Proof that water does not equal H2O

[brain in a vat]

If water = H2O then I can substitute the word "water" with the word "H2O" and it will be truth preserving.
P1: John believes that he is drinking water.
P2: Water = H2O.
C: Therefore John believes that he is drinking H2O.

But it's possible for John to believe that he is drinking water and not H2O. (Perhaps he never heard of H2O.)
P1: John believes he is drinking water.
P2: John doesn't believe he is drinking H20.
C: Therefore water doesn't equal H2O.

Because if there is a possible situation where x and not y, then x =y is false.

[The Voice of Time]

you never mentioned that John had to know what H2O was.

the conclusion should be that "Therefore John believes that he is drinking water which is H2O"

[mickthinks]

If water = H2O then I can substitute the word "water" with the word "H2O" and it will be truth preserving.

The truth about peoples beliefs is not preserved in that kind of transformation. Which is how dramatic irony works ...

Oedipus believed he had killed a stranger and had married the queen of Thebes, and the stranger was his father and and the queen was his mother. However, Oedipus did not know he had killed his father and married his mother - which is kind of the whole basis of Sophocles's play.

[Arising_uk]

If water = H2O then I can substitute the word "water" with the word "H2O" and it will be truth preserving.
P1: John believes that he is drinking water.
P2: Water = H2O.
C: Therefore John believes that he is drinking H2O.

But it's possible for John to believe that he is drinking water and not H2O. (Perhaps he never heard of H2O.)
P1: John believes he is drinking water.
P2: John doesn't believe he is drinking H20.
C: Therefore water doesn't equal H2O.

Because if there is a possible situation where x and not y, then x =y is false.

All this shows is that a belief is not necessarily true and epistemic logic does not truth preserve in the same way that propositional logic does.

1. John is drinking water
2. Water is H2O
3. Therefore John is drinking H20

or

Quantified,

1. All water is H2O
2. John is drinking water
3. Therefore John is drinking H2O

[Impenitent]

Little Johnny died last night,
his face, we'll see no more-
for what he thought was H2O,
was H2SO4

-Imp