Ironically, lightbulbs are the paradigmatic example of invention being messy and of multiple discovery; multiple discoveries in general is covered by Kevin Kelly in ch7 of What Technology Wants (online draft):

An incandescent light bulb based on a coil of carbonized bamboo filament heated within a vacuum bulb is not inevitable, but "the electric incandescent light bulb" is. The concept of "the electric incandescent light bulb" abstracted from all the details that can vary while still producing the result — luminance from electricity, for instance — is ordained by the technium's trajectory. We know this because "the electric incandescent light bulb" was invented, re-invented, co-invented, or "first invented" dozens of times. In their book Edison's Electric Light: Biography of an Invention, Robert Friedel and Paul Israel list 23 inventors of incandescent bulbs prior to Edison. It might be fairer to say that Edison was the very last "first" inventor of the electric light.