In defence of logical nominalism: reply to Leftow - Swinburne, R (Cambridge University Press, 2010)
This paper defends (especially in response to Brian Leftow's recent attack) logical nominalism, the thesis that logically necessary truth belongs primarily to sentences and depends solely on the conventions of human language. A sentence is logically necessary (that is, a priori metaphysically necessary) iff its negation entails a contradiction. A sentence is a posteriori metaphysically necessary iff it reduces to a logical necessity when we substitute for rigid designators of objects or properties canonical descriptions of the essential properties of those objects or properties. The truth-conditions of necessary sentences are not to be found in any transcendent reality, such as God's thoughts. ‘There is a God’ is neither a priori nor a posteriori metaphysically necessary; God is necessary in the sense that His existence is not causally contingent on anything else.