Theseus' Ship Changes and Yet Remains Theseus' Ship

I propose to solve the paradox of Theseus" Ship by demonstrating that the essence of an object, contained within the greater equation of a relationship between it and another object, changes without ever changing the sum of the relationship. Following that I demonstrate that the only way Theseus" Ship changes are if either Theseus or the Ship is exchanged with a new object. In the case of Theseus" Ship there are two objects: Theseus and the ship. There is an additional quality which is the relationship between the two. Necessarily this relationship is an ownership imposed by Theseus on the ship. This is logically necessary as the ship doesn't contain or define the relationship. In a state of nature A does not own B. Ownership is imposed by A upon B because ownership is an act, and an act is an outward force upon the state of nature. Naturally both objects exist; the subject Theseus acts to own his ship. The ship is therefore not influencing the relationship except in being there. This relationship can be described thusly: Theseus' Ownership + Ship = Theseus' Ship Theseus" Ship = Theseus' Ownership + Ship If, Ship = X wooden boards, a keel, a masthead, a wheel, Y sails Then we'd say: (x+WB) + Ka + Mb + Wc + (y+S) = ShipD ShipD = (x+WB) + Ka + Mb + Wc + (y+S) In this case the variables associated after a part - such as a or b - represents the type of that object installed. For example let's say in regards to the masthead there are 5 different types of masthead available to Theseus. Mb may equal anything between M1 and M5. We won't worry about the other parts since it complicates the endeavour without adding to the argument. Finally, ShipD is the total sum of part-types and changes whenever any of the variables change. If the ship firstly possessed M1 then the equation resembled: (x+WB) + Ka + M1 + Wc + (y+S) = ShipD ShipD = (x+WB) + Ka + M1 + Wc + (y+S) Then if he replaces M1 with M2 the equation now resembles: (x+WB) + Ka + M2 + Wc + (y+S) = ShipD ShipD = (x+WB) + Ka + M2 + Wc + (y+S) In this case ShipD will be a different quantity, therefore the ship has changed. But when we're discussing how the ship relates to Theseus, Ship is summed as Ship regardless of the composition of the equation; because D never changes the fact of "Ship" or how the ship relates to Theseus. Or otherwise, ShipD `33; = Ship Ship " `33; = ShipD Therefore despite changes to ShipD: Theseus' Ownership + Ship = Theseus' Ship. The changes to the ship can always be expressed as a change to the ship, but not a change to how the ship relates with Theseus. Now, you may ask "If Socrates takes Theseus' Ship, is it still Theseus's Ship". The answer is no. It could only be the case if Socrates changes the values accordingly: Ship = Theseus' Ship, But despite this possibility it is incorrect to state that: Ship `33; Theseus" Ship Since Theseus is no longer imposing his ownership on the ship Socrates may also say: Socrates' Ownership + (Theseus' Ship - Theseus' Ownership) = Socrates' Ownership + Ship = Socrates' Ship And if Socrates trades the ship for an apple, (Socrates' Ship - Ship) + Apple = Socrates'Ownership + Apple = Socrates' Apple Therefore it is logical that though the qualities of the ship can change, Theseus" Ship remains Theseus" Ship unless the relationship between Theseus and the Ship changes or if the ship is exchanged for another kind of object.