# Ship Of Theseus

## The Paradox

> The ship wherein Theseus and the youth of Athens returned from
> Crete had thirty oars, and was preserved by the Athenians down
> even to the time of Demetrius Phalereus, for they took away the
> old planks as they decayed, putting in new and stronger timber
> in their places, in so much that this ship became a standing
> example among the philosophers, for the logical question of things
> that grow; one side holding that the ship remained the same, and
> the other contending that it was not the same.
>
> Plutarch, Theseus

So did the ship remain the same even if all the parts were entirely
replaced?




## My Answer

It depends on what "the same" means.

Identical: Nope.
Isomorphic: Hell yes.

We have to explicitly set the category though.

So this means that you don't remain the same but your DNA remains
the same.


### Note

"A and B are identical" means that you can substitute A with B in
every proposition without altering the truth values (True/False),
and vice versa.

In other words, for any arbitrary P, if "A is P" is true (or false)
then "B is P" is also true (or false), and vice versa.