Lewis states that “we can agree with Parfit that what matter is questions of personal identity is mental continuity or connectedness….matters in question of personal identity-even in the problem cases-is identity” (Lewis 1976) Lewis provides another version of identity that is compatible with psychological continuity and it could handle intransitive cases as an example fission paradox. The fission paradox shows that common sense is inconsistent with the transitivity of identity. The fission paradox is the hypothetical scenario that single person can split into two continuant person which they are not related to each other and they are not psychologically continues each other.
In conclusion, the Lewis gives an unconvincing argument to support this case that identity theory of mind however, he is not succeed in supporting is claim that identity of matters because identity does not preserving our common sense intuition of identity. On the other hand, Parfit content with qualitative identity in cases of survival and thinks that numerical identity does not