If we assume that we, as humans, have no knowledge a priori from our creation, and that we instead are only more or less certain about any given proposition, then we must start to examine the most basic propositions in our world. The goal, in so doing, is not to determine some empirical probability that we have for any specific proposition or type of proposition, on average. Nor should we be naive enough to believe that we might be able to order our confidence in any two specific propositions. Although confidence can be expressed on a continuum from 0 to 1, we resign our practical ability to fall short of precisely determining our internal confidence in any given proposition, much less a strict comparison between two propositions in which we have similar confidence.
Rather, by examining some propositions, we can perhaps discover how our brains operate in practice, by producing a rough classification which distinguishes certain problems from others. Then, we might generally say that we are naturally inclined to be more confident in the truth of some propositions than others. Another way of stating our goal is that we might classify the order of complexity of a given proposition, based on the constituent elements of that proposition - much in the same way as a grammar teacher might be able to evaluate the complexity of a sentence based on the parts of speech, syntax, and vocabulary of which it is comprised.
The concept of ex post determinism, which I have referred to here as scientific determinism, is not a new concept by any stretch. Various forms of determinism have been proposed and debated over the last several centuries, and while the boundaries I have laid out may differ, the idea that events are deterministic is well trodden ground.
Perhaps one of the most extreme, or pure, forms of determinism is represented by Laplace's demon. "Laplace's demon" is the name given to the ideas posited in a passage late in Laplace's life on probability (available here). In simple terms, Laplace expressed the idea of pure determinism: If the position and speed of all particles in the universe are known at a time t=0, then the state of the world at a later time t=1 can be perfectly calculated. Laplace, an early statistician, perhaps most clearly demonstrates the divide between frequentist (or probabilist) and Bayesian modes of thought: You may notice that Laplace's demon seems to have nothing at all to do with statistics as we know it today.
Having defined science, I should revisit first a prerequisite to applying this definition of "science" to the construction of problems and their solutions. It is necessary to understand what is implied by ex-post "certainty", which may be more accurately described as determinism.
Determinism simply describes the concept that a process (X) will lead to some outcome (Y). X may be concrete, such as in the case of an object striking another. X may also be abstract, such as the calculation of an arithmetic expression. In either of these cases, the result will be Y chosen from a range of all possible outcomes (the possibility set). Note that, insofar as it is a concept, Y may be "nothing" and still would constitute a valid outcome for X, as would the complete end of existence for all objects and concepts related to X. In short: Define a process X to be an event in time, space, or mental construct which must result in an outcome Y. We can assume that only one outcome Y can possibly occur, creating a one-to-one mapping from X to Y (more on this below).
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.
