[FRIAM] P Zombie Couches

[Jon Zingale]

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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