Seven puzzles: twin earth

Here is how Sainsbury and Tye present the twin earth puzzle.

Suppose there is a planet (far, far, away)---call it 'twin-earth'---which is exactly like our planet except in one respect: where on earth there is water, made of H₂O molecules, on twin-earth there is a similar-looking and tasting liquid made up of XYZ, a compound unknown in earthly chemistry.  We'll refer to this stuff as 'twater', though this word belongs neither to the language used on earth, nor that used on twin-earth.  Like water, twater is colourless, tasteless, odourless, and wet.  On twin-earth, twater comes out of taps, fills lakes, falls from the sky, and so on.  On twin-earth, there is no water.  The twin-earth word 'water' refers to the local water-like stuff, twater.

Earth and twin-earth are so similar that everyone on earth has a duplicate on twin-earth: duplicates have all their intrinsic properties in common.  When anyone on earth does anything, their duplicate on twin-earth does something intrinsically the same.  Moreover, the English spoken on earth is duplicated on twin-earth by a language that sounds and is spelled just the same: twin-English.  On earth there's a word 'water', which refers to water.  On twin-earth there's a similar sounding word. But it cannot refer to water, for there is no water on twin-earth.  Rather, 'water' in twin-English refers to twater.

Tim, on our planet earth is holding a glass of water.  Speaking sincerely in English, he says, 'Water is wet'.  He expresses the belief that water is wet, so his belief is true if and only if water is wet.  Whether twater is wet is irrelevant to the question whether Tim's belief is true.

Tim's intrinsic duplicate, Tom, on twin-earth, is holding a glass of twater.  Speaking sincerely in twin-English, he says, 'Water is wet'.  He expresses the belief that twater is wet, so his belief is true if and only twater is wet.  Whether water is wet is irrelevant to the question whether Tom's belief is true.

Tim's belief, which is about water, is not the same as Tom's belief, which is about twater.  How is this possible?  Tim and Tom are intrinsic duplicates. Intrinsically, there is no difference whatsoever between them.  So how can there be a mental difference, a difference between their beliefs.

They summarise thus,

Someone can be the same in all intrinsic respects as their 'twin'---their duplicate on twin-earth---even though they think different thoughts.  mental properties are intrinsic, and thoughts are mental, so twins shouldn't be able to think different thoughts!

In their section on their solution to the puzzle Sainsbury and Tye simply say,

Tim and Tom have different concepts, respectively WATER and TWATER.  The concepts have different origins, WATER having been introduced in Tim's community, and TWATER having been introduced in Tom's entirely distinct community.  The different acts of introduction guarantee difference of concept.

Hmm.  Sainsbury and Tye seem pretty confident they know a priori what the earth term 'water' and the twin-earth term 'water' refer to.  I think this is an empirical question.  We should take earthly Tim to twin-earth and ask him if the water-like stuff he finds there is water.  Likewise twin-earthly Tom could be brought to earth and set the same question.  Given Tim and Tom's ignorance of chemistry and the stated similarity of earth and twin-earth neither would have a reason for saying 'This water-like stuff isn't water'. So in both languages 'water' refers to both water and twater.  Despite the separate originations, WATER and TWATER are the same concept and have a common referent, the motley of water and twater.  The twins do not think different thoughts.