Pedant’s Paradox

About the series: Examining logic problems and paradoxes and dismantling them, because I am just that picky. Feel free to debate my answers. (Yes I am aware most of these have mathematical answers, but they’re dressed  in real-world examples so they can be looked at with real world logic).

The Problem: The Athenians preserved Theseus’ ship for posterity. This meant replacing damaged parts as they wore out over time – the sails, the timbers, the decorations. At what point is it no longer Theseus ship?

The Answer: This is a curious one because there isn’t any true answer, but it is an interesting debate.

Some people would argue that it stops being Theseus’ ship when the last original part is replaced. This overlooks one thing – that the ship is not just its physical existence, it is its design. A question that must be asked is whether the original sailors would recognise it. If Theseus could see it today and immediately identified it as his ship, would anyone have the right to gainsay him even if all the timbers had been replaced?

I’ll go back to programming for an example. In Object Oriented Programming you have a class, which is a type of object and an instance, which is a specific member of that class. In this case we have a class: Ship and an instance: Theseus’ ship.

To make it easier to understand, let’s take a more radical change. Suppose we had class Password and an instance Mary’s password. Mary forgets her password, so she changes it to something completely new with no link to the old one. The new password is still Mary’s password. It still does everything the old password did, it unlocks the account, it needs to be remembered etc.

It isn’t Mary’s password any less because the letters have changed. It had better not be, since if it isn’t Mary’s password the login program won’t work and Mary’s locked out!

So going back to class: Ship and instance: Theseus’ ship, is changing the timber enough to make it not his ship? Or is it the point where the program – in this case the population of Athens – no longer recognises that instance as Theseus’ ship no matter how much it may have changed?

There is an extended problem, where the rotting planks are used to construct a vessel at another location so there are now two Ships of Theseus, and the issue is determining which is the true ship. This is more easily disposed of by anyone familiar with how quickly wood rots and sails break down. The second constructed ship will never at any one time have the entire body of Theseus’ ship present at its location. The fact the ship may have timbers from the original does not make it the original.

As a side note, this issue has actually been encountered in aircraft restoration – if parts of two spitfires are used to restore a third, which aircraft does the restoration count as in terms of flying hours, etc? It counts as the aircraft originally registered, not the ones used to restore it regardless of parts. The Iron Duke steam engine was broken down to save space in 1919 only to have a replica rebuilt at a new location using many of the salvaged parts less than a year later. The new engine still counts as a replica, not the original.