Or so it would seem. This paper will present two closely programmes investigating the notion of provability as represented in relevant logic. The first investigates the notion of provability in a version of Peano arithmetic based on relevant logic. The second looks at what happens when we construct a relevant modal logic with modal principles taken from the classically based modal logic which captures the notion of provability from classically Peano arithmetic. This paper will present both of these programmes and discuss the problems and prospects involved in each.
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