The Essential Consequence of the Axiomatic Law of Universal Congruity

Yes, I realise the title is disgustingly long, but it had to compete with A Groundwork for the Metaphysics of Morals, which is a German title in translation—so that’s not really fair.

FYI: ALL THE POSTS ON THIS THREAD MAY, from now on, BE FOUND UNDER THE ALUC CATEGORY. Thank you.

Acts of Reason

From the little research I have done, I have found that the concept of speech acts mostly has its origins in the philosophy of one J. L. Austin.  Austin proposed the theory that certain forms of speech are actions in themselves.  For example, whenever one begins a sentence with “I promise …” an action beyond the mere act of speaking is being performed—the act of making a promise.  Likewise, whenever people persuade, inform, or rebuke using speech, they are performing speech acts.  On the most basic level, a speech act is any form of speech by which an act beyond the mere pronouncement of words is performed.

Similarly, I should like to propose that there exist forms of thinking that may be called “thought acts,” or “acts of reason”.  These include acts such as believing, assuming, and expecting.  By the very thought, “this is true,” the act of belief is performed.  The thought, “this will happen,” constitutes the act of expectation.  These are forms of thinking that constitute actions beyond the mere act of thought itself; however, they are still only thoughts, or declaratives, found in the nonphysical realm of the mind.  Notice that both in the case of speech acts and acts of reason, the acts that are performed are normative.  Nothing physical takes place, for example, when a person makes a promise, but we still consider promising to be an action.  Therefore, promising, like all other speech acts and acts of reason, is an action that takes place in the nonphysical realm.  Hence the nonphysical is, in part, active.

This fits nicely with our usage of grammatical theory to explain the nature of the nonphysical.  Declaratives may be active or passive just as they are by grammatical convention.  However, it is important to realise that this is something of an extended usage of those terms.  For example, suppose Mr. Smith looks at his dog, Charlie, and thinks, “Charlie is eating”.  By doing this, Mr. Smith has performed an act of reason, and his declarative is active in two ways: (1) Just as grammatical theory would tell us, the declarative is active because the subject (Charlie) is performing an action (eating), but also (2) the declarative is active because it constitutes the act of believing (Mr. Smith believes his dog is eating).  Let us call this first meaning of “active” “grammatically active,” and the second meaning, “functionally active”.

Activity and Passivity (Voice)

It must be understood that all thoughts can only be called active or passive in the context of a particular verb.  Speech acts demonstrate this phenomenon more clearly: the speech, “I promise to love and obey” is active in the context of the verb ‘to promise’ but passive in the context of the verb ‘to run’ because the speech itself constitutes the act of promising, but not of running.  Hence, if this speech causes a bride to run, it has not performed a speech act in so doing, though it has passively caused that action.  (But of course it still performs the speech act of promising, and therefore is active in that context.)  The same will be true of acts of reason.  Every thought has a functional voice only in the context of a particular verb.

To better understand what it means for a thought to be functionally active, let us consider what it means for one to be functionally passive.  In grammar, when a sentence is in the passive voice, its subject is being acted upon rather than doing the act.  For example, if Mr. Smith had instead thought, “Charlie is being eaten,” his thought would have been grammatically passive.  However, the thought is still functionally active, as we are using the term, because it still constitutes the act of belief.

The functional analogue of grammatical voice is simple.  If a thinker is performing an action, his thought is functionally active, but if an act is being performed on the thinker, his thought is functionally passive.  The functional voice of a thought is the same as the grammatical voice of the clause which describes the thought’s action and in which the thought is the direct or indirect object.  For example, in the clause, “Mr. Smith believes the thought, ‘Charlie is being eaten,'” the thought is the direct object of Mr. Smith’s believing, and the clause is grammatically active (i.e. Mr. Smith is acting upon the thought); therefore, the thought is functionally active in the context of the verb ‘to believe’.  However, in the clause “Mr. Smith is troubled by the thought, ‘Charlie is being eaten,'” the thought is the indirect object, but the clause is grammatically passive (i.e. Mr. Smith is being acted upon by the thought); therefore, the thought is functionally passive in the context of the verb phrase ‘to trouble’. Hence, believing is an act of reason constituted by the thought, but troubling is not.

This discussion might bring to mind a rather intriguing inquiry:  Is not ‘troubling’ something that occurs in the mind?  If so, should we not expect it too to be an act of reason?  Indeed, I believe we should, but only when paired with a different thought, which in the context of such a verb, would be active.  More on this later.

Relevant Qualities of the Nonphysical

Recall this explanation of the nonphysical which I wrote in my post on the Axiomatic Law of Universal Congruity (henceforth, ALUC): “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.”  From this we see that the nonphysical can be embodied in human cognition.  We do suppose that the nonphysical is a realm of truths and falsehoods that exists with or without human awareness of it, but humans can also think about it, and in so doing, embody some part of the realm within their minds.  For example, the properties of fractals were, for a time, normative facts sitting out in the nonphysical, waiting to be discovered, until finally they became embodied in human understanding once the proper math was completed.  To be clear, let us henceforth refer to the nonphysical as it exists independently of humanity as “The Nonphysical Realm,” and as it is embodied in the minds of persons, it will be called “a nonphysical realm”.

(I wrote at the beginning of this post that acts of reason occur in the nonphysical; this statement may now be refined.  More specifically, acts of reason occur in a nonphysical realm; that is, they occur in the mind of the person doing the thinking.  Hence, when I say that a thought constitutes an act, I mean exactly that—a functionally active thought, as it exists in a nonphysical realm, is the same thing as a nonphysical act.)

Also notice from the above quote that human embodiment of the nonphysical is related to human will.  As I have written, “all that is required for the spawning of an object in the nonphysical is the decision [i.e. act of volition] that it exists”.  Hence, when Mr. Smith performs an act of reason in his mind, he is willing the spawning of a functionally active declarative in a nonphysical realm.  Indeed, acts of reason are the purest forms of willed acts, for whenever people act on their wills, they first intend to do something, and then attempt to do it.  But it is this second step that is often corrupted by misinformation and inability.  Indeed, even the first step (of intending) can be corrupted by logical fallacy or falsehood of premisses; i.e. a person can intend to do good, and out of that willed act, intend to do something that he or she thinks is good, but is mistaken.  In this sense, the relationship between acts of reason and general intentions of will is similar to the relationship between the intentions and the outcomes of a character’s actions in a play.  In both cases, we often come across “purposes mistook fallen on the inventors’ head”.  This is why Kant traces the character of a will all the way back to its noncontradiction with itself.  That is, the quality of a will can only be determined by examining the self-coherence—or lack there of—of the will’s initial intention, the intention of being good or evil, from which all other intentions are derived within more specific contexts.

This point will be important later on, but I digress from my present purpose.  What must be understood at the moment is that acts of volition are also acts of reason because intending is an act of reason.  (This harkens nicely back to the model of the soul with two faculties: the intellect and the will.  Without intellect, a will is just a random decision maker; therefore, in order for a will to be free, any act a will makes must also be an act of reason.)  To justify the claim that intending is an act of reason, we will turn to the model of functional voice developed earlier, but first we must understand a nuance that further complicates our model of acts of reason.

Human Thought

Thinking is, by nature, paradoxical.  As I have argued elsewhere, reality is infinite. Therefore, all passive thoughts and acts of reason are subject to infinite ignorance.  However, as we have found in the ALUC post, “every understanding and misunderstanding of a given scope of reality is congruent to that of the whole“.  Hence, the paradox of thought is as follows:  Thinking is, by the nature of reality, required to be infinite, but by the nature of humanity, it seems it is finite; ergo, all human thought must be inaccurate—and in fact, infinitely inaccurate.  But yet, we know, by the ALUC, that human understanding is congruent to accurate understanding, even with all its fallacies.  Thus a dichotomy exists between the validity and falsehood of thought.  To solve this paradox, we must understand the meaning of the mathematical jargon in this philosophical context.

Though it may seem a bit crude, it will be useful, for a moment, to think of the accuracy of human thought as a scalar quantity.  Suppose that any given thought has a measurable quantitative parameter of “truthiness,” if you will.  In theory, a perfectly accurate thought would have an infinite truthiness value (because reality, the truth, is infinite), but human thoughts have truthiness values that are lower than this.  The question becomes: how much lower?  Because human thought is subject to infinite ignorance, we know that its truthiness is infinitely lower than that of the theoretical ideal, but this fact alone does not tell us by what order of infinity human truthiness is less than perfect validity.  For that, we must turn to the ALUC.

By the ALUC, we know that human thought is congruent to the theoretical ideal.  In math, two systems are congruent when they differ only by a scaler multiple.  For example, two triangles are congruent if each of the sides of one triangle relates to each of the respective sides of the other by a common ratio.  Hence, a pair of congruent triangles can be derived from one triangle by multiplying the lengths of each side by the same number.  Therefore, if human truthiness is both congruent to and less than perfect validity, it must be a fraction of the whole.  Hence, the difference between human truthiness and perfect validity is a lower order of infinity than that which describes the magnitude of perfect validity.

All this may sound a bit distant from the actual philosophical thread at the moment, so allow me to draw the connection:  Recently, a friend of mine and I met and discussed the ALUC.  Upon reaching the section about the limitlessness of conceivability, our discussion branched away from the piece slightly as we began to ponder the plausibility of human beings conceiving of the infinite.  I leaned towards the belief that humans can conceive the infinite, and my friend took the other side.  “Imagine a thousand elephants,” he prompted me, “now imagine one thousand and one elephants.  What’s the difference?”  His point was that when one conceives of anything on a very large scale, the detail of the concept is sacrificed.  My mental image of a thousand elephants is the same as my mental image of one thousand and one elephants.  This is because when I conceive “a thousand elephants,” I am not really picturing an exact number of elephants, but rather some large sum of them.  However, as I argued, my mind does differentiate between the concepts themselves.

In calculus, there is a somewhat cliché idea that “infinity is a concept not an number”.  This is usually taken to mean that we can’t treat infinity like an ordinary number (i.e. we can’t perform arithmetic with it), but we can understand it as an idea.  Thus, in a sense, one cannot “wrap one’s head around” the infinite, but in another sense, humans must be able to conceptualise infinity by virtue of having a word for it.  So, while I cannot conceive one thousand different elephants at the same time, I can think the thought, “one thousand elephants,” and differentiate it from the thought, “one thousand and one elephants,” both of which have different significances to me.  In this way, a human thought can be congruent to infinite thought, which is necessary in order for it to be congruent to perfect validity.

Rational Processes

In planning for this essay, it was at first my desire to write about acts of reason in terms of individual “rational processes,” or processes of the mind, rather than in terms of what we have hitherto been calling “thoughts”.  A thought, as the term has been here used, is a declarative which exists in a nonphysical realm (a person’s mind), but people don’t always think in “thoughts” in this sense of the word.  Sometimes people think more abstractly.  For example, when a composer invents a piece in his head, he is thinking, but he is not producing concrete declaratives.  Hence, thinking may take on various forms, some of which are hard to embody in words, but in all forms, thinking is made up of many rational processes.  When Mr. Smith sees Charlie’s state of distress, his mind has to take in the empirical facts (the things his senses tell him about) and process them with a number of rational processes before he is said to be thinking, “Charlie is being eaten”.  The declarative is itself a rational process, but it is made up of “smaller” rational processes.

Indeed, by the nature of reality we know that a perfectly true thought has, associated with it, infinite rational processes, each of which constitutes the act of understanding one of the infinite parts of reality.  In this way, a perfect rational process must be made of multiple other perfect rational processes, each of which are made of others ad infinitum, thus forming an infinite, self-similar structure.  Of course, human thought, being only congruent to accurate thought, does not quite form this structure, but creates a congruent structure.

This model helps us to fix some of the awkward uses of language that have been made thus far:  Some may have found it strange to call “believing” an act beyond mere thinking.  We may, indeed, be tempted to suppose that believing cannot be an act of reason at all, for the verbs to think and to believe are often used interchangeably (e.g. “I believe you are correct” or “I think you are correct”).  And if believing is the same as thinking, then when Mr. Smith thinks, “Charlie is being eaten,” he is not performing any act beyond the act of thought itself, and therefore he is not performing an act of reason.  But there is also good reason to suppose that thinking and believing are not always the same thing, for it seems it is possible to think something without believing it.  The thought that Charlie is going to be okay may cross Mr. Smith’s mind without him believing it, for there is a difference between Mr. Smith thinking, “Charlie is well,” and him thinking that Charlie is well.  Hence, it may have been slightly inaccurate to say that Mr. Smith’s thought was the act of reason which was being discussed.  Perhaps instead, the act of reason is a different rational process in which Mr. Smith actually believes the aforementioned thought.  This rational process, however, is impossible to embody in words.  And so our language must be stretched when discussing acts of reason.

Perhaps we might say that the thought “Charlie is well” constitutes the act of believing only when it is believed.  This works the same with speech acts.  If an actor in a play says “I promise …” then he has not actually made a promise.  He only truly makes a promise if he says the words in conjunction with performing the normative act.  However, we still understand the words as being, themselves, the act of promising.  They are the manifestation or embodiment of the act, though the act does not necessarily occur upon their verbalisation, but cannot occur without it.  Likewise, Mr. Smith’s thought constitutes the act of believing if he believes the thought.  It is in his thinking “Charlie is well” that he believes it, though he can also think those words without believing them.

The Rational Process of Intention

The above argument was necessary in order to understand how intention is an act of reason.  We might say that Mr. Smith intends to do something when he thinks “I will save Charlie”.  However, some may not like this usage of language.  It seems that Mr. Smith is likely to never think the words “I will save Charlie,” but rather, will simply intend to do it.  Hence, intention is some abstract rational process which is hard to put into words.  Therefore, in order to determine the functional voice of intending, let us use the method arrived at earlier, but represent the rational processes of intending as a variable.  Suppose ‘A’ represents Mr. Smith’s intention to save Charlie.  The clause which describes the thought’s action might then be worded, “Mr. Smith intends A”.  Hence, Mr. Smith’s intention, A, is the direct object of an active clause, where Mr. Smith is performing an action, and therefore, intention is functionally active.  Hence, acts of volition are necessarily acts of reason.

The Volitive Nature of Emotion

In my post, “A Philosophy of Love,” I arrived at the conclusion that love is an act of volition.  I now wish to complicate this claim.  Indeed, not only is love an act of volition, but all emotion is a manifestation of the will.

The only reason a person feels any emotion at all is because he or she chooses to care about things.  If Mr. Smith hadn’t decided in advance to care about Charlie (to love the creature, in a sense) then he would have never been troubled by the fact that Charlie was being eaten.  Thus, Mr. Smith’s being troubled is an extension of his will to love.  This is why I began with a philosophy of love—all the other emotions are derived from love or the lack there of.  Hamlet feels grief because he first chose to feel love.

Some may find this notion absurd.  Surely, whether I like it or not, I will feel sorrow if, for example, my arm is chopped off.  However, it seems evident that my sorrow over the loss of a limb is only made possible by my original decision to value my limbs and the things I can do with them.  Inevitably, I will feel physical pain upon disarticulation, but any emotional pain is still a nonphysical act which takes place in a nonphysical realm, and must, therefore, be a willed act.  The fact that emotional pain felt over the loss of a limb is volitive only strikes us as strange because the decision to value one’s body parts comes so naturally.  It is like subscribing to a weekly news letter on the internet.  Whenever you sign up for anything, the option to subscribe to the news letter is almost always checked by default, and so it is easy to passively decide to subscribe.  (By the way, if you do not wish to be subscribed to this blog, click here.)  Likewise, it is natural to passively decide to feel certain emotions.

This gives us good insight into the inquiry raised earlier regarding the functional voice of the verb ‘to trouble’.  Recall that because the clause, “Mr. Smith is troubled by his thought,” is grammatically passive, his thought is functionally passive.  What has not been said hitherto is that functionally passive thoughts may still be understood as acts of reason; however, they are passive acts of reason.  Mr. Smith is passively deciding to be troubled.  (Realise that the above clause is grammatically passive in the context of the verb ‘to trouble,’ but it is grammatically active in the context of the verb phrase ‘to be troubled’.  That is, the act of troubling is being performed on Mr. Smith, but Mr. Smith himself is performing the act of being troubled.  In some languages—Latin, for example—there is a single verb that means ‘to be troubled’.)  This lets us differentiate between emotions that are actively willed and those which we passively decide to feel.  For example if we say, “Mr. Smith loves,” then he is actively conducting an act of reason because the clause is grammatically active, but if we say, “Mr. Smith is grieved,” then he is passively conducting an act of reason.  Hence Mr. Smith actively decides to love, but passively decides to be grieved as a result of that love.  Notice that we may say, “Mr. Smith is feeling grief,” and find that he is actively feeling grief, but he is nonetheless passively being grieved.  He has actively chosen to feel his grief by choosing to think about that which grieves him, but he as passively chosen to be grieved by such a thing.

Something

And so, emotions, whether active or passive, are acts of reason.  To feel is to think, and to think is to feel.  Emotion is a form of reasoning; a complex construct of concrete thought.  This construct must be congruent to the fractal that is reality.  Hence in its theoretical form, an emotion is made up of infinite rational processes—though human emotion is only congruent to such a construct.  And so art, the discourse of emotion, is the discourse of infinite reason.  There is no need to temper emotion with reason or reason with emotion, because both are the same thing.  Emotions are fractal constructs of reason.

Therefore, just as good philosophy must rely on sound reasoning, so must good art rely on fractal constructs of sound reasoning, on sound feeling.  Just as we demand philosophy to be noncontradictory with itself, self-coherent in its reasoning, so must we demand that art be self coherent in its emotion.  Hence, those who say, “there is no right or wrong in art,” are wrong.  There is much philosophy to be written, but there is certainly also a right and a wrong in philosophy, and likewise, while there is much art to be created, there is also a right and a wrong in art.

Mr. Smith ended up saving Charlie and everything turned out okay … for now.

Was that an actively active act of reason?

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:

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˚ 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”.

A Singular Application of Levels of Recursion

A friend of mine recently showed me the following question which I believe can be found online somewhere (besides here):

If an answer to this question is chosen at random, what is the percent chance that it will be the correct answer?

A. 25%

B. 15%

C. 50%

D. 25%

There is actually nothing wrong with this question.  If one looks at it at the trivial case level, it actually doesn’t have an answer, and therefore, an answer must be assigned arbitrarily in order to see the rest of the system work its way out, thus any answer given is ultimately arbitrary.  The question is, in this sense, like asking “What is the correct answer to this question?” which is really just nonsense.  However, ignoring that, lets suppose we assigned our trivial case the answer “B. 15%.”

This selection, while creating an arbitrary answer on this level, the trivial case, causes a relative correct answer of A or D on the next, lets call it the second, level of recursion.  There being two correct answers on the second level of recursion makes C the right answer on the third level, and thus on the fourth level we are back to A or D.

This is not a paradox, it is just a matter of an indeterminate level of recursion, which I find, as you probably could have deduced from the title of this website, quite fascinating.

Of course, the absolute answer to this question is that is does not have an intelligible answer anymore than does the aforementioned question, “What is the correct answer to this question?”  However, if we assume the trivial case for no reason (i. e. we chose it trivially˚), then I think the most convincing answer would be the “infiniteth” level of recursion, which, because the system has no limit, no end behavior, would be best put into the words “none of the above.”

In a later post, I might well invent a less trivial application or come across it by necessity; I just found this one interesting.

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˚ O dear.  I’m really not that funny am I.

The Self-evident

I have, of late, gotten into several discussions with some less absolutist based minds.  Therefore, it seems fitting that I should generate a list of some of the self-evident axioms of logical argument in order that the dividing line between it and relativism might be made more clear.  I will provide no support for these statements for they are rooted well in the bowels of the mind and therefore, though they are hard to argue about one way or the other, are intuitively understood even beyond all the flashy rhetoric that they might be wrapped in.  I will likely add to and revise this list as time goes on.  I would much appreciate comments if anyone has a suggestion of any sort.

Logic must be accepted in order to accept any of the human faculties.

It is illogical, or perhaps more accurately, it goes against the fundamental principles of the acts of thinking and believing, to not believe in absolute truth.

It is illogical to believe logic to be incapable of discovering truth. This also may be restated, “the act of belief requires logic.”

Reality may only exist one way or another, not multiple ways, and therefore there is no such thing as metaphysical chance.

The root cause of reality, or reality itself (if it is its own root cause, this is only a matter of wording) is limitless and Absolute (this is somewhat of an extension of the second item).

One may not acquire and drop metaphysical assertions, like causality, at the convenience of forming a single metaphysical model.

Causality is a necessary factor in metaphysics just as it is so in formal logic.  That is, we cannot believe in a chain of reasoning without believing in cause and effect.

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I would also like to clear up a list of common misunderstandings:

Reason does not require the visible patterns in nature to have metaphysical significance, it only requires that there be such thing as reality.

Logic is intuitive, not rhetorical nor provable.

Logic could not have arisen by chance because there is no such thing as metaphysical chance (see above).

Logic could not have arisen from an arbitrary cause because if such a cause were to cause logic, then it could not be called arbitrary, by very definition, but would too be logical.

The Art of Thought

It is not uncommon that upon entering a metaphysics discussion with an atheist or agnostic I find my intellectual partner to be rather excited about and in agreement with most all of what I have to say.  Usually, I find that people react most positively to my arguments, almost with a feeling that they know it’s true even beyond any intellectual inquiry–it simply “sounds so right.”

I am not writing this to tell you how great I am at debate or the like.  That is entirely irrelevant.  What makes my debating so effective is the content of its argument.  I cannot, in fact, come up with any other reasonable explanation for why what I have to say would resonate so well with others except that perhaps it’s because it’s true.  Indeed, it seems our minds have some sort of mechanism in their design such that they recognize truth when they see it.  I theorize that perhaps just as our souls are made for Heaven and may only find their perfect function there, so are our minds made for truth.  When we hear something true, it resonates with us better than something false simply because our minds were built for it.

It is for this reason that romantic philosophy is not entirely pointless.  It sounds strange that one would turn away from logic and “towards the emotions” to be used as faculties in the quest for truth.  What merit can be found in what one “feels to be true?”  But, while I would certainly not replace the role of logic with that of the emotions, a gut feeling about truth should by no means be regarded as utter human deficiency.  In fact, and with a largely overly simplified model, I believe that it is upon the marrying of these two faculties that our greatest intellectual progress is made.  If God made our minds to house truth, then it should be no surprise that they would have an instinct as to what is true.

Humanity must largely rely on this instinct in the debate between absolutism and relativism as well as for establishing any kind of logical scope.  While we cannot logically prove that logic is true, we know it is.  This is the art of thought.  For, as C. S. Lewis describes in his essay “Is Theology Poetry,” truth is very much like a pleasing aesthetic.  This is why much of good intellectual writing, even prose, seems like poetry, and why, conversely, much of good poetic or fictional writing is based upon sound philosophy. As Aristotle writes in his Poetics, and pardon my failure to find an exact quote: good poetry (as in theatrical tragedy) portrays the sort of thing that might happen if the beginning circumstances arose in real life; in other words, it is pleasing to the audience that the plot should follow the same “rules” or “natural progression” that real life does.  Thus good thinking and good art are much the same thing.

Fractal Reality

When playing a musical instrument, all that needs to be done is the bowing of strings, pressing of fingers, and or blowing of air.  If these things are done just right, a beautiful sound will come out.  Therefore, one might say that a professional trumpet player is a master of buzzing his lips and pressing keys, but this is rarely what comes to mind when we think of great brass musicians and is also rarely the first thing on the mind of a great performer in action.  Rather, a musician spends his or her mental energies almost entirely on the art of sound.  A trumpet player does not think about every single muscle in his lips and every single electric single that must be sent through his nerves to produce a lovely buzz; he thinks about sweet things or dark things or sad things.  He might create a story in his mind that invokes emotions that match the music, or perhaps remember a part of his life in which he felt the same way–if his thoughts are so clearly defined.

Computer science is the methodical manipulation of binary; all that is required for a program to function properly is for the electrons in a series of wires to dance about in just the right pattern at the right time.  Therefore, a good programmer could be said to be one who has perfected the craft of creating and running electrical physical systems, but this is not what is taught in computer science classes.  A computer programmer spends his mental energy on formal logic and the devising of logical systems in which conceptual objects are created and manipulated as required by the processes of the program.

These two phenomenons are examples of what I will call the complex or figurative model of reality.  Complex reality is the model we function on in everyday life.  Even that statement is a member of the complex model because it is not true on a simple or literal level.  Truly, it is impossible for something to be purely a member of the complex or purely a member of the simple, all things and ideas are members of both to varying degrees; however, the complex is the dominate model.

The complex model is the stuff that most would say, at least upon first consideration, isn’t ultimately real.  For example, in the case of the computer programmer, his concept of the “objects” he is creating in “memory” is absolute rubbish when it comes down to what is happening physically in the machine.  A computer doesn’t know what an object is; in fact, it doesn’t actually “know” anything.  A computer is a piece of metal with electrical and magnetic charges distributed in a specific arrangement throughout it.  Therefore, the programmer’s complex model of objects in memory isn’t real, but is rather a mimesis of reality.

Notice, even this description of the complex model is mimesis of what the model actually is.  The complex model represents Absolute reality; whereas in my example, the model is representing physical reality (the reality of the computer’s physical processes).  Therefore, even my description of the complex model is a member of the complex model.

The simple model is much more difficult to isolate because it is not really used.  The simple is the Absolute reality.  It is a set of individual metaphysical zeros and ones that are then interpreted and understood within the complex.

One of the reasons I’m bothering to present these two models is that some people do not appreciate the difference.  There are always those people who think every question has a simple, concrete answer.  Such a person might ask the question: “Do dog’s go to heaven?”  And not be satisfied until they get a yes or a no.  A friend of mine once asked me that and I began my response by saying something along the lines of, “it depends what you mean by dogs.”

This misunderstanding of the models of reality can lead to great confusion in many biblical doctrines.  For example, the Bible seems to suggest that saints go directly to heaven the moment they die, saint don’t rise from death until the coming of Christ on the last day, some people will rise before others, and eternity is not bound to time.  There are many more such conflicting doctrines, but these four alone will drive crazy anyone who does not have some sort of grip on the complex model of reality.

Then there are those who only understand complex reality.  These are the people who think that truth is whatever you make up inside your mind.  Just as the monitory system is not backed by gold, so are ideas not backed by absolutes.  These people often seem rather confused when in a debate or intellectual discussion–always chaining their mind about what’s real or what matter’s, and never following any train of thought longer than it gripes their minds with pleasurable stimulation.  Indeed, if they would be most honest with themselves, they would admit that they probably aren’t really after much more than the pleasure of philosophizing, because they have no concept of truth to pursue.

The question now becomes: which one of these models is the accurate depiction of reality (i.e. the Absolute depiction)?  The answer is neither and both.  A third model best describes the reality that is worth believing in, the one in whose belief we already, inevitably function.  That model is the model of Fractal reality.  The fractal model of reality is a model in which reality is composed of infinite simple reality.  Understand that if simple reality were to exist in any finite “quantity,” as I will call it, the complex model of it would be intrinsically false.  That is, if I had some finite string of Absolute zeros and ones, and I said that they made up a ploppel, I would be wrong; they only make up a finite string of zeros and ones, because that is what they are.  But if I had an infinite string of said binary, it could very well simultaneously be a string of binary and literally be a ploppel.  Therefore, it would be entirely true to say both that such a string is a set of zeros and ones or that it is a ploppel.  This is Fractal reality.

We truly function on Fractal reality (notice, I wasn’t lying when I said we function on complex reality either, because Fractal reality is just as much complex as it is simple, though I meant function in a different sense at that point).  If we believe that a person’s being and its respective character cannot be confined to any written description, and yet it does Absolutely exist and possess concrete qualities, then we believe in fractal reality–where a being and character is made up of infinite concrete qualities.