying Omnipotence: A Reply to Beall and
& Guillermo Badia
University of Connecticut
Johannes Kepler University Linz
Beall and Cotnoir (2017) argue that theists may accept the claim that God’s omnipotence is fully
unrestricted if they also adopt a suitable nonclassical logic. eir primary focus is on the infamous
Stone problem (i.e., whether God can create a stone too heavy for God to li). We show how
unrestricted omnipotence generates Curry-like paradoxes. e upshot is that Beall and Cotnoir
only provide a solution to one version of the Stone problem, but that unrestricted omnipotence
generates other problems which they do not adequately address.
Keywords Logic; Curry’s paradox; Omnipotence; Stone problem; Theological
Beall and Cotnoir (2017) put forward a solution to the Stone paradox associated with
God’s omnipotence. eir solution involves adopting a fully nonrestrictivist version of
omnipotence—that there are no limits on God’s powers—and proceeds by the use of a
gappy subclassical logic K3 toarguethattheputativeparadoxdoesnotresultinnegation
inconsistency. e purpose of this paper is to present a version of Curry’s paradox using
unrestricted omnipotence to show that the paradoxes related to omnipotence threaten
not just inconsistency, but triviality. e main observation we wish to present is a logical
to couch a theology with unrestricted omnipotence.
Curry’s argument is a dierent kind of paradox from the stone and the liar (for
instance) in the sense that it does not involve negation. Curry’s paradox exploits standard
(or absorption) principle: ϕ → (ϕ → ψ) ⊢ (ϕ → ψ),orthecloselyrelatedprincipleof
assertion: ((ϕ → ψ) ∧ϕ) → ψ.
e argument has many forms confronting class theory,
set theory, provability logic, truth theory and even validity theory among others. It
appeared for the rst time in a 1942 paper by Curry (1942).
We can take unrestricted omnipotence to mean the collection of all sentences of the
(O) God can make it the case that ϕ.
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Thought 7 (2018) 119–121 © 2018 The Thought Trust and Wiley Periodicals, Inc. 119