As may be gathered by reading some of my other posts, I do have a few biases, which I will spell out. The first is that everything existing in the natural world can be explained by natural processes only. The second bias is derived from the first, and that is that anything outside of the natural world can not interact with the natural world unless it's through natural processes. The third bias is that the only way to know truth is via the scientific method. And the fourth bias, is that truth is approached asymptotically: certainty is impossible.
What do I mean by the natural world? I equate it with physical reality defined by the 4 dimensional space-time that we humans experience in our lives. This leaves open the possibility of extra-dimensional entities interacting with our reality, although such interactions can only occur via the four primary physical forces. All natural processes are measurable in principle, although in practice, our technology may not be adequate to resolve all the details of these processes. Without modern technology, it would not be possible to measure or manipulate electric or magnetic fields, yet they have always been measurable in principle. Physical or Natural Laws are the interactions of these natural processes with physical reality, so as such it makes no sense to state that natural laws can be suspended. In the case that a physical law appears to have been suspended or 'violated', it would be more proper to state that we do not have all the details of the case in question and have not grasped the limitations of our understanding of the physical interactions.
An example of this would be the change in behavior of objects at extremely high velocities. The laws of physics appears to be violated. But this appeared as such because our understanding of the relationship of objects with velocity was not adequate with Newtonian physics. Newtonian physics is what drops out, when the limit of the ratio of an object's velocity to the speed of light approaches zero. Special relativity becomes Newtonian physics at low velocities. Newtonian Physics has been used for the majority of the planet's civil and mechanical engineering projects and we have landed humans on the Moon and rovers on Mars using it. It is not complete, but we have a better understanding of its limitations for velocity. (and size, gravitational fields)
I admit that the statement "the only way to know truth is via the scientific method" seems absolute, but given the other options, I can't see any alternative, valid statement. There are 4 methods of knowing, or as Charles S Peirce puts it, "Fixating Beliefs": Tenacity, Authority, Reason, and Science. I will briefly go over each, although Peirce did a much better job in his essay, "The Fixation of Belief", .
The first method of knowing is Tenacity or the method of personal revelation. This method reduces down to a person fixating on a belief solely due to personal revelation (ideas which came to her out of the blue) and stubbornly holding on to that belief despite anything, usually evidence to the contrary.
The method of Authority depends on the supposed superiority of an outside agent to determine or settle truth. The agent can take the form of a person or meme. It depends on the ability of the authority to overcome disagreements as long as those subject to the authority remain subjected. The Bible and Qur'an are examples of agents of Authority.
The method of Reason relies solely on "what is agreeable to reason". This is an intellectual method, but is subject to whims of modes of thinking and paradigms. It can be logically based but not linked to evidence.
Lastly, there is Science. This method depends on empirical measurements, self testing, criticism and continuous improvement. Science is an algorithm, a process of learning that methodically approaches truth, and as such, it may never reach Truth.
So does this rule out a 'supernatural'? That depends on what is meant by the 'supernatural' If, as most claim, the supernatural is 'beyond nature' and not subject to natural laws, then I would submit whether or not a supernatural exists is immaterial. Anything that is claimed too be supernatural is beyond our knowledge or capability to know. All claims of a supernatural interacting with our world are therefore automatically suspect, and in fact, make no sense. Any claim of knowing the supernatural is also suspect. At best, those entities that appear at first glance to be supernatural are indeed natural: we just do not have the understanding of the physical processes. Isaac Asimov once said that a sufficiently advanced technology would be indistinguishable from magic.
TO BE CONTINUED (amended, edited, etc.)
Peirce, C.S. (1877), "The Fixation of Belief", Popular Science Monthly, vol. 12, pp. 1-15.
Charles S. Peirce, Selected Writings