Another thing people seem to forget is that plastic requires oil. It's relatively easy to move from gas to electric cars, I don't know of an alternative for plastic production however.
For at least "important" uses of plastic you can make it from plants. I haven't looked to see how the volume of plastic consumed compares to, say, the corn crop though.
The chemical industry requires oil and gas as both a raw material and a source of industrial heat. The fossil-derived industrial heat may be replaced by electricity produced from various sources, including nuclear. Secondly, if electricity becomes relatively abundant, that could create an economy completely independent on fossil fuel, since you can convert just about any generic organic matter (and ultimately from CO2 and water) into chemical products.