This article bears on four topics: observational predicates and phenomenal properties, vagueness, strict finitism as a philosophy of mathematics, and the analysis of feasible computability. It is argued that reactions to strict finitism point towards a semantics for vague predicates in the form of nonstandard models of weak arithmetical theories of the sort originally introduced to characterize the notion of feasibility as understood in computational complexity theory. The approach described eschews the use of nonclassical logic and related devices like degrees of truth or supervaluation. Like epistemic approaches to vagueness, it may thus be smoothly integrated with the use of classical model theory as widely employed in natural language semantics. But unlike epistemicism, the described approach fails to imply either the existence of sharp boundaries or the failure of tolerance for soritical predicates. Applications of measurement theory (in the sense of Krantz, Luce, Suppes, & Tversky (1971)) to vagueness in the nonstandard setting are also explored.

In his published Gifford Lectures, Professor Michael Dummett asks ‘what would it be for there to be a universe devoid of sentient beings? What would be the difference between God's creating a material universe, in the whole of which there never was any creature able to experience it [‘a unidead’, in Moonan's shorthand], and His creating nothing at all? … What difference would its existing make?’ He answers: ‘there would surely be no difference…’ and ‘unless there are sentient and rational observers, it would not be possible for either observation or inference to occur’. (Thought and Reality, 97.)

Some theists might find this a disconcerting restriction on divine power; and if in addition realist, might put it down to a refusal of realism for the range of language in question. In this article, however, I presuppose a coherent realism for the range, and argue that Dummett's contentions can hold for realisms too, and ought not to disconcert serious theists. What is crucial is not (just) whether you are prepared to understand your assertions in an ‘anti-realist’ rather than a realist manner, but whether or not you are prepared to use ‘God’ to stand for something not finite in any way, if there is any, and for nothing else in extra-mental reality. Dummett's Giffords are metaphysically serious: where it would matter if there were no God.