  We present a simple alternative to Mackey's account of the (infinite)
inequivalent quantizations possible on a coset space G/H. Our reformulation is
based on the reduction ${\rm G \rightarrow G/H}$ and employs a generalized form
of Dirac's approach to the quantization of constrained systems. When applied to
the four-sphere $S^4 \simeq {\rm Spin(5)/Spin(4)}$, the inequivalent
quantizations induce relativistic spin and a background BPST instanton; thus
they might provide a natural account of both of these physical entities.
