We define rules that describe the universe. If they are accurate, philosophically precise descriptions of reality, then they hold up in all cases. Otherwise, they are limited to the approximating realm our minds imagine.
Clarke's Second Law wisely reads as follows..
"The only way of discovering the limits of the possible is to venture a little way past them into the impossible."
In exactly the same way, one can determine whether a definition's logic holds up universally by testing whether it works at the extremes, in the reality that the indiscrete numbers represent, as opposed to only working in the discrete realm the mind imagines. Thus, I often symbolize the extremes of a situation through the indiscrete numbers: 0, 1, and ∞, the symbols for extremity of value.
Want an example? Einstein derived his famous equation by reasoning at the extremes: photons exhibit no mass, yet the maximum theoretical velocity (the speed of light); furthermore, he imagined his thought experiment within a deep space scene, implying practically no gravity or other external forces involved. Such controls tend to take the form of 0 and 1 extremes: nonexistences (such as no gravity) and universals (such as continuous lack of gravity), respectively. A photon was excellent to do a logical thought experiment about, since its extremes exposed the hole in the fallacious assumption that "momentum is dependent only on mass". As the article explains..
First of all, let us consider a particle of light, also known as a photon. One of the interesting properties of photons is that they have momentum and yet have no mass. This was established in the 1850s by James Clerk Maxwell. However, if we recall our basic physics, we know that momentum is made up of two components: mass and velocity. How can a photon have momentum and yet not have a mass? Einstein’s great insight was that the energy of a photon must be equivalent to a quantity of mass and hence could be related to the momentum.
By thinking metacognitively, he reevaluated this assumption at the extremes of his thought experiment, realizing that momentum is dependent not only on mass, but energy as well. And ofcourse the formula is this insight in algebraic form; Einstein ends up demonstrating this in showing that mass and energy are equivalent in proportion to the speed of light; energy = mass * the speed of light squared.
What makes the extremes in any context so important is that they will reveal, through metacognitive reasoning resulting from logical thought experimentation and other methods, whether the foundations of a system of logic hold up in all cases or if they break down and fail, to be proven nonuniversally applicable.
Infact, as part of my philosophy, I have discovered that even our basis of logic itself is imperfect, for it is a contrivance for human convenience, based on the lesser contrive of discretion. However, this means it is still tremendously useful for the conveyance of other (necessarily discrete and human) thoughts, such as those followed in unlearning imprecise understandings. Just, I will usually be explaining how false assumptions lead to contrivance and confusion. You will find that understanding the philosophy of The Equivalencies is more a process of unlearning than one of teaching.
It is most helpful to evaluate reasoning at the extremes, because my philosophy primarily deals with metaphysical questions. This is due to the 'meta' component of the word 'metaphysics' – the aspect of looking at the context of the subject instead of only the subject. So metaphysics, as a philosophy for understanding the context of the science of physics, relates to dealing with and comprehending scopes, levels, derivatives, or other terms for thinking about the subject by looking beyond its direct evaluation.
By definition, metaphysical topics include: being, knowing, substance, cause, identity, time, and space. They are the context for everything we discuss. Which means they are those concepts which one has difficulty providing context for, because they are metacontextual. These concepts are also deemed "abstract", "with no basis in reality", by the definition I found. However, I think this classification is confusing labels with reality. I find discussion of the metaphysical themes to be more of a grasp toward understanding reality than discussion of numbers, names, or any other more specific – and thus (I'm arguing) abstract – topics ever are. I think there is a confusion of specificity (such as, for example, the identification of an animal species in the wild) with reality (because specificity is practical). To truly get a feel for the way reality is, it must be understood that specificity is contrived, and thus more abstract than the first principles of things that are the defined topics of metaphysics. That is to say, identifying a bear in the forest is a more abstract thought process than discussing the apparent flow of time, because the idea is more complicated, more thoroughly contrived due to being specific. You can see the structure of each specificity visually, like so:
(2) grizzly bear
In this nested depiction, the level 0 is the holistic level of no specificity. 1 is the level of the topics, and 2 is the specific level of subtopics. The depth of contrivance of ideas of grizzly bears and time are being compared.
The point is, while it's often more practical to talk about specific things, like what kind of animal you see (what if it's dangerous – it's useful to give it a name so others are aware of the danger), it's actually more abstract. Time is so essential to existence that it is talked about in the context of nothing less that which is most real, the universe. It's talked about in a subholistic, and thus minimally-yet-still-slightly -abstract context. The only thing less abstract would be that which we don't talk about, our actual sensations and experiences, the level 0. That's what's perfectly precisely real, making it the epitome of all these words approximating reality... and as such it is always more real than the ideas of any discussion.
By the meta manner of understanding, the way in which evaluating reasoning at the extremes is helpful is that it allows reasoning to go beyond the immediate scope of the subject, while still staying relevant; by considering the extremes of a subject, you can find the continuity between that subject and others. You can think in a holistic manner, evaluating the highest scope of consideration so as to stay as consistent as possible. This continuity is critical because the whole universe is continuous, real only as an equality, and so understanding must be consistent as well.