Let's examine two people claim ownership of a chair of two different spatial positions. It is surly possible that an individuals may own two separate chairs that reside in two different spatial positions. It's not however possible for there to be a property violation unless both parties claim the same spatial position. This is hard to both imagine and explain without rambling.
It may be argued that an individual sitting in one chair but claiming ownership to both is not a conflict within the same spatial position. Yet, it is. The owner of both chairs is claiming ownership of both a single spatial positions that two chairs happen to reside within. The area of ownership is simply larger.
It may be argued that the owner of the chairs is not claiming ownership of the actual ground which the chair resides but instead the actual chair. The problem then becomes, is the second individual claiming ownership of ground which the chair resides? If so, then the conflict is redefined as one over land, not chairs. In this case, either the true owner must either give preference or remain impartial. If he remains impartial, then it would default to first come first serve. Why?
It may be argued that someone can continuously own something over an interval of time and therefore it is hard to distinguish an actual unit of time for two people to have a conflict, i.e. two individuals have a conflict over an interval of time. This is true, but it doesn't negate our premise. The interval of time in which a conflict occurs is the unit of temporal order.
It may be argued that I may own something without actually residing within the position of ownership. Again, this is true but not a problem. It may be true that i can own two chairs and not sit in either of them and there is still a conflict of ownership when you sit in them. I need not claim use the way in which you claim use. I may enjoy the chair untouched and a decoration while you wish to sit in it. Therefore, there can still be a spatial conflict even if I am not wishing to use the chair the way you wish to use it. Thus, since i own the chair over a continuos amount of time, any segment of that interval you claim ownership (even use) is thus a conflict.
What would duel ownership outside a spatial and temporal order look like? It is intelligible. If i sold you a product, you and I cannot both claim ownership to same product even if it resides in the same position at two different times. I would claim to the product before the transaction and the money after the transaction, you, vice versa. These two variations in time don't allow for a conflict. We will bypass a potential fraud for now
If we both have claims of two spatial positions then there again can be no legitimate conflict then our issue would look something like. Let us not forget that there may always be issues with knowledge, but there can be no inconsistency in our premise.
A thought experiment/possiblility
Given the claim that property conflict cannot occur unless two or more individuals claim equal ownership of both a position and time we cannot proceed to infer that every duel claim of position and time will result in a conflict. To claim ownership of something implies that you are willing to defend your claim, even if said defense is nothing more than verbally expressing your complaint. Without both parties proceeding to defend their actions, no conflict may occur. If I own a chair that someone sits on when I'm not around cannot be a property violation until i claim there is one and take action to prevent or control it. The problem with this line of reasoning is apparent. If someone steals from me, even if I don't know who the thief is, is clearly a property violation. However, if someone steals something that I didn't know, or had forgotten I knew, I owned, there is not property violation. This happens often. I have many pens in my home to which I know not where they came from. I too know of pens I've purchased that are not within my home. I'm not sure a property conflict is suitable here but I can see the confusion. Again, if someone is murdered., they can't proceed to prevent or control their murder after the fact that they are murdered. Yet, murder is clearly a property violation. But who is it a violation to? Most would say the murdered but I'm not too sure. Maybe it is a violation to other...creditors, insurance payers, family, etc?
There seems to be a paradox here, granting that my thoughts are not muddled.
Per Hoppe, two individuals cannot claim duel ownership of some thing at the same moment in time (Even under something a unusual as conjoined twins to which W. Block and I will demonstrate in a forthcoming paper). Yet a property conflict cannot exist unless two individuals claim ownership of the same thing at the same time.
Thus, ownership of the same position at the same point in time cannot exist (Hoppe), yet, conflict cannot exist except when two or more individuals do claim ownership of some position within the same point in time.
If one individual claims
Individual 1 Individual 2
Spatial 1 Time 1 Spatial 2 Time 2
Spatial 2 Time 2 Spatial 1 Time 1
S1T1S1T1
S1T1S1T2
S1T1S2T2
S1T1S2T1
S2T1S1T1
S2T2S1T1
S1T2S1T1
The reason why Hoppe's claim must be true is simply within the definition. There is no scenario which can il-legitimize it because we can define any scenario at any moment in time as having only one owner. If a partnership were to form and two individuals had a dispute over what to do with a certain property. Even in a partnership where the details are not defined, ownership is simply divided in the profits and divided when the property is sold. The actual property itself is subject to whoever molds it at a certain point in time, if two individuals pull horse in opposite directions, then it can be said that ownership is divided into the parts each has their hand on. To prove that Hoppe's theory incorrect you must be able to show that at any point in time, theft could not occur.

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