Can the Conditional Analysis Strategy Help Physicalism?

Braddon-Mitchell (2003), Hawthorne (2002), and Stalnaker (2002) provide a physicalistic argument that depends on the following two conditionals. If we experience dualistic pain, zombies are possible. On the other hand, if the actual world is physicalistic, zombies are impossible. Based on these conditionals, it is derived that zombies are conceivable but this does not entail their possibility. This line of argument for physicalism is referred to as the Conditional Analysis Strategy (CAS). I claim that the CAS does not help physicalists defuse the zombie argument. To show this, I first suggest that there are three possible interpretations of the strategy: the CAS explains the zombie intuition by virtue of the conceivability of zombies; the CAS conditionally disproves the entailment-link from conceivability to possibility; the CAS unconditionally denies the entailment-link I argue that none of the three understandings brings good news to physicalism.