Intelligence

νοῦν δή τις εἰπὼν ἐνεῖναι, καθάπερ ἐν τοῖς ζῴοις, καὶ ἐν τῇ φύσει τὸν αἴτιον τοῦ κόσμου καὶ τῆς τάξεως πάσης οἷον νήφων ἐφάνη παρ᾽ εἰκῇ λέγοντας τοὺς πρότερον.


Indeed, when someone said that there was in nature, just as in animals, a mind, a cause of the good, cosmic order and of all the arrangement of things, he seemed like a sober man compared to those before him, who argued otherwise.

-Aristotle, Metaphysics 984b

But how relevant are the blueberries?

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.

venn diagram figure 1
Figure 1

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.

Figure 2
Figure 2

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.

A Philosophy of Love

Having wished to write a post on the essential consequence of the Axiomatic Law of Universal Congruity for quite a while now, I finally realised that I cannot present the argument I wish to without first posting a brief philosophy of love.  That being said, please realise that this is a philosophy of love, and hence, if you have come here in search of advice on how to pick up members of the opposite sex, you have “landed in the wrong place,” so to speak.  Anyway, here’s the post:

Immanuel Kant begins his argument in A Groundwork for the Metaphysics of Morals with a beautiful premise.  After discussing the importance of using “pure philosophy” (as opposed to more inductive, or empirically based, methods of reasoning), he writes this powerful sentence: “It is impossible to conceive of anything at all in the world, or even out of it, which can be taken as good without qualification, except a goodwill” (Kant i – xiii and 1).  Among the many implications we can draw from this premise is one concerning the substantiality with which Kant regarded the human will.  For Kant, man’s will is the very thing that defines him; it’s what allows us to call a person “bad” or “good” without reference to any exterior systems.  A will is, if you would allow me to embellish the concept, the thick, molasses-like substance of a human being.  Indeed, in Christian theology, the words “will,” “soul,” “spirit,” and “heart” are often used interchangeably.  Therefore, those things in life which relate to a person’s will, relate to the most intimate part of him or her†.

One may, of course, believe otherwise.  There is nothing that rationally necessitates the supremacy of the will in human identity, it’s all just a matter of how one defines a human.  Is a human perhaps a living creature with twenty-three chromosomes?  Or maybe a rational being that lives on earth?  However, any such metaphysical questions seem of little value to my argument at present, and therefore, I simply ask that any objection you might have with the above assertion be regarded as a misunderstanding of my usage of the term “human” within this thread of posts, for I will use the word to mean, essentially, a free will.  One is free to believe that a “human” in the sense that I use the word, is actually called a “rock,” but if that were the case, I would simply ask such a reader to mentally replace any references I made to “humans” with references to “rocks”.  For what is important in metaphysics is not so much the definitions of words as the definitions of things, and therefore, one cannot raise a metaphysical objection to the above premise, as it simply serves to set up a linguistic framework.

With that in place, let us turn to a discussion of love.  As you probably know, the Ancient Greeks referred to love using primarily four terms: στοργή (storge), φιλία (philia), ἔρως (eros), and ἀγάπη (agape).  All four of these can be translated as “love,” but can also be individually translated as “affection,” “friendship,” “romance,” and “charity”.  However, there are also other Ancient Greek words that may be translated as “love”.  For example Ἀφροδίσια (Aphrodite), the name of the Greek goddess of love, is also the proper noun “Love”.  Love, in this sense, is the kind of love with which the goddess was associated, i.e. the physical aspects of the love that exists between men and women.  Because each of these translates as “love,” they may all be thought of as different definitions or usages of the word.

Perhaps, in modern times, one might like to add another part to all these definitions of love and say that love is an emotion.  And once that has been done, a modernist may feel quit satisfied that he or she had formed a nice, hefty and broad definition of love, and then may retire from further inquiry.  However, I would like to propose that such a thinker has made a mistake.  But remember, metaphysics deals with defining things, not words, and so my objection is not to any given definition of the word “love,” but to a contradiction that arises by considering emotion to be a second component of each of the above mentioned.

We may group all the above definitions of love in two categories: the intellectual, and the physical.  Each of the Greek loves have elements that fall under either of these categories; however, agape may be considered the most purely intellectual of loves, and Love herself, the most physical.  The contradiction I have mentioned lies in considering physical love to be an emotion.  An emotion, as most understand the word, is something related more closely to the cognition than the body, and hence, may not be directly caused by a physical incident.  Take Hamlet as an illustration:  when Hamlet is stabbed with an unbated rapier, he feels physical pain, but in order to feel emotional pain, something nonphysical must happen: he must lose a loved one.  In this case, it is not the physical fact of the loved one’s death that causes him pain, but the nonphysical fact that his relationship with that person (whether his father, mother, girlfriend, or others) has ended.  When Ophelia dies, he doesn’t groan that physical blood is no longer pulsing through her arteries, but traces his grief all the way back to a single source, which is manifest in his groan, “I loved Ophelia”.  Therefore, if love is to be an emotion, it cannot be a purely physical phenomenon, but we should rather expect it to behave as any other emotion.  Like grief over a death, love should be something that stems from a nonphysical event which is associated with a physical one.  Where grief may stem from the nonphysical termination of a relationship associated with a physical death, love may be the emotion which stems from agape and is associated with Aphrodite.  Thus, if love is to be called an emotion, it may not also be physical, though physical processes may be associated with it.  Hence only the intellectual category of love may be called an emotion.

Notice my usage of the words “stems from”.  I am essentially saying that love, the emotion, is caused by agape.  That is, the emotion of love is caused by charity or, as it is sometimes translated, “unconditional love”.  It may sound silly to say that love is caused by unconditional love, but this little word-game actually harkens back to The Nature of Causality.  In other words, since causality functions in reality as logic does in the nonphysical, an effect can be understood as a reformulation of its cause, just as a conclusion is a reformulation of a premise.  Therefore, what is truly being said is that the emotion of love is a reformulation of charity.

With that being as it is, we must ask, what is the cause of charity?  The answer is will.  Indeed, the only way a person can love someone unconditionally is by so choosing (for if one loves for any other reason, he or she is loving on the basis of a condition), and hence the emotion of love, being a reformulation of charity, is also, by the transitive property of causality, a reformulation of will.  In other words, love, the emotion, is purely an act of volition.

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† Of course, many will notice that in this first paragraph of mine, I have done little to support my (or Kant’s) premise with deductive argument, but have instead relied almost entirely on the aesthetic of the concept.  The idea I have presented is, in a sense, aesthetically pleasing, and therefore, its rhetoric lies in our own desire to believe it.  I will turn to qualifying the premise in a moment; however, I must first urge you, my astute reader, to remember this phenomenon—of arguing by aesthetic—as we will find ourselves better suited to asses the validity of such a method of argument later on in this current thread of blog posts.

Work Cited

Kant, Immanuel. The Moral Law. Trans. Paton, H. J. Johannesberg Bay: Hutchinson & CO, 1948. Print.

The Axiomatic Law of Universal Congruity

I am afraid this post will be a particularly difficult read for some audiences, but I do believe that most people should be able to get something out of it if they try hard enough.  However, if any of my readers should happen to have a degree in philosophy—for whatever strange reason—I should expect that he or she will find this particularly interesting.

If there’s something you don’t understand, please comment; ask questions.  I don’t have an editor (such is the nature of blogging) and so it is likely that the piece could use some revision, and questions from readers could help with that process.  No question is too shallow; even if you don’t understand this at all, readers and I could benefit from any question you might come up with.

In order to accommodate for this article’s richness in footnotes and such, I have implemented a new format: Whenever you see a *, click on it to open the footnote in a new tab, and whenever you see a word highlighted, click on it to open a note that has been included for increased accessibility—also in a new tab.  When you hear the chime, turn the page.  For a printer friendly version of this post, click here.

Please read scrupulously; it should make sense.

Introduction

I would like to propose an argument for the necessity of the fractal structure that I have hitherto used for modelling Reality.  In my post, “Fractal Reality,” I have begun to describe the practicality of understanding reality as an infinite structure of concrete truths; however, by my assessment, I have not adequately addressed the necessity nor the consequences of such a model.  I intend to undertake the former of those tasks here and complete the latter in a later post, but I suspect I might end up using more posts than that for a more complete investigation of this subject.

The nonphysical

In order to model reality, we must begin by considering what reality is.  It seems the most obvious place to begin such an inquiry is with the debate between materialism, idealism, and dualism.  However, as delightfully cliché as such a method of argument would be, I find it infeasible.  For it doesn’t seem reasonable for me to use logical argument, something from the purely “idealistic” realm, to ponder the validity of the materialistic realm.  Just as it doesn’t make sense to debate relativism using absolutism, so is the materialist required to hold his or her beliefs without theoretical reason, for the existence of nonphysical reasons for a set of beliefs seems to imply a belief in the nonphysical.  However, by the same thinking, we might also suppose that holding a set of beliefs at all constitutes the act of investing faith in the idealistic realm.  Therefore, within a reasonable scope of thinking, one may be either an idealist or a dualist, but not a materialist.  Whether one happens to be a dualist or an idealist is immaterial to this argument at present so long as it is agreed that there is at least some component of reality that is nonphysical.

With that in place, let us examine this nonphysical component.  We might consider this component to be something like Plato’s world of forms; that is, the nonphysical is a sort of normative understanding of reality.  Things in the nonphysical behave in accordance with our cognition.  For example, whenever one imagines a circle, it exists in the nonphysical, because all that is required for the spawning of an object in the nonphysical is the decision that it exists.  If I decide that there is a circle of radius R, then there is.

Let us further explicate this nonphysical realm by using the physical realm as its analogue.  If we presume that the physical realm is governed by the laws of physics, we might similarly regard the nonphysical as being governed by the laws of logic.  Therefore, while I can decide that a circle exists in the nonphysical, I cannot decide that a square circle exists, as that defies the laws of logic.  We may also understand the physical realm as being perceived by us via our five senses, but the nonphysical realm must be perceived through a nonphysical sense: our reason.  All this seems a quite necessary part of any scope in which logical argument can have significance.

Definition of logic

Continuing with our analogy, let us define logic.  We are able to use the word “physics” in two primary senses: (1) physics is a field of study, a branch of science, and (2) physics is something that belongs, in some sense, to a physical system (e.g. the physics of airplanes).  Likewise there are two common uses of the word “logic”: (1) logic is a field of study, a branch of mathematics, and (2) logic can belong to a nonphysical system, an argument.  We often speak of “the logic of an argument,” or “the logic behind an argument.”  This is the thing that I wish to define.  Logic in this sense is a chain of reasoning, or to be broader, a normative construct, that adheres to the laws which govern the nonphysical.  As has already been said, the laws that govern the nonphysical realm are the laws of logic, in the first sense of the word.  So logic in the second sense is a normative construct that adheres to the laws of logic in the first sense.  Therefore, to examine logic in this second sense, we must understand it in the first sense; hence I propose the question: What are the laws of logic?

In order to arrive at the laws of logic, it seems prudent to make a distinction between laws and methods.  On the surface, it appears that the laws of logic must be very complex and there must be many of them.  We could list all of the logical operators, explain how they work, and use them to derive what we would call the “rules of inference,” but I would categorise all such work as the derivation and identification of functional methods of logic.  The methods used to solve physics problems involve complex mathematical equations, but the actual laws of physics are the reasons that physical systems behave in a way that can be modelled by such methods.  For example, it is a law of physics that matter is subject to gravity, but it is a method of physics to use a parabolic function to model gravity.  Gravity itself is the way physical systems behave, and all formulas and explanations about gravity merely constitute a methodology for understanding that behaviour.  Indeed, the laws of physics are the very things that make physics what it is; all the rest can be viewed differently by different people and still function.  That is, I can write the equation for gravity differently, and I can use different words to define gravity, but I can’t change what gravity is.

The same is true of the methods and laws of logic.  The laws of logic are what make logic what it is.  On a fundamental level, I would argue that there exists only one law of logic, in this sense, and it is the law of noncontradiction.  (Ironically, the law of noncontradiction is considered the “second law” of aristotelian logic, but I regard the other two as “methods” under the linguistic framework I have set up.)  Noncontradiction is the only law of logic because it alone is what the methods of logic are intended to accommodate for.  A logician can execute an intricate and extensive proof with all sorts of complexities, but when he or she gets to the QED at the bottom, noncontradiction alone is what makes it all logical.

This seems an easy premise to object to.  Surely, if noncontradiction were the only requirement, logical argument could include all sorts of absurdities.  For example, one might argue, “All chickens are green; Hamlet is a chicken; therefore, Hamlet is green” .  And by this understanding of logic, that argument is logical; it doesn’t contradict with itself.  What’s wrong with the argument is not that it is illogical but that its premisses are false.  Therefore, it must be understood that an argument may be logical and still not accurately reflect the empirical facts of reality.  However, a logical argument which accurately reflects reality in its premisses will also accurately reflect reality in its conclusion.

Therefore, logic is that which is noncontradictory with itself.

A qualification of reality

And now I will indirectly return to the discussion from earlier regarding materialism and idealism.  The definition of logic which we have just arrived at tells us what logic is, but not how it functions.  Logic is designed to accommodate for its function: that of discovering truth.  Logic describes reality to us via the derivation of conclusions from premisses.  Hence, we suppose that if we are given accurate premisses which describe reality, we can manipulate them using any number of methods, and so long as we adhere to the law of logic, the law of noncontradiction, we will arrive at an equally accurate conclusion about reality.*

This tells us something of the nature of reality.  As it turns out, all reality must adhere to the law of logic, not just the nonphysical.  For the very reason that logic has the law it does is that we presume reality to have that same law.  That is, reality is naturally subject to the law of noncontradiction, and the nonphysical is thus modelled after such a stipulation.

Calculus

And now I should like to explain some calculus to make this argument more clear:

In calculus, infinity is assumed.  That is, if there exists any system that increases without bound, then it is assumed that the system approaches infinity.  Hence, we can determine what a system will approach, i.e. its limit, based on its rate of change.  If a system increases at a decreasing rate, it will have a finite limit, but if it increases at a constant or increasing rate, the system will approach infinity.

The second mathematical concept that must be understood before the argument may continue is orders of infinity:

This is something of a paradox that we live with in calculus.  It is supposed that, while one system might have a limit of infinity, another might have a limit of infinity squared, and though both are equal to infinity, the one is infinite times less than the other.  Hence the limit of y = x as x approaches infinity is infinity, but the limit of y = x ^ 2 as x approaches infinity is infinite times greater than the former infinity.  In fact, the application of any operation of higher power than addition/subtraction to infinity will affect the order of infinity (i.e. infinity times, to the power of, etc. any finite number is a different order of infinity).

Why the nonphysical is infinite

Let us suppose that the nonphysical realm, which is subject to the law of logic, is a subset of some “conceptual realm.”  This conceptual realm is not subject to the law of logic but is made up of everything that can be conceptualised.  In fact, such could be its analogous law: the law of conceivability.  By this I mean that all things in the conceptual realm are governed by the law of conceivability, which dictates that all its subjects must be conceivable.  Let us call each of these “things” in the realm “declaratives,” meaning statements in the indicative mood.

I would argue that this conceivable realm is infinite—that there is no limit to what can be conceived.  By this, I do not necessarily mean that there is no limit to what the human mind can conceived, but that there is no limit on conceivability in itself (I do not wish to make any comment on the former of those claims).  This is because there is no limiting factor on the system of conceivability; the law to which it is bound excludes nothing from its domain, and therefore, if we imagine the realm as some universe that expands as an omniscient being continues to conceive of more and more things, there is no reason we should expect its expansion to ever slow down.  It is a system which increases at a constant rate, which means that it approaches infinity because infinity is assumed.  However, the nonphysical is a subset of this conceptual realm in that it is possible to conceive of illogical things, but by definition, such things cannot spawn in the nonphysical (e.g. a square circle).

This poses a problem.  If we look at the nonphysical by itself, we may very well expect it to be a finite realm, for the more things which are spawned in the nonphysical, the harder it is to come up with things that don’t contradict any of them.*  One might relate the expansion of the nonphysical to the covering of an elaborate lie.  As a suspicious other asks the liar for more and more information about the subject, the liar’s task becomes more and more difficult as he tries to avoid contradicting himself through creativity and strategy.  The difficulty lies in the fact that each thing he says is required to be in noncontradiction with the growing construct of falsehood that has come before it.  For this reason, it seems the nonphysical must have a limiting factor; it appears to be decreasingly increasing, which, in calculus, means that it has a finite limit.

However, appearances are often deceiving, and a statistical approach to the problem proves such to be the case here:  As has already been said, the nonphysical is a subset of the conceptual, where the conceptual is an infinite set of declaratives.  For every declarative, there exists a negation.  For example, if there exists a declarative, A, which states, “the pen sits on the table in the room,” then there also exists a negation, ¬A, which states, “the pen does not sit on the table in the room”.  Both A and ¬A are, in this case, dependent on other implied declaratives, the most obvious one being a declarative, B, which might state, “the room has a table in it”.  Therefore, spawning ¬B in the nonphysical excludes the possibility not only of spawning B, but also of spawning A or ¬A, and therefore one might at first suppose that this reduces the number of possible inclusions by a greater quantity than that which has been included; i.e. we have included only one declarative, ¬B, but in so doing have excluded two: B and (A or ¬A).  However, we have also opened up the possibility of including other declaratives which are dependent on ¬B.  For example, declarative C might state, “the absence of furniture makes the room feel bland”.  Both C and ¬C would have been excluded by spawning B; therefore, while by spawning ¬B, we exclude the possibility of spawning two other declaratives, we do the same, in quantitative terms, by spawning B.*  In fact, within an infinite set of declaratives, there will exist an equal amount of declaratives which become includable as which become no longer includable upon the affirmation or negation of any given declarative.  This is because within a finite set of declaratives, X of them might be excluded upon the inclusion of declarative A and Y of them upon the inclusion of ¬A, but we have no statistical reason to suppose that either X should be greater than Y or Y greater than X (for in fact, A could be reassigned the value of ¬A, in which case, X and Y would also switch values), and therefore, on average, X is equal to Y, which means that, in the case of an infinite set of declaratives, X always equals Y.*

What this tells us then is that with every expansion of the nonphysical, an equal number of declaratives become includable in the nonphysical as become no longer includable, and therefore, the percentage of declaratives in the conceptual which may be added to the nonphysical remains constant.  Thus, the nonphysical is a fractional subset of the conceptual, and is therefore infinite (though by a lower order of infinity than that which describes the magnitude of the conceptual).

By this model, we should indeed expect the system to behave the way it did in the case of the liar.  For the liar is only capable of thinking of a finite quantity of declaratives quickly enough to use them (I’m still making no comment on the full capacity of the human mind).  Therefore, while each addition to his lie is opening up an equal number of possible additions as it is taking away, some of the new possibilities are not present in his finite selection of declaratives, and he is therefore only affected by any of the exclusions which happen to be in said selection.

A nonphysical construct can now be defined as “any infinite construct which is noncontradictory with itself”.  We should expect there to be multiple such constructs based on the calculus.  Theoretically, there are infinite declaratives that exist in the conceptual which were excluded from the original nonphysical construct, but any one of those can serve as the starting point for an entirely unique, infinite, nonphysical construct.  Thus, there are at least two possible nonphysical constructs, but only one reality, and for this reason, it must be possible to conceive things that are not real.*

A definition of reality

From two sections ago (“A qualification of reality”), we have found that it is possible to put anything which exists in reality into the nonphysical, and anything that exists in the nonphysical might exist in reality.  One must then ask, does everything in the nonphysical exist in reality?

I do not so much wish to answer that question directly, but rather propose a model of reality that relates very specifically to the nonphysical.  Elsewhere on this blog, I have discussed The Necessity of the Omnipotent.  In that post, I wrote that due to the nature of causality—causality being an inescapable facet of reality under the logical scope—there must exist something in reality that is somehow “omnipotent,” or as the word came to be used in the jargon of the piece, “uncaused.”  This primal cause argument is often referred to as the “cosmological” argument by people even more esoteric than myself.  Simply put, there must either be a primal cause which exists without cause and which caused all the rest of reality or else there must be an uncaused, infinite chain of causality that makes up reality.  As I have elsewhere observed, the two of these possibilities seem very much to be merely two different ways of expressing the same thing: the omnipotent, or uncaused, thing is both the cause of reality and the essence of reality.  All this means that reality is necessarily infinite.  Everything is real.

That being the case, reality is an infinite construct that adheres to the law of logic; in other words, reality might be defined as “that which is noncontradictory with itself.”  I say “that which,” and not “a subset of that which” because reality includes all existing things that are noncontradictory with themselves.  By definition, nothing exists outside of the domain of reality.  I do not mean that nothing can be imagined that does not exist, but rather, everything that exists is a part of reality, and all those things are noncontradictory.

Because reality is infinite, we know that it is made up of infinite declaratives, for the phrase “reality is infinite” could be reworded “there exist infinite truths”.  Therefore, reality has the exact same form as a nonphysical construct: it is an infinite construct of noncontradictory declaratives.  The law of logic rules both the realm of the nonphysical and that of reality and insists that their respective systems be defined by their noncontradiction with themselves.  In other words, they are defined in terms of themselves.

The singularity of reality

Saying that reality is defined in terms of itself may seem prima facie objectionable to some.  It is not immediately evident that reality is defined in terms of itself, but rather that each of its parts are associated with certain qualifications that relate them to each other part (by “part” I mean “declarative”).  But as it turns out, these qualifications do in fact serve as definitions as well.  A definition is a description for which only one thing is qualified to match.  This is the nature of the noncontradiction qualifier.  We understand reality as being entirely causal, even in the realms beyond the natural (see “The Necessity of Causality in the Logical Scope”), and as such, reality must exist in the only possible state which is logically permissible.  For each set of causes has but one set of effects; it is not possible for some part of reality to be different than it is unless its cause is also made to be different than it is, and then that cause’s cause would have to be modified as well, and one would need to trace the whole thread all the way back along the infinite chain of causality until he reached the Omnipotent, who would also need to be changed, which is an Omnipotent impossibility (see “Absolute Nonsense”).  Hence, if we change any single declarative that makes up reality, it will be in contradiction with the whole, and for this reason, the system of reality is defined by noncontradiction.  Noncontradiction describes each part of the system such that only one thing is qualified to match the description.  And because the system is defined by noncontradiction with itself, it may be said to be recursively defined.

The structure of reality

To better understand what sort of structure this forms, we must subscribe for a moment to a scalar model of reality.  It is generally presumed that any individual is capable of perceiving some portion of reality, but not the whole; i.e. everyone knows something, but no one knows everything.  However, I would like to propose that the “something” which everyone knows is a particular scalar view of reality.  What each individual knows about reality is not just some random subset of the whole, but some finite-scaled scope, however incomplete, of reality.  By this I mean that a person may know or be capable of learning all sorts of things on a given level, but there will be some nuances of reality that are, in a sense, too “small” or “detailed” for anyone to understand, as well as some truths that are too large.  We can’t comprehend the entire universe, and neither can we understand why protons and electrons attract and repel.  We might think of this scalar construct as something that is explored via inquiry.  That is, we might be within one scalar scope when we know A, but when we ask how A works, we move to a finer scope, and when we ask what A does in the context of systems outside itself, we move to a coarser scope.  However, though not perceivable all at once, each of these scopes are contained within one another, and there are infinite of them.

It is this concept of unperceivable scopes which troubles many a modern thinker into some form of relativism.  It is supposed that if there exist infinite scopes which we cannot perceive, then all our knowledge is useless.  However,  the recursive nature of reality at which we have already arrived would suggest that such a conclusion does not follow.  For in fact, every level of reality is defined directly in terms of every other level.  As I have said, it is not the case that the parts of reality merely relate to each other according to noncontradiction, but that, under this scalar model, each level defines each other level via noncontradiction.  This creates what appears to be a paradox on the surface.  Each level is defined as the only thing that is noncontradictory with each other level.  In other words, if a level of reality A contains a finer level B and B contains C, then A is the only thing that is noncontradictory with B, but C is also defined as the only thing that is noncontradictory with B.

Most will think I’ve simply made a slight oversight in inventing this paradox.  One solution might be as follows:  (1) It is not that A is the only thing which is noncontradictory with B, but that it is the only thing which is noncontradictory with B and C, and hence, each part is allowed to be the only thing noncontradictory with the remaining structure outside of itself.  As compelling as such a solution to the paradox is, it is not entirely sufficient.  For we do expect A to also be noncontradictory with itself, and so it must be the only thing which is noncontradictory with A, B, and C, but in that case, B is also the only thing noncontradictory with A, B, and C.  However, there is a second possible solution to the paradox that deals with the structure of the levels:  (2) Perhaps B is the only thing which is noncontradictory with existing inside of A, and C the only thing that may exist inside of B.  But even this does not solve the issue all together.

Each of those parts—A, B, and C—is the only thing which is noncontradictory with the whole in its particular structural context.  B is the only thing which does not contradict A, B, and C when it is structurally related to those parts in the particular way that it is.  Think of it like a car engine.   In a car engine, the only thing that may function in the particular place where the cylinder is located is the cylinder itself.  If we put the gas tank where the cylinder is, it would contradict the function of the machine, but the gas tank is noncontradictory with the function of the car when it is located in the place it is supposed to be.  In other words, each of the parts of the car are noncontradictory to its function when they are structurally related in but one particular manner.  However, in the case of the levels of reality, structure is redundant.  We presume there to be infinite levels of reality all of which contain each other.  Therefore, while C is structurally related to B in one way, B is also structurally related to A in the same way, and there are infinite other levels in which A is contained as well as infinite other levels which are contained in C.

C is the only thing that can structurally relate to B in the way it does, but B relates to A in the same way.  With this being the case, we can suppose that A, B, and C are different from each other, but they cannot be unsimilar.  “Contains” is a transitive relationship; that is, if A contains B and B contains C, then A contains C.  Clearly, this does not mean C is structurally related to A in the exact same way that B is, but the relationship is similar—congruent, if you will.  And because each of the levels of reality are what they are in accordance with their structural relationship to the rest, the levels themselves are also congruent.  This gives rise to The Axiomatic Law of Universal Congruity: “Every understanding and misunderstanding of a given scope of reality is congruent to that of the whole.”  Some readers might find it humorous to call this a “Categorical Declarative”.*

Therefore, reality is self-similar.  On every level from which we observe reality, we see something that resembles the whole.

There are many consequences of The Axiomatic Law of Universal Congruity which I am very excited to tell you all about, but I imagine that if you have bothered to read this far, you are already far too kind, and I cordially thank you for your interest.  In light of that, I will refrain from subjecting you to any further mind numbing activity.

If I imagine people more esoteric than myself, then they exist.

The Nature of Causality in the Logical Scope

if a then b => if !b then !a

Doesn’t that make sense? Why do people act like it doesn’t?

Causality is such a difficult phenomenon to isolate. This is a large part of what makes tragic plays so stimulating–we can argue for hours about what really caused all the dead bodies to pile up at the end; was it Hamlet’s slowness to act? his uncle’s murder? or perhaps Polonius’ regulation of his daughter? The best answer is generally something along the lines of, “it was all these things and more”. For maybe if Hamlet weren’t so prone to depression, if Laertes hadn’t come from France, or the dang Dane, Hamlet the late, had just decided to take his nap somewhere else or a little later in the afternoon, the whole catastrophe could have been avoided. This brings up the whole discussion of chaotic theory on a sociological level. Because perhaps even smaller changes could have been made to the history than the ones I have mentioned if they were made earlier on. Maybe if Hamlet the late had gone to bed earlier the night before, he wouldn’t have needed to take a nap˚. And maybe he would have gone to bed earlier if he weren’t busy doing such and such, and perhaps such and such wouldn’t have had to be done if… We could, theoretically trace the whole history back to the beginning of time; at which point, if a single molecule, floating in space, had been displaced by a fraction of a micrometer, Gertrude might never have married, Hamlet might have never been born, and perhaps even Denmark might never have become a nation.

Personally, I find this is fascinating. It certainly says something about the nature of causality. Every little, fractal detail of the cause has a profound impact on the effect. This is an even bigger deal when it comes to a consideration of the Omnipotent, for He is the beginning of time and the root cause of all reality. I’ve included a definition of the rule of modus tollens at the beginning of this post, with whatever disregard of formal symbols, for this reason. Many a tricky relativist likes to try to weasel his way around causality, often suggesting that every event and quality of reality is the result of nothing and our minds are merely erring in seeking out patterns and reasons for things to result from other things. As far as I’m concerned, that’s fine; if a person doesn’t believe in reality, then I should even less expect him or her to believe in the causal nature of reality. But what doesn’t work, by my assessment, is the attempt to separate causality from the logical scope. Logic, by definition, assumes the principles of modus ponens and modus tollens, or more simply, the concept of an “if then”. Therefore, it seems to be quite impossible to have logic without having causality. For logic assumes that the validity of a premise determines, or causes, the validity of a conclusion.

Within the absolutist scope, metaphysical reality is assumed to be, to some extend, comprehensible via the normative reasoning of the human mind. In a way, reason is the only metaphysical entity that we are undeniably conscious of (if you will pardon my casual use of the term metaphysical). Though reason is expressed as physical phenomena in the brain, the pure properties of logic, that express themselves in the mind, must be considered metaphysical, or as I am using the word, real but not tangible. Because of this, there is a sense in which reason must dictate our beliefs as to the qualities of reality as it exists beyond the purely physical. Just as we assume physical reality to have the qualities which are perceived by our five sense, we must also assume metaphysical reality to have the qualities perceived by our sixth sense–our mind. If the fact that we see in colour leads us to believe that the universe is colourful, then the fact that we reason causally must lead us to believe that the normative is causal. And if we believe there is anything beyond the physical–which we must believe, for by the very act of thinking logically, we are engaging such a realm–then we must believe that reality is ultimately beyond the physical†. Therefore, in the same sense of the word, “reality” is ultimately causal in nature.

This being established, we must consider the nature of causality as it exists in reality to be the same as the nature of causality as it exists in reason. Let us consider what this nature is.

It may be useful here for us to rethink the conventional concept of a logical proof. Proof is commonly thought of as a sort of sequence of steps that lead from a given to a conclusion. This is all fine and well, but let us consider what it really means. If the rules of logic are universal, then a proof is not the act of taking one thing and transforming it into another, but rather the human explanation of why one thing is also another. Take a mathematical proof for instance. If we want to prove that 0over0 equals one in the context of “limit x–> 0 f(x) = sin(x) / x”, we take the function and limit as a given, go through a series of steps, and show why it equals one. But we have not in fact converted one concept into another. We have merely shown that by logic, the one concept is the other, for at the end of the proof, we realise that the given expression is equivalent to the concluded one. There is no conversion process from premise to conclusion; proofs only serve to show us that a premise is the same thing as a conclusion.

In the same sense, we must also consider causality to be, like proofs, a human way of understanding that a cause is, normatively, the same thing as its effect. Therefore, returning to the Omnipotent, He must in this same sense be, as the primal cause, the same thing as His effect. This is why I so often write that He is reality. And thus, if He is everything that is Real, He must possess every quality that is Real. Therefore, if we assume that our reason is Real, then we must believe Him to be rational. To me this is the easy part of the argument. It is self-evident that the cause of all Reality would have to be rational if there is such a thing as reason. Reason must be linked, by causality, all the way to the beginning of existence, the primal cause. And only things that are not real in some sense* may posses “qualities” not possessed by the Omnipotent (see “Theology of Non-being”)˚. All this follows from (or is) what is written above.

And now a point of interest: What also “follows” from above is that the Omnipotent is very large. Certainly, we already knew He was infinite and we are “finite,” but the Hamlet example can give a very good explanation for this. If every effect is affected by smaller and smaller details of its cause the further along the chain of causality that it gets from that cause, then with the Omnipotent having existed eternally before time began, we must believe that we are the effects of his infinitesimals. That is, if the Omnipotent is a giant fractal at the beginning of reality (and really making up all of reality), then we, being effects that exist some infinite distance along His causal chain, must be caused by the smallest possible details of Him, and therefore, are the smallest possible details of Him. However, it is important to note that, with Him being the highest possible order of infinity–paradox that that is–even his infinitesimals must be infinite, and therefore, while He is infinitely greater than us, we are still, in this sense, infinite ourselves, so long as we actually exist.

This means that the Omnipotent is capable of considering us infinitely, while at the same time conceiving an infinite universe, and for that matter making an infinite number of other infinite creations all of which He plans for and cares about infinitely. This seems to present a reasonable rebuttal to the objection that there cannot be a personal God because the universe is so large.

Such is one of the arguments that Richard Feynman brings up in the following video. He doesn’t really focus exclusively on that topic, but he says some other interesting things as well, which I thought made the video worth posting:

____________________

˚ Okay, I suppose it was “his custom always in the afternoon”, but still, would he have upheld that custom even if he wasn’t tired? Of course there is no definitive answer to such a question, but that’s my point: the causality is hard to isolate.

† For it is only beyond the physical that we are ultimately able to say that something exists, as the very notion of existence is a normative principle, and all the qualities of reality are normative, because, while we might describe a physical object as having “physical qualities” those qualities themselves are concepts (ex. an apple is red, but redness is a concept). This might just sound like a word game to many, and I realise that I may be over simplifying a much larger issue–and one that is largely disagreed about–but consider it as this: Somewhere in your mind, you differentiate between the way you view and understand the physical and the conceptual. You, by your very nature as a human, attach to those to realms particular values. That is, each of them means something different. Whether you want to call the one or the other “more real” doesn’t really matter much to this argument, so long as you realise that when I discuss reality, I will be referring to the conceptual or normative, and not just as it exists in our minds, but as it actually exists, even beyond them. For I am assuming–the absolutist that I am–that two plus to actually equals four, not that it just happens to in our minds. Without this sort of assumption, there is no actual point in thinking at all (in the same sense of the word “actual”).

* As darkness can be said to be a thing, but is really nothingness, it is the absence of something, so can there be things that are defined by their lacking of realness, they are the absence of realness.

˚ Here is another way of looking at the irrationality of evil discussed in “Theology of Non-being.” Irrationality is allowed to exist in evil, though it is not a quality possessed by the Omnipotent, because evil is, in a sense, “unreal”.

On Probability

That’s such a stuffy tittle.  You might call it “The Possibility of Probability,” or “What Happens With Chance,” if you like.

I thought I might be of some use to my readers if I were to write a brief article on this subject.  Please note that this is primarily a philosophy paper and not a mathematics one; though, of course, the two subjects are, as all subjects, inseparable and hard to distinguish from one another.

It is, and rightly so, the most commonly accepted model across all subjects that all probability is metaphorical.  From basic physics, we reach the self-evident conclusion that all physical systems have a predetermined out come from the moment they are set up.  Therefore, when this principle is applied on a macro-level, we reach the modern understanding of Chaotic theory; that is, that the entire universe is one giant physical system, composed of the interactions of countless smaller systems, that has had a predetermined course of action from the moment it was set up.  Thus, according to our understanding of physics, there was a one-hundred percent chance, since the dawn of time, that you would be sitting in the exact spot that you are currently, at this exact time, reading this exact sentence, and thinking the exact thoughts that you are thinking right now.

Of course probability is still a very useful concept in many cases.  One excellent example is genetics.  We still use the assumption that inheritance is “random,” and therefore, that the mathematical principles of probability can be applied to determine the “likely-hood” of one trait being passed on versus another.  This method of evaluation is very practical because the chaos involved in the system is so developed that it can be assumed to be random–it functions much like a small angle approximation.  However, according to our larger model, there is no such thing as randomness in the literal sense.

It is imperative that we understand the universality of this principle, even as we venture into metaphysics.  In the absolutist’s scope, probability is still only metaphorical when it comes to metaphysics, and one can use the physical metaphor of probability as an analogue to the metaphysical one.  As I have indicated in my post on fractal reality, there is a fine line between the metaphorical and the literal, and perhaps even no line…metaphorically.  But in the case of probability, there definitely is a line, as the actual relationship between the metaphor and the reality it represents can be entirely understood by the human mind (that is, if anything really can).

In metaphysics as in physics, the whole principle of metaphorical probability is designed entirely for the sake of convenience, and is not actual believed when it comes down to what is really happening.  Thus, in physics, we can estimate the probability that a cannon firing a tennis ball will hit its target, while in reality, we know that if we had every specific detail about the set up of the system to an infinite degree of accuracy, we could know for sure whether it would.  Likewise, in metaphysics, we can say that there is a freedom of the will such that at any given time it has a certain chance of making one decision over another, but in reality, we know that if we knew every single detail about the soul (which is fractal), we could say for certain which decision it would make.  That’s not to say that the soul isn’t free, but that its freedom is not bound to time.  All of time is a metaphor when it comes to metaphysics.  The whole story of a soul choosing between death and life is thus an embodiment of the soul in the medium of time, all though, a complete knowledge of the soul outside of such a scope would allow for a knowledge of the soul’s every decision “before” it was made.  It is as if, in both metaphysics and physics, time is merely a way of looking at a complex system part by part.

To take this a little further, consider a four-dimensional cube.  We can only express such an object in the form of a hypercube, which is a three-dimensional object that changes shape over time, thus expressing each of the different four-dimensional angles form which the real object can be viewed.  But in four dimensions, all those angles are present without any need of morphing.  Likewise, a fractal-dimensional physical or metaphysical system must be expressed by morphing a “three-dimensional,” or what I will call, “normal-dimensional” (to avoid a bias towards physics), one over time.  (and I said this article wasn’t about math)

But when we talk about the limits of either of these systems, we must set aside our normal-dimensional perceptions and likewise our metaphorical probability.  There is no “chance” that the end or beginning of time did or will look one way or another physically or metaphysically.  It just was, will be, and if we are to be most literal, is.  Thus, when we talk about the qualities of the Omnipotent, there is no chance that they are one thing or another, they just are what they are.  This understanding excludes the possibility of an arbitrary Omnipotent “happening” to cause an intelligent humanity.  In the literal sense, nothing about metaphysics is random, and because when we discus the Omnipotent’s first action of causing, we are referring to a limit, even the metaphor of chance is senseless.  Therefore, if we are to say that humanity is intelligent, then we must also say that the Omnipotent is intelligent.  For an understanding of logic cannot “happen” to arise from nowhere.  It must, at the limit of causality, have been present in the origin of reality.

As for the objection that computers are “more intelligent” than the human beings that have created them (this objection was posed by a commenter).  My answer is, no they are not.  The intelligence that this, and all my arguments on the Omnipotent, are referring to is the one upon which the scope of the argument depends.  That is, the argument depends on the fact that human logic is capable, to some extent, of finding and understanding metaphysical truth.  That we can build a computer that emulates some of the mathematical algorithms of the human mind does not mean that we have created something “intelligent” in this sense of the word.  It only means that we have found a way of putting that human intelligence into general terms, much like writing it down.  If I throw a baseball through a window, I have broken the window, not the ball.  In the same way, it takes a human to know that a particular circuit pattern will perform a particular task, but the circuit pattern doesn’t know the first thing about the matter, it is only a tool which is being used by someone who does.  Therefore, computers, which have no understanding of human logic, are not intelligent at all.