Gordon Cooper

Libertarians propose that if agents are to act freely they must have alternative possibilities open to them and control over which possibility becomes actual. To secure alternative possibilities, libertarians must accept that our free actions are undetermined events. Proponents of the “luck objection” to libertarianism argue that undetermined events are not the sorts of things over which agents can have control. In what follows, I defend the luck objection against three of the more promising libertarian rejoinders.

The base units of the SI include six units of continuous quantities and the mole, which is defined as proportional to the number of specified elementary entities in a sample. The existence of the mole as a unit has prompted comment in Metrologia that units of all enumerable entities should be defined though not listed as base units. In a similar vein, the BIPM defines numbers of entities as quantities of dimension one, although without admitting these entities as base units. However, there is a basic ontological distinction between continuous quantities and enumerable aggregates. The distinction is the basis of the difference between real and natural numbers. This paper clarifies the nature of the distinction: (i) in terms of a set of measurement axioms stated by Hölder; and (ii) using the formalism known in metrology as quantity calculus. We argue that a clear and unambiguous scientific distinction should be made between measurement and enumeration. We examine confusion in metrological definitions and nomenclature concerning this distinction, and discuss the implications of this distinction for ontology and epistemology in all scientific disciplines