But there's social contracts on top of that. Copyright is one such. It's not a right at all - it's a privilege (specifically, monopoly grant on distribution of certain information), that we as a society have decided to grant some people, because it incentivizes them to do things that we as a society want them to do.
Coincidentally, this also applies to regular property in a broad sense. The shirt that you wear on your back is yours in a physical sense; but, say, an apartment that you own and rent out in New York while living in California is only yours because the society declares it to be, and enforces that on your behalf - you don't have a natural right to such property, it's a social contract.
And no, I'm not a communist. Not anymore so than this guy:
"It is a moot question whether the origin of any kind of property is derived from nature at all... It is agreed by those who have seriously considered the subject that no individual has, of natural right, a separate property in an acre of land, for instance. By an universal law, indeed, whatever, whether fixed or movable, belongs to all men equally and in common is the property for the moment of him who occupies it; but when he relinquishes the occupation, the property goes with it. Stable ownership is the gift of social law, and is given late in the progress of society."
- Thomas Jefferson, 1813
[1] Personally, I've put a few small open-source projects online and do take the stance that people can use them however they want, I assert no control over their use (I request attribution). But I don't make money from writing code so I'm not saying I think everyone else should do this.
That wouldn't be a full substitute for copyright though. For example, if they broke the contract and distributed the code I don't think you could prevent other people from distributing it further.