Truthmakers that keep naturalists up at night

Christians are supernaturalists. That is, they believe that there are things that exist which are neither material (where material is understood to encompass both matter and energy) nor supervenient upon the material.

(Definitional aside on supervenience: if x is supervenient upon y then x is irreducible to y (it is a new kind of thing) but is nonetheless dependent upon y for its existence.

For instance, smoke supervenes on fire.

Many naturalists concede that not everything is material (that is, matter/energy) but whatever is not is nonetheless supervenient upon matter/energy. For example, they would argue that consciousness supervenes on the neuronal synapses of the brain.)

But do all things that are not material supervene on the material? Or are there entities irreducible to the material and not dependent on the material for existence? If the latter, then this falsifies naturalism defined as everything being either material or supervenient upon the material.

Could the naturalist redefine naturalism to encompass entities which neither are reducible to the material nor which supervene upon it? Perhaps. But such a scenario would have at least a whiff of Antony Flew's famous "Invisible Gardener" parable. Although Flew used the parable against theists who forever redefine theism in light of new data until it becomes nearly meaningless, we could launch the same charge against the naturalist: they keep redefining the boundaries of "natural" until it becomes a mere cipher.

Anyway, we're getting ahead of ourselves. Some time ago some of these issues came up in the thread to my post "The atheist that left me at a loss for words." Conversational Atheist has been interested to continue this conversation, and I thought it would make sense to do so in a brand spankin' new post, so here we are.

In that previous thread I said: "The FACT that the interior angles of a triangle in Euclidean space add up to 180 degrees is not itself constructed, it is discovered."

Conversational Atheist agreed. This is discovered, not constructed. Now a fact is a fact because something makes it a fact. That thing is called a truthmaker. Naturalism by its classic definitions (e.g. Democritean materialism and supervenient materialism) has believed that the only truthmakers are objects, events, and states of affairs which exist in space and time. So the fact that I am now typing depends on the state of affairs of me now typing. That state of affairs in space and time is the truthmaker for the fact.

Here's a problem though. What is the truthmaker for the objective fact that the interior angles of a triangle in Euclidean space add up to 180 degrees? Note that it cannot be something in space and time since this fact is in nowise dependent on the Big Bang or the continued existence (let alone the initial origination) of the universe. So the truthmaker of this fact seems to be something that exists outside of space and time and thus is not dependent upon space and time.

If the naturalist is to accommodate this fact then he seems obliged to concede truthmakers that utterly burst the boundaries of the materialist and supervenient definitions of naturalism. Or he seems constrained to deny as objective facts things which are indeed objective facts.

This, it seems to me, is a problem.