I'm wondering if the following statement is fully correct:
Voltage causes current through a closed circuit, but through an inductor it is the change in current that causes a voltage.
Obviously there is no current without voltage. In a simple DC circuit there's no doubt that voltage causes the current to flow.
However in AC circuit with an inductor, the voltage drop across the inductor is proportional to the rate of change of current. So we can have 0 voltage + peak current and vice versa.
But I wouldn't say that current causes voltage in this case, because there would be no current change without a voltage source connected to the circuit!