One of my favorite Christian apologists likes to point out that there are many things that exist, that science cannot account for directly. Science can be used to observe evidence for these things' existence, but not the things themselves. The criteria used applies to supernatural as well as the ordinary realms.
Naturalism is the idea that the only things that really exist or matter in the universe are physical things operating according to natural laws. There is no God outside of the system. There are no miracles. There are no hidden forces that drive the universe. There are no souls or spirits. There are no prophecies. There is no inspired Scripture. It's just physical stuff operating according to physical laws.
Source: Dominos, Determinism, and Naturalism
An example of something that exists that we cannot measure directly, only indirectly, is anything in the past. There is no physical way to measure things in the past. We can only measure today's evidence of it.
Another example would be something like a "motive." A motive can exist without direct evidence to proves it exists. We can measure things that result from the motive, but the motive stands alone, undetectable. But who denies the existence of motives?
Saying that science is the search for naturalistic evidence falls short when dealing with things like the past and motives. Yet we have branches of science that deal with both:
- Ontology - the study of the nature of being, existence, or reality in general and of its basic categories and their relations.
- Epistemology - the study of the nature of knowledge and how it relates to similar notions such as truth, belief, and justification.
Many times, the above are classified as philosophy but they are science all the same. Whereas pure philosophy can deal in unprovable realms, ontology and epistemology can deal in the provable, even though there are no direct physical or naturalistic aspects to study.
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