I am not entirely sure I get the argument, though I suppose I get what is at stake. The argument reveals itself as a *hanami* argument in that *dualism* stands to gain a lot from the argument's acceptance and stands to lose little to nothing from the argument's rejection. The Wikipedia explanation leaves me cold, though I like that each time I read it I read something different.
For instance, I am unclear why imagining a possible world where some property fails to exist is sufficient for establishing the same property as failing in ours. On the one hand, the argument hinges on a fidelity criterion, that some worlds fail to be identical by some "additional" property. On the other hand, there is the inconceivability of excising such a property (non-trivially) from the collection of all comprehensions. For instance, consider the following possible worlds: 0. A possible world where all of the integers exist except for the number 2. One glaring criticism with this example is that there does not exist such a possible world, that is, the integers having a two is a necessary fact. That "couchishness" is in many ways less easy to probe than the integers likely draws attention away from such details regarding possible worlds logic. 1. A possible world with the Integers and without even integers has implications for the basic operations of arithmetic. In particular, what happens when one adds two numbers? Further, removing the evens means removing a countable number of things, but over the space of relations, excision may be uncountable. 2. It is worth thinking about the topology of the space of relations. A world with p-zombies may produce a punctured *plane of immanence* that behaves very differently than its convex counterpart, i.e, comes with a different set of expectations about the world and thus calling equality into question. The idea is that the relations themselves can be interpreted as a kind of endomap on the powersets of the world. Fixed point theorems like Brouwer's or Banach's then are possible consequences of the continuity of such endomaps; the convex worlds guarantee "having" such a fixed point where the punctured worlds do not. 3. It is arguable that our world only produces approximate symmetry, and yet affords the notion of actual symmetry. In such a case, symmetry appears as a kind of spectre, a limit point not actually belong to the world. To some extent, I can see physicalism as the thesis that all such properties are in the closure of our world and therefore in our world. 4. Lastly, what could I mean by a world where everyone "has" a ham sandwich? Is "having" a sandwich a function of agreement, proximity, or whatever? What aspect of the p-zombie argument relies on qualia? Can it effectively run the same over any kind of property?
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