Patents aren't private property. They're a government-granted temporary monopoly. In the absence of government, there's still some notion of property, but no notion whatsoever of patents.
Yes, they are. (Particularly, they are intangible personal property.)
> They're a government-granted temporary monopoly.
All "property" is government-granted monopoly in the control/use of some thing (sometimes dependent on a grant from another private party, but still ultimately government granted), concrete or abstract. Some are temporary (this is true of real and tangible personal property, too), some are permanent.
> In the absence of government, there's still some notion of property, but no notion whatsoever of patents.
Outside of government/legality, there's certainly still some notion that things, concrete and abstract, can belong to certain people such that it is wrong to "steal" them, and that certainly includes ideas. The particular details and names of particular classes of property are, of course, products of people, over time, spending time teasing out vague notions into more detailed sets of rules -- which, in the case of property rights, is something that tends to happen in the context of government (not always by government, but you don't even have developed philosophy of property rights without government existing to create a stable enough society for people to spend time writing rather than defending their immediate personal possessions and survival necessities.)
A patent is, ultimately, a negative entity. Before a patent is granted, anybody can make certain objects or perform certain techniques. After it's filed, the patent owner's rights remain unchanged, but everybody else is restricted from doing those things.
Humans have an intrinsic idea of "property" that the legal idea is built upon. A two-year-old child understands the idea of "mine". People still own things when government is not present, they just have a harder time enforcing that ownership.
Patents, on the other hand, are an entirely governmental construct.
Thank you. I guess cash currency isn't really property either. It is backed by the "full faith and credit" of the government so it is like a IOU that the government requires you to accept to settle existing debts.