I consider whether a contradiction may be deducible from the proposition that God does not exist. First, I expose a candidate counterexample to a key premise in Swinburne’s argument against the deducibility of a contradiction from God’s non-existence. Second, I present two new strategies one might use to deduce a contradiction. Both strategies make use of Tarski's T-schema together with developments in other theistic arguments. One argument is a conceptualist argument from necessary truth for a necessary mind, and the other (...) is a two-stage contingency argument for the same conclusion. The purpose of this article is not to decisively defend these arguments, but to expose new territory relevant to investigating the nature of God's necessity. (shrink)