Should the expression "p" be executed by the aid of the soft pedal or through the fingers?

The soft pedal serves to change the quality of tone, not the quantity. It should therefore never be used to hide a faulty piano (or soft) touch. Mere softness of tone should always be produced by a decrease of finger-force and a lessening of the raising of the fingers. The soft pedal should be employed only when the softness of tone is coupled with a change of colouring, such as lies within its range of action.