This is an old question, reaching back to the 18th century, when copyright applied only to writing. A writer takes resources available to all – language, symbols, ideas, etc. – and mixes them with his labor to produce a new work. The question was whether investing that labor in the work gave the writer a natural right to control over it. One court case said yes, and overruled the term limit on copyright.
There is another question, however. Do the common resources (language, ideas, etc.) belong to all? Or do they belong to no-one? In the former case, the writer needs the permission of the community in order to assert a natural right on his work. In the latter case, they have no business interfering in his right1. This is assuming natural rights exist at all. Are rights given by God, do they already exist somewhere out there, or are they created by human beings? In the latter case, the whole argument for natural rights is short-circuited.
Later court decisions found that although a writer might have a natural right to his work, enforcing that right impinged too much on the freedom of others. Instead, the law was grounded on the economic principle that it should encourage writers.
Another way to approach this is the idea of authorship, which arose in the 18th and 19th centuries. According to the Romantics, authors played a special moral role in society. Furthermore, their works were unique personal expression of themselves. This was an innovation. The idea of human creativity wasn’t widely accepted until the 20th century; many non-Western cultures that still do not share it.
Of course courts aren’t run by philosophers. The ideal of the romantic author who creates something original from nothing has been very influential in intellectual property rulings. It appears to resolve a number of serious inconsistencies in intellectual property law2. In practice it creates as many problems as it solves. It’s also just just plain wrong: authors don’t create from nothing.
For most creators, the question of rights is rendered moot by the fact that they neither own nor control their work. This is famously the case for music, but is prevalent in other fields.
1 Peter Drahos, A Philosophy of Intellectual Property.
2 James Boyle, Shamans, Software & Spleens.