Besides, it's fallacious to imply that people need "incentives" to innovate. I'd wager there are much more people who are hindered by the patent system than there are people who would stop innovating just because there's no more monopoly to be had by being the first to apply for some legalese nonsense.

It's utterly absurd to imply any sort of ownership or rights to an abstract concept. The very notion of it should be grounds for attesting insanity. Instead, we should focus on free flow and exchange of ideas, tight cooperation and incremental development off each others' discoveries.

So no, they shouldn't be patentable. Nothing should be.