I'm afraid I know nothing about philosophy. However, for a part of my course I'm currently studying the mind body problem. Many of the theories I come across can neither be proven nor disproven by scientific means. Is there a word to describe this phenomenon?
the term you are looking for is unfalsifiable, according to Collins Dictionary:
unable to be shown as false, although possibly not true
Attribution: Collins English Dictionary. Copyright © HarperCollins Publishers
First, I am not aware of some "technical" term for such theories... and perhaps one is not needed beyond "untestable theory," which is, of course, commonly used in science.
In physics, for example, there are hypotheses, such as quantum entanglement, string theory, or parallel universes that arise out of logical extensions of given theories and problems, but present serious challenges for the experimental verification scientists require. In such cases, conceiving of such a possible experiment can require great genius and imagination.
I may have this a bit wrong, but in the case of entanglement, first thought to be untestable, Bell's theorem provided an experimental scenario, recently applied. In the case of string theory, the verdict is out, and in the case of parallel universes, it may be logically impossible to test. Caveat: Again, I am not up on the latest here.
Generally, it is considered "reputable science" to propose new theories only with accompanying proposals as to how they might be confirmed or falsified, as Einstein famously did with general relativity and his proposal for detecting the gravitational bending of light. Because such an experiment had not even been thought of before, and was considered highly unlikely, the positive results found by Sir Eddington carried great conformational authority for Einstein's theory.
Aside from "untestable theory," what else might such explanatory speculations be called? Well...speculations, for one. Or they might be called logically-linguistically "meaningless" if they are proposals with no correlating "real content." They might be dismissed as "metaphysical," if they entail entities without causal or other "physical" properties, and are therefore obviously untestable.
We might also refer here to Kant's "Antinomies of Pure Reason," conflicting propositions that are not susceptible to solution by use of reason, let alone experimental proof. Kant's examples included the existence of God or a "necessary being" and whether or not the universe has a beginning in time. Oddly enough, the discovery of cosmic "background radiation" by researchers is now considered evidence for a datable "beginning" of the universe. So the expanding framework of science may alter what sorts of theories can or cannot be tested in accord with scientific method.
Again, short answer: "untestable theory..." or, for greater emphasis, "bucketful of moonbeams."
Empirical means "derived from or guided by experience or experiment" or "provable or verifiable by experience or experiment" (here).
You might call a theory not testable empirically a nonempirical theory.
Even better, in contemporary philosophical parlance, metaphysical usually connotes being beyond the orbit of scientific, empirical testing. Thus you might call a theory not testable empirically a metaphysical theory.
There is no natural native word in English to describe this situation. In informal thought, it is somewhat vague what 'scientific' means, and 'proven' and 'disproven' sound like math terms.
But in the domain of academic philosophy, these terms have more technical meanings. 'Scientific' has come to mean, over hundreds of years of philosophical argument, using sensory data (and by extension tools that transform sense data) to support a statement.
Also, a universal statement is difficult to prove (you'd have to test everything which is just not possible), but it could be disproven (a single counterexample/a failed test). An existential statement can be verified by giving a single tested example. The first is falsifiable and the second verifiable.
You're wondering what to call a statement that is neither falsifiable nor verifiable. This is at the heart of the 'demarcation' problem between science and non-science (or what is sometimes called metaphysics).
Things which cannot be proven/verified or disproven/falsified are then called metaphysics or metaphysical.
Pejoratively they might be called 'unscientific', 'philosophy'
'Untestable' is less pejorative and leans towards the one-sided 'unverifiable'.