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Published online by Cambridge University Press: 24 October 2008
This paper is a reply to Stephen Davis' ‘A Defence of the Free Will Defence’. With the aid of some elementary modal logic, some of the inner workings of Davis’ argument are explored, and the nature of the opposition of the Davis argument to the Mackie thesis is made plainer. It is concluded herein that while the Davis argument is interesting and illuminating, it is not conclusive, as Davis appears to think, and that the burden of proof remains on the opponent of the Mackie thesis, i.e., the Free Will Defence defender.
page 325 note 1 Davis, Stephen T., ‘A Defence of the Free Will Defence’, Religious Studies, Vol. 8, No. 4, December 1972, 335–44.CrossRefGoogle Scholar
page 325 note 2 Mackie, J. L., ‘Evil and Omnipotence’, Pike, Nelson (ed.), God and Evil (Englewood Cliffs, N.J.: Prentice-Hall, 1964), p. 56.Google Scholar
page 327 note 1 For an account of the ‘standard Lewis systems’, T, S4 and S5, see Hughes, G. E. and Cresswell, M. J., An Introduction to Modal Logic (London, Methuen, 1968), chapters 2 and 3.Google Scholar System T (due to Robert Feys) is the basic system of which S4 and S5 are extensions. T was proved equivalent to the System M of von Wright by Sobocinski in 1953. The essentials of System T are quite simple (for our purposes).
System T
Ax. 1: L p ⊃ p [Axiom of Necessity]
Ax. 2: L(p ⊃ q) ⊃ (L p ⊃ L q)
Rule I: If α is a theorem, L α is a theorem [Gödel Rule of Necessitation]
Definition: M p = df ∼ L ∼ p
Also note that System T is an extension of PC: all truth-functional rules and theorems are assumed to hold.
page 329 note 1 ‘∼ (p ⊰ ∼ (Mp & M ∼ p))’ is not a theorem in the standard Lewis systems.
page 329 note 2 Vide Hughes, and Creswell, (op. cit.), p. 28.Google Scholar
page 329 note 3 For some systems of this type see Feys, Robert, Modal Logics (edited with some complements by Dopp, Joseph, Nauwelaerts, E., Louvain, Belgium, 1965), p. 133 f.Google Scholar