I don't think you can say something is owned because it is an extension of one's consciousness. A stolen object can still be used as an extension of the thief's consciousness, yet the thief does not have a valid claim. Your theory is able to explain what is able to be owned, but it is not capable of establishing who the proper owner is.
You could say that the proper owner is the first person to use an object as a tool, but by doing so your theory is essentially a restated version of the homesteading principle:
[E]very man has a property in his own person. This nobody has any right to but himself. The labour of his body and the work of his hands, we may say, are properly his. Whatsoever he removes out of the state that nature hath provided, and left it in, he hath mixed his labour with, and joined to it something that his own, and thereby makes it his property. It being by him removed from the common state nature placed it in, it hath by his labour something annexed to it that excludes the common right of other men. For this labour being the unquestionable property of the labourer, no man but he can have a right to what that is once joined to. . .
He that is nourished by the acorns he picked up under an oak, or the apples he gathered from the trees in the wood, has certainly appropriated them to himself. Nobody can deny but the nourishment is his. I ask then when did they begin to be his? . . .And 'tis plain, if the first gathering made them not his, nothing else could. That labour put a distinction between them and common. That added something to them more than nature, the common mother of all, had done: and so they become his private right. And will any one say he had no right to those acorns or apples he thus appropriated, because he had not the consent of all mankind to make them his? . . . If such a consent as that was necessary, man had starved, notwithstanding the plenty God had given him. We see in commons, which remain so by compact, that 'tis the taking part of what is common, and removing it out of the state Nature leaves it in, which begins the property; without which the common is of no use.^1^
Once an item becomes property, the owner may transfer the ownership to another person. therefore there are two legitimate ways of obtaining property: either by homesteading it, or by mutual exchange. If a dispute arises between two people, the burden of proof is on the accuser; if the accuser cannot prove that they have a legitimate claim to the item, then they may not use force to repossess it.
I recommend you read The Ethics of Liberty by Murray N. Rothbard (or at least the first two parts) for an introduction to this theory of property as well as an introduction to natural rights. I would also recommend Against Intellectual Property by N. Stephan Kinsella, who states that what makes something ownable is its scarcity, and explains how this effects the idea of intellectual property.
John Locke, An Essay Concerning the True Origin, Extent, and End of Civil Government, V. pp. 27-28, in Two Treatises of Government, P. Laslett ed. (Cambridge: Cambridge University Press, 1960), pp. 305-7. Quoted in Murray N. Rothbard, The Ethics of Liberty (New York: New York University Press, 2002), pp. 21ff.
I don't think you can say something is owned because it is an extension of one's consciousness. A stolen object can still be used as an extension of the thief's consciousness, yet the thief does not have a valid claim. Your theory is able to explain what is able to be owned, but it is not capable of establishing who the proper owner is.
You could say that the proper owner is the first person to use an object as a tool, but by doing so your theory is essentially a restated version of the homesteading principle:
Once an item becomes property, the owner may transfer the ownership to another person. therefore there are two legitimate ways of obtaining property: either by homesteading it, or by mutual exchange. If a dispute arises between two people, the burden of proof is on the accuser; if the accuser cannot prove that they have a legitimate claim to the item, then they may not use force to repossess it.
I recommend you read The Ethics of Liberty by Murray N. Rothbard (or at least the first two parts) for an introduction to this theory of property as well as an introduction to natural rights. I would also recommend Against Intellectual Property by N. Stephan Kinsella, who states that what makes something ownable is its scarcity, and explains how this effects the idea of intellectual property.