What Putnam's argument actually establishes is that a brain in a vat's utterance of 'We are not brains in a vat' would be true

The important fact for Putnam’s argument is that whichever of these possible meanings is had in vat-English by ‘I am a brain in a vat’, that sentence, as used by a BIV, will be false. We saw that in sense (i), ‘I am a brain in a vat’ would be false in vat-English, since a BIV would never have (perceptual) experiences as of being a BIV. Putnam does not explain why ‘I am a brain in a vat’ would be false in both senses (ii) and (iii). Brueckner (2016: 4) suggests that since in sense (iii) both ‘bra