Dependence, Necessitation and Non-Reductive Physicalism

This thesis will build on recent work in the Philosophy of Mind by investigating underdeveloped ideas in Metaphysics. More specifically, this thesis is about formulating physicalism, the idea that everything in the world can be fully explained by reference to the ontology of physical science.
Most contemporary versions of physicalism are formulated as strong modal theses. The truth of contemporary physicalism thus depends on the goings-on of remote possible worlds. I will explore formulations of physicalism that do not carry these strong modal commitments. I will show that, despite being philosophically controversial, such formulations are coherent and able to solve serious problems in the literature.
My central research questions are as follows:
Q1 Must metaphysical dependence relations necessitate?
Q2 Are metaphysical dependence relations that do not necessitate at odds with physicalism?
I aim to explore ways of answering "no" to both questions.
Think of metaphysical dependence as the synchronic analogue of causation. In Jonathan Schaffer's words, just as causation "drives the world through time", so metaphysical dependence "drives the world up levels" (Schaffer 2016:59). An example of such a relation is composition. Metaphysical dependence relations are important for a specific brand of physicalism (non-reductive physicalism) that is central to this proposal.
It is often thought that metaphysical dependence relations must necessitate:
Necessitation: If G metaphysically depends on F, then it is impossible that G occurs in the absence of F. (Rosen, 2010:132)
If some molecules arranged table-wise compose a table, then any like molecules arranged table-wise also compose a table. It is thought that, if this principle fails, then physicalism is false. (If some molecules compose a table in one situation but do not in a qualitatively identical scenario, then the table must be dependent on something further. Suppose that molecules and arrangements exhaust the contents of the physical world, then that something further must be non-physical, and physicalism is false.) I will explore ways of contesting both intuitions. That is, I will explore the possibility of a non-necessitating metaphysical dependence relation that is physicalistically acceptable.
Necessitating relations cause problems for physicalism. Let my zombie twin be an exact physical duplicate of me. Thus, with respect to the ontology of physical science, my zombie twin and I are qulitatively identical. However, my zombie twin has no phenomenal consciousness (there is nothing it is like to be my zombie twin).
P1 I can conceive of (i.e. coherently think about) my zombie twin.
P2 Whatever I can conceive of is possible (though it may not be actual).
C1 My zombie twin is possible.
P3 If my zombie twin is possible, then physicalism is false.
C2 Physicalism is false.
P3 is true because physicalists also believe:
(A1) Physical facts necessitate mental facts.
Thus, at any possible world, a duplicate of my living brain (or perhaps my body) should be accompanied by my mind. Thus, on contemporary formulations of physicalism, my zombie twin should be impossible (Chalmers, 2009).
The standard view is that, if the physicalist can resist the zombie argument, she must challenge (P1) or (P2) - adopting niche views on the connection between conceivability and possibility. Physicalists never challenge (P3), since the commitment to necessitating relations is taken for granted.
Call this argument a "modal scope objection". There are numerous modal scope objections, each turning on the "wide" modal scope of physicalism (that is physicalism'scommitment to necessitating relations).