Ferenc András

The Russell's paradox concerns the foundations of naive set theory. This short short paper is about how it can be interpreted in other contexts and has significance in the world of commands. Understanding the paper assumes that the reader is broadly familiar with the foundations of set theory and its history. The text contains many formulas and therefore the reader should be comfortable in the world of logical formulas. My example is somewhat similar to the barber paradox. There, too, we are puzzled by the feasibility of a task. In the case of the barber paradox there is a solution: the barber is a woman, in my example there is no such escape.

To solve the ship of Theseus puzzle, you need several keys. First of all, we need to fix the application condition of the physical object—it is a vehicle or an object memory; then the identification criterion—the ship was named The Ship of Theseus when he boarded it; and finally the re-application criterion—a ship (or an object memory) when it is the same ship (or object memory) as before. The degree of change from the previous and reference states must be given. The identity of physical objects over time can be expressed by the uniformity of the time slices of the persisting objects. Uniformity exists from the point of view that these instances are temporal cross-sections of the same object; they may differ in other characteristics; there are no general a priori principles independent of practice. The definition of identity is decided by the community of language users. The two states of an object are the same as long as the rate of change of state remains below the threshold value relative to the reference. The two states of an object are similar as long as the change is below a threshold value with respect to each other. Similarity can be described by a tolerance relationship. The mathematical relation describing uniformity is formally an equivalence relation, just as the relation describing identity is an equivalence relation. A physical object is identical to an equivalence class when we speak of the object's identity over time and identical or not identical to an element of the equivalence class when we speak of the object having changed or ceased to exist.