The zombie argument for dualism is commonly misunderstood. [For a broad overview and assessment of the argument, see my 'Zombie Review'.] In particular, misunderstanding the precise role conceivability plays in the argument often leads to overly hasty dismissals. In this post, I want to set out and correct three such misunderstandings. Let me begin on a conciliatory note by emphasizing that many conceivability arguments are no good. Each of the common mistakes discussed below begins by correctly noting a certain way that conceivability arguments can go wrong. But in each case, I will show, the zombie argument -- properly understood -- avoids the identified pitfall.
(1) In ordinary language, to call something 'conceivable' is just to say that you're not certain it's impossible. But such mere prima facie conceivability does not entail metaphysical possibility. There can be non-obvious or unknown necessities -- just look at mathematics. So clearly 'conceivability' in this sense doesn't prove anything much at all. That's true enough, but the zombie argument does not invoke 'conceivability' in this loose sense. Instead, it invokes the technical notion of ideal conceivability, or what can be conceived without (even implicit) contradiction. This stricter sense of conceivability more plausibly entails possibility. (The flip side of this is that it makes the premise [zombies are conceivable] more controversial!)
(2) Another common objection is that Kripke's discovery of the necessary a posteriori shows that some claims (e.g. "water is not H2O") can be ideally conceivable without being metaphysically possible. That's true, but a proper understanding of the Kripkean necessary a posteriori reveals that it is limited in scope. Kripkean complications arise only for concepts (like 'water') where the primary and secondary intensions diverge. Importantly, we can tell by conceptual analysis whether this is the case. We can tell, for example, that our water concept rigidly designates "the substance ___, whatever it is, that is the actual watery stuff of our world." But then to run a valid conceivability argument we simply need to take care to avoid those problematic concepts, and employ only their 'semantically neutral' (purely descriptive/qualitative) analogues: e.g. the qualitative term 'watery stuff' in place of the kind term 'water'. (Most everyone agrees that it's metaphysically possible that watery stuff be other than H2O: Twin Earth itself is an example!) Since the zombie argument can likewise be stated using semantically neutral terms, this suffices to defang the standard Kripkean objection.
[Since this post is getting overly long, I've shifted the third section to a new post.]