The study of epistemology attempts to separate what we know from what we merely believe. This distinction can take on various forms, but generally the things we "know" without equivocation are rather few and are not very interesting things, if anything at all. We know of existence - of ourselves, of others, of objects. But when it comes to relationships between things that exist - and specifically, interactions between things that exist through time and space - we find that there is very little that is definite. How can we know, without a doubt, that the laws of gravity and the natural world will hold in the future, that the sun will rise tomorrow? First, let us put aside the nature of knowledge itself to revisit later. It will be essential to fully define terms for use in later constructs.
I prefer to make a clear distinction between science and (for lack of a better term) non-science. Here I use "science" to mean the study of any process in time, space, or mental construct which has a deterministic outcome - or, to be more precise with terms, the study of deterministic processes. This does not mean that the outcome was infallibly predictable at a time prior to the interaction. In fact, it does not mean that the outcome was even observable to us. It simply means that the interaction resulted in an outcome which conceivably could have been predicted with certainty.
To elaborate on this definition: This encompasses all autonomous physical processes - for example, the classic example of one billiard ball striking another, but also more elaborate processes such as volcanic eruptions, chemical reactions, weather patterns, the movement of atomic particles, space matter, and so forth. These sorts of phenomenon are colloquially defined as science. But it is easy to see that we may not be able to predict the outcome with a high degree of certainty, or in fact any degree of certainty at all, depending on the complexity of the problem.
This definition of "science" also includes human interactions which lack the exertion of free will in the form of conscious decision-making. The top card in a deck is deterministically predictable, despite the apparent randomness generated by the shuffling of the deck. This shuffling is a human interaction, but there is not a conscious effort on the part of the dealer to affect the outcome (assuming he is not a cheat or a magician). Moreover, the outcome of the top card resulting in this process is the same - and thus, is equally predictable - whether the card faces up or down. Thus, the outcome in question need not be observable to be predictable with certainty (if a tree falls in the woods...).
Note that this definition of "science" is not meant to try to redefine the word for any purpose other than to build upon it as a foundation for further thought. Having defined science in this way, we might use the term to demarcate matters of epistemology inherent to any sort of problem we encounter.
Some will take issue with my choice of the word "certainty" in the definition. I must emphasize that "certainty" is not meant to convey our knowledge or predictive power, but rather the ex post result. The important thing is not that the outcome can be known beforehand, but simply that an outcome (which might conceivably have been predicted) will result.
Items in grey text above are topics of further consideration which will be linked back to this article (and this article updated to reflect the discussion of those topics as they are available here).