Reduction by re-telling

A reductionist argument might go as follows. If you can take any story that ostensibly involves the existence of X's, and re-tell it without mentioning X's and without 'losing something' in the re-telling, then conclude that there aren't any X's. It's a bad argument. Either the re-telling means the same, but avoids mentioning X's by name. In which case we haven't avoided mentioning X's at all. It's as though we translated a story about ships into German, thus avoiding use of the English 'ship' by using the German word 'Schiff'. We have avoided the English 'ship', but we haven't avoided mentioning ships. Or the re-telling really doesn't mention X's at all, in which case the requirement that we aren't 'losing something' (ships, e.g.) is violated. You can't fail to mention X's in a re-telling without failing to mention something that was in the original story, and so the argument is obviously not valid.

Yet this is precisely what Peter Inwagen's argument against the existence of ships appears to do, when he re-tells the story of the Ship of Theseus.

Once upon a time, there were certain planks that were arranged shipwise. Call then the First Planks. . . . One of the First Planks was removed from the others and placed in a field. Then it was replaced by a new plank; that is, a carpenter caused the new plank and the remaining First Planks to be arranged shipwise, and in just such a way that the new plank was in contact with the same planks that the removed planks had been in contact with, and at exactly the same points. Call the planks that were then arranged shipwise the Second Planks. A plank that was both one of the First Planks and one of the Second Planks was removed from the others and placed in the field and replaced (according to the procedure laid down above), with the consequence that certain planks, the Third Planks, were arranged shipwise. Then a plank that was one of the First Planks and one of the Second Planks and one of the Third Planks . . . . This process was repeated till all the First Planks were in the field. Then the First Planks were caused to be arranged shipwise, and in just such a way that each of them was in contact with the same planks it had been in contact with when the First Planks had last been arranged shipwise, and was in contact with them at just the same points. (Peter van Inwagen, Material Beings (Cornell UP, 1990) 128-129)

Perhaps I have missed his point, but it appears to be that we can re-tell the story of the ship such that there is nothing in the standard version of the story that is not captured in the re-telling, and the re-telling does not mention ships, ergo there is no need for ships. If that is his argument, it involves the obvious fallacy I describe above. He begins "Once upon a time, there were certain planks that were arranged shipwise". What does that sentence mean? Does it mean the same as 'Once upon a time, there was a certain ship'? Does the expression 'shipwise arrangement of planks' mean the same as the word 'ship'? In which case the re-telling does mention ships, just as a German version of the standard story would mention ships (although by the word Schiff, of course). Or does it mean something different, something that is not a ship? In which case there is something in the standard version of the story (which begins with the assertion that there was a ship) that is not captured in the re-telling (which asserts only the existence shipwise arrangements of planks). Either way, the conclusion does not follow. Either the re-telling does assert the existence of ships, in which case it does not imply the non-existence of ships. Or it doesn't, in which case something has been lost in the re-telling, and the requirements of the argument are violated.

This casts some doubt on Vallicella's assertion here that Invagen "is a brilliant man". The argument does not strike me as brilliant at all. But perhaps I misunderstand it.