In my last two posts which build the foundation of my epistemological framework, I have described how the complexity of problems can be defined through building a hierarchy of constructs and relationships in the order of their complexity. There, I briefly describe the most basic elements with a rudimentary explanation for its complexity ranking as a standalone element. To follow, I described the most basic element, existence, and the general concept of abstraction, which allows us to discuss doubt as a concept which is the abstraction of certainty.
Let us build on the previous discussion here of the nature of knowledge as being inherently probabilistic. Let the certainty of the truth of any given proposition X be represented as Pr(X) in standard statistical notation. Suppose X is some basic proposition with the lowest level of complexity: "The spoon exists," for example, where a spoon is observed on a table in front of you. Having experienced the spoon in front of you, and indeed, currently experiencing it in front of you, you would have supreme confidence in the existence of the spoon. You could not provide a logical proof of the spoon's existence, but you could say that you are as close to absolute certainty in this proposition as one may be; in other words, the limit of Pr(X) approaches 1 in this case. For ease of demonstration, let's suppose Pr(X) = 0.9999.
A proposition expressing existence takes the form "X is". This form of proposition is the most basic form and can serve as a building block from which other, more complex propositions can be constructed. Let us examine more closely the nature of existence and the implications for the use of existence as the lowest-order proposition.
Any animate being can be shown to demonstrate the awareness of existence. Animals, though they are not self-aware and thus may not be cognizant of the concept of existence, will nevertheless react to stimuli in a manner consistent with the awareness of this concept. A dog, for example, will not attempt to run through a wall; it recognizes the existence of the wall and can understand that its efforts would be in vain. It, perhaps, does not know this innately, but through experience it becomes highly confident that the wall exists. Similarly, its eyes will follow an object that it is interested in, such as a ball or a morsel of food; this action directly represents the recognition of the existence of those objects.
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.
The assumption made about the limits of our knowledge is key to developing further theories on how we process information to come to an understanding of higher-order problems, as well as our construction of choice sets when faced with choices (whether ethical or preferential in nature). Here I will argue the skeptical view that we may know nothing infallibly. It is important to specify what constitutes knowledge, then subsequently to realize that we do not possess it. Finally, I will consider the implications of this - if we do not possess knowledge, what do we possess?
To know a fact is to say that the fact cannot possibly be incorrect. Consider an object in front of you. If you were to close your eyes, you would expect that object to remain in front of you when you were to open them again. Nevertheless, it is conceivable that the object may no longer be there. There are myriad explanations for why this might have occurred - in fact, there are infinite possible explanations, just as we can conceive of infinite explanations for why an action did not cause a reaction, as we have seen.
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).
