I've been thinking about Amos' statement..."Physical science limited to physical data sets up a self-asserting system of logic."

That's really an exaggeration/distortion of what physical science does. It simply measures and weighs what can be measured & weighed, and does not attempt to go beyond that. (If some individuals assert that they KNOW there is nothing else, they thereby implicitly go beyond what science qua science does.) The 'system of logic', properly understood, is not meant to refer to anything except its own parameters.

This does not mean that there must BE something beyond what science can measure, but only that we can conceive of the possibility. To define that concept as 'existing' because we name it is an equivocation on 'existence'.

Those who, like Amos, assert that 'mere' matter cannot give rise to all of the 'experiences' we have linguistic references for, must bear the burden of defending hypotheses that go far beyond the 'measurable'. "The burden of proof..." etc.
   It seems to me that ^metaphysical entities and realms can, by definition, only be explicated by using linguistic conventions that, when approached closely, react metaphorically much like physical stuff such as cotton-candy and blue smoke.

It is not science, but (some)metaphysics, which sees in conciousness some conditions which involve self-referential logic.

Eppur si muove indeed...and we can now measure what Galileo saw... but Eppur si cogito is a bit more elusive.