Intellectual reader, I invite you to imagine with me a malleable set of declaratives. By this I mean a set of logically related statements that can be altered for the purposes of experimentation; we can take away, add, or reposition declaratives and observe what becomes of the rest of the set. Our first observation will be the way in which each component part is related to each other. Only two sorts of logical relationships may exist between any given pair of statements, though these relationships may be described multiple ways and are best expressed as magnitudes, not booleans. In other words, it is best to discuss the extent to which a certain relationship exists rather than the fact of its existence or lack thereof.
We will here only discuss one of the two relationships: that of logical consequence. To describe this relationship, we may refer to declaratives as either “following from” one another or else “being contained” within each other. A concrete example is in order: suppose I held before you a black pen; if I were creative enough, I could talk about the pen forever, because there are infinite truths that may be said of this black pen of mine. But suppose, of all the possibilities, I chose to say to you, “this pen exists”. The use of the demonstrative pronoun ‘this’ brings into language all the infinite qualities that the pen possesses; hence, “this pen is black” follows from, or if your prefer, is contained within “this pen exists” because the former is a subset of all the infinite truths contained within the latter.
So picture the two declaratives as a venn diagram; in this instance, it is not a conventional-looking image (figure 1). But if we were to consider another example, the diagram would look more familiar: suppose instead I said to you, “this pen uses black ink, and all pens that use black ink write clearly”. Now you might reply, being the clever reader you are, with another fact that follows and is contained within the previous two; “if that is so,” you would answer in your decorous manner, “then this pen writes clearly”. Aside from our admiration for what a sensible and insightful logician this response makes you out to be, we are now struck by the complexity of a logical phenomenon. Presently we have two statements that intersect to form a third (figure 2), so “this pen writes clearly” follows from the union of “this pen uses black ink” and “all pens that use black ink write clearly”.
Kindly notice that each bubble in the diagrams above may vary in size, depending on what order of infinity it represents. Notice further that, in our second example, A and B share certain common facts, which set of declaratives we call C, but also have some differences. So how closely related are A and B? The answer is a simple measure of area, and it describes a notion that I will call ‘gravity’. To express the formula for gravity, I will refer to the area of a statement X with the symbolic convention, ∫X. So the gravity between A and B in our example is Γ = ∫C / (∫A + ∫B).
This expression solves two important problems. The first is that of defining a scope, a sector of reality that is coherent. Consider an example: you tell a friend that, on theological grounds, you believe it was immoral for him to steal blueberries from Mr. Dimmesdale, and in his contemplative manner, he says, “but ‘God works all things together for the good of those who love Him’, so my deed will ultimately come to good”. You are both right, but he has misapplied a teleological perspective to an analysis of the action itself. The fact that he brought up exists in a larger scope than the matter you are discussing. And defining a scope is no subjective matter, to express it mathematically, we must first make one more definition: a “gravitational average” is the average gravity that one statement bears on each other member of a set. With that in place, a scope is any set of declaratives that exists such that each member has an equivalent gravitational average.
The second issue that gravity solves is that of distinguishing normal functioning from dissociative functioning. Dissociative functioning is a section of a proof of actions on which an alternative declarative bears greater gravity than the primal premise. For a more in-depth discussion of this, see Is Hypnosis Self-Evident? A Concise Philosophical Inquiry, in which post I describe the concept of gravity in different terms that nonetheless mean the same thing.
It seems prudent to define one last term: the Quantum Model of Reality. If we picture reality as a black-board with an infinite area, on which each infinitesimal point represents a fact (and those combine to from larger facts), by the Quantum Model of Reality, we are able to draw lines on the board to sector it off into quantum regions contained within one another; in other words, we can draw a larger circle around a smaller one ad infinitum, where each circle represents a valid scope that is defined in terms of a gravitational average. This is why, elsewhere on this blog, we have referred to reality existing in ‘levels’. In practical application, “God works all things together for the good of those who love Him” can only be discussed in relation to other notions of equal size, and Mr. Dimmesdale’s blueberries still ought be returned.