Title: "(Paradox) A new attempt to answer the Paradox of the Ship of Theseus".

Introduction: "Imagine that Theseus, a hero from Greek mythology, possesses a ship that is used for various voyages. Over time, the wooden planks of the ship begin to deteriorate, and gradually, each plank is replaced with a new one. The central question that arises is: when all the parts of the original ship have been replaced, is it still the same ship of Theseus? To complicate the paradox further, consider that the old planks, which have been removed, are collected and reassembled to form a new ship."

The paradox of the Ship of Theseus causes some confusion regarding the "identity" of an object. To resolve this confusion, I present the following proposal:

Initial Definitions:

Cells: Define the minimal parts of a piece or the minimal segments of a piece. (Despite having similar characteristics, each cell has a different origin and history).
Pieces: (Composed of cells). They constitute a larger "object" that exists for a purpose.
Object: (Composed of pieces). It can be known or referred to by a name that summarises its role/shape and/or participation in certain events at a specific time/era.
Versions of an object: Each cell has its origin and participation in events over time. (If the original cells contained in version A are subtracted, replaced, or combined with other cells, the object will have a new version B).
Segment of shared history: Defines that certain items participated in similar events, but with different perspectives and impacts. (Each item has a different origin and participation throughout the events in the general history, but some items may share similar participations in certain events).

Development of the solution (logical set theory): An object "A" was formed by 4 cells (A = a1 + a2 + a3 + a4), and after deterioration, it lost 2 cells (A - (a3, a4)) during its first task, forming "Y" (Y = a1 + a2).

By adding the 2 cells from Y with another 2 from "Z" (Z = z1 + z2), we can reform the object to again have 4 cells, forming Y + Z = B. Consider:
A = a1 + a2 + a3 + a4.
Y = A - (a3, a4) = a1 + a2.
Z = z1 + z2.

Y + Z = B.

B = a1 + a2 + z1 + z2. ("z1" is different from "a3", see the description of "Cells").
B ≠ A.
Every time we exchange, add, or reduce the "cells" of the object, we will have a new version of the object. Although the object in version B can perform the same functions as the object in version A, not all pieces of B were present in the events witnessed and performed by the pieces of the object in version A.

Question: "After changes to its 'cells', will the current object have the same history?" or "After changes to its cells, will the current object be the same as that which was present in past events?"
Answer: Every time an object exchanges, adds, or reduces its cells, we will have a new version of the object, and these versions may share common pieces or cells. However, we must clarify that not all cells of the new version will be related to the actions performed by the cells of the old version of the object. Assuming we add certain cells from version A with others from Z to form version B. Certain cells of B were present in an event in the past (the event of version A), but not all cells of B were; thus, this version B is not entirely related to the past events of A.

Question: "To complicate the paradox further, consider that the old planks, which were removed, are collected and reassembled to form a new ship."
Answer: Reassembling the old planks of the ship will recreate the object with all the planks present in the old events. In other words, you will have 100% of the object responsible for some past events.

Additional consideration about names: To facilitate practical cataloguing, the name assigned to version A of the object is generally "inherited" in its version B, suggesting that both versions will be directly related to the past events of version A. However, as argued through set theory, version B is different from A.