As the carbon atom appears due to its versatility in every known life forms, there's a potential conjecture that presents this periodic element as organic matter. Or say compounds having this atom. Is it rational?
If you see a diamond, an allotrope of carbon, or with other words pure carbon arranged with other structure creating a different form, it looks like that doesn't have life of its own. Well some living people carry it in their hands and the market goes wild sometimes with diamonds, but they aren't organic.
Recent claims of organic matter in Mars maybe answer to this particular conjecture. Carbon appears in multiple minerals around the planet with coal perhaps as a nice example, mixing hydrogen, nitrogen, oxygen and sulfides. Coal could proceed from organic decomposition, although it's still needed another theory that states how the sand goes alive during some time, because in an origin the planet shouldn’t have more than this to start.
Some sources cite "organic matter" as a chemical substance formed by carbon-carbon or hydrogen-carbon bonds. This way anyone could create organic matter, and plastics included! They don't pass as organic from our viewpoint.