Panpsychism and emergence are two popular foundational approaches to the hard
problem of consciousness. Both approaches appeal to many for precisely the
same reason: they represent palatable alternatives to more exotic approaches
such as (full blown) idealism and interactionist dualism while seeking a
distance from most forms of physicalism deemed unsuitable for tackling the
hard problem. Emergence typically assumes that consciousness "pops out",
usually  at a certain level of complexity while panpsychism pushes experience
all the way down because of the difficulty in locating such a level of
complexity at which consciousness can be said to emerge. This description
suggests that panpsychism and emergence are utterly at odds with each
other. Despite this, recent efforts at rapprochement have begun, perhaps
driven by their common affinity to physicalism. In this work, we begin by
carefully delineating where panpsychism and emergence stand vis a vis
physicalism with the expectation of not only aiding synthesis efforts but
potentially going beyond both approaches as well. Most forms of physicalism
face the problem that their accounts can proceed without being accompanied by
experience. While philosophers such as Stoljar have suggested that the hard
problem is a reflection of our ignorance of the physical ultimates, this is
ultimately unsatisfying unless a positive account is given. Unfortunately,
these ultimates, if they exist, are Rumsfeldian unknowns that are known to be
unknown and we cannot expect to easily arrive at them. However, we can examine
panpsychism and emergence for flaws in the hope that these will reveal the
outline of the inscrutable ultimates. Panpsychism faces the combination
problem - or the relationship of the macro-experiential to the
micro-experiential, whereas emergence faces the complexity problem - or the
specification of a level at which subjects pop out. When we examine both
approaches for flaws, we find, much to our surprise, a common flaw - the
inadequate treatment of compositionality. We find it very hard to conceive -
most likely due to the unitary nature of experience - of macro-subjects
composed of micro-subjects and we have found it difficult thus far to map a
mid-level subject to a quantitative measure of complexity. We argue that both
drawbacks are indicative of basic flaws in the treatment of
compositionality. We began with the assumption that flaws in panpsychism and
emergence provide clues to physicalist inscrutables underlying experience. If
compositionality is related to such an inscrutable, then we can ask the
following questions: Can a fundamental compositionality - accompanied by
experience - be compatible with physicalism? In particular, does fundamental
compositionality run afoul of causal closure and/or does it fit within a
spatio-temporal process picture of physicalism? We examine possible answers to
both questions taking care to demonstrate exactly how a fundamental
compositionality forces us to modify standard pictures of physicalism. In
closing, while it appears that panpsychism - with emergence used to solve the
combination problem - may indeed become the standard bearer, an intriguing
alternative - physicalism with a fundamental compositionality - is waiting in
the wings to be fleshed out.