Yes, "the Brain," I do: "private property" is either something I have taken from nature and improved; something I have purchased; or something I have been given as a gift. I own right and title to it, and no one else does--unless I sell it to them, or give it to them. Using those resources (land, labor, property) to produce something is downstream from ownership. At that point whatever I own (tools and all) become means of production--and I can own them just as you can.

But all property rights are derived from the principle that (on the horizontal plane) I own myself and my time--that I am a unique individual with unique volition, unique purpose, and unique wants. The collectivism of Marx is downstream from his whacky monist ontology: that we were all primordially "one" and that individuality (with individual desires and property) was "the Fall" led to "alienation from Ourself" and that the only way to return was to "realize our Oneness." He was a gnostic. Just read his nonsense. There's a reason he ended up a madman beating at the air.

Your economic system (so far as it follows Marx's) rests on the fallacy of the "labor theory of value." Menger destroyed that theory. If the labor theory of value is correct then why does undeveloped land have any price at all? Why does the same glass of water have a higher price in the middle of the dessert than it does during a jungle rainstorm? Because value is not derived by its labor input: it's derived by subjective individuals employing means to achieve their desired ends.