Okay, but consider the alternative -- that the existence of a non-materialistic reality is assumed without empirical (i.e. material) evidence. If that were to be accepted as a given, then we might build a pseudoscience on that foundation, one that would burden everyone with assumptions about empirically untestable, non-objective properties of reality. We would have created psychology.
Quote: "Empirical evidence (also empirical data, sense experience, empirical knowledge, or the a posteriori) is a source of knowledge acquired by means of observation or experimentation.[1] The term comes from the Greek word for experience, Εμπειρία (empeiría)."
The definition goes on to contrast empirical evidence with reasoning and other ways of approaching analysis -- all the non-materialist approaches.
Read the quote again, you're begging the question.
Empirical evidence is experiential by definition - it can be material evidence if it relates to claims about matter, but it can also be evidence about other domains.
Ex. If God exists, then religious experience is empirical evidence of this. It is not probably not material evidence however.
> Read the quote again, you're begging the question.
Yes, perhaps I am to some extent.
> Empirical evidence is experiential by definition
I would have said it relies on tangible evidence, material evidence. Its status as an experience by an observer, if present, is secondary. I say this because evidence can be gathered without anyone experiencing it directly. Consider Curiosity on Mars. If we read a mass spectrometer's results radioed back to Earth and draw conclusions on that basis, it's a stretch to assert that we've experienced the evidence. Its interpretation certainly involves an observer, but not the evidence gathering itself -- that is often automated, even here on earth.
> Ex. If God exists, then religious experience is empirical evidence of this.
No, I think a spiritual experience contradicts the direct, physical sense of empirical. I usually regard empirical evidence as that kind of physical evidence that forces different, similarly equipped observers into agreement on its meaning.
Example -- when the CMB was confirmed in the mid-1960s, it killed off the last hope for a steady-state universe. Until then the Big Bang's critics were theorizing that the universe created new matter between the galaxies, so even though the universe was clearly expanding, this didn't mean it had a beginning or an end. The CMB detection, which wasn't really anyone's direct experience, falsified this alternative to the Big Bang. And it's objective in the sense that anyone can set up and detect the same evidence using indirect means -- not by direct experience.
I don't know what you mean by "spiritual experience" but I think the previous comment about "religous experience" was referring to tangible, observable phenomena, like a man rising from the dead. This is empirical evidence (i.e. based on experience) but may not necessarily be measured in SI units. Data like this may lead to defensible logical conclusions that (because they are immaterial) cannot be tested experimentally.
I think most people will agree with me that we have the sensation of control over our own actions and yet it's not something that's directly testable per se.