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“You can use logic to justify almost anything. That’s its power and its flaw.” from Star Trek: Voyager, “Prime Factors”

“Logic will get you from A to B. Imagination will take you everywhere.”

That’s what Einstein (assuming he put Relativity to good use and succeeded in time-traveling) could have told Aristotle, the Greek philosopher, after being introduced to his daughter, Pythias, which the father was quick to qualify as utterly good.

“It’s unfortunate you make no allowance for utter badness,” Einstein could have added. “Your daughter could illuminate your senses and your mind like a fiery town fire, instead of a timid campfire.”

Aristotle would not—could not—acknowledge this since the laws of logic he himself established (for the most part) some 2400 years ago, would only allow to be one OR the other. The river of Time has been kind to his laws, but the ice that protects its uninterrupted and unquestioned flow is cracking; and perhaps a sharp knife tipped in objective reality shall make it through.

Since the onset of humanity and the rise of a cognitive culture, the birth of Logic was inevitable, evolving into a formal science, dedicated to both the study of modes of reasoning (which are valid and which are fallacious) and the application of valid reasoning. In specialized fields such as mathematics, philosophy, semantics and computers science, and more widely, in our daily lives, the laws of logic are mainly used to distinguish which reasoning is valid and which reasoning is fallacious, such validity being predicated and determined by a reasoning’s logical form, not by its content.

That may not be entirely true since, after close inspection, we discover that content as it relates to the nature of things and the individuality of human beings does not readily apply to Aristotelian logic—no matter what the form.

For example, the argument: I am truthful OR I am a liar, (connected by the exclusive operator/conjunction OR), is valid in accordance with Aristotelian logic. Conversely, to state that I am truthful AND I am a liar, (connected by the operator/conjunction AND) is a fallacious argument, according to the same logic—the content’s quality, and not the form, invalidating the argument. To claim the reverse would create a paradox a statement or group of statements that leads to a contradiction or a situation which (if true) defies logic or reason.

However, when we superimpose the paradox over factual reality, it ceases to be one. When we examine our life experiences, we cannot deny that we have lied countless times (the reasons for which are irrelevant). And, in our defense, we can also acknowledge that we’ve told the truth myriad times. For all intent, we are all truthful people AND all liars, expertly practiced in both, and not one OR the other.

Even the stoical logician Chrysippos’ Liar paradox, which has brought many a thinker to the brink of mental exhaustion, is easily solved by discounting Aristotelian logic. The semantic argument is simply stated and succinct as:

“I always lie.”

A constant liar could never make such a statement since it would be the truth.

A constant truther could never make such a statement since it would be a lie.

A sometimes liar/sometimes truther (capable of both truth and lies) could make such a statement—any statement for that matter, whether it is a lie or a truth.

The last argument proves a solution does indeed exist. Paradoxes in others fields also bear renewed scrutiny, having been dismissed as anomalous outliers by the long prevailing logic.

In mathematics, an infinite series is expressed as:

1 + r + r2 + r3 +…rk + …; where ǀ r ǀ is less than 1 and k tends towards infinity.

For some time, mathematicians could only provide an approximate numerical solution to sums of this form, until clever algebraic manipulation succeeded in closing the expression and describing the series in finite form as:

1
——
1 – r

The problem could now be expressed as infinite AND finite.

In quantum mechanics, wave–particle duality postulates that all particles exhibit both wave AND particle properties. This duality addresses the inability of classical concepts like “particle” AND “wave” to fully describe the behavior of quantum-scale objects. Grasping for an explanation, some postulate the paradox is as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

The latter diagnosis carries with it monumental significance. It suggests we need only step out of the space-time continuum (moving from being a part of the observation to being a truly independent observer) to discover how the Universe truly works—or at the very least, discover how else it works.

It’s not an easy task, having been beaten down, blinded to otherwise obvious factual realities, and put to sleep all our lives by the tyranny of Aristotelian logic.

 

THE TIRANNY of the ARISTOTELIAN LOGIC: You are either with me OR you are against me.

“You seem to be in quite a pickle,” Einstein (still on his time-travel tour) could have told Galileo, an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution.

“I may have been able to keep you out of the dog house,” Einstein could have then insisted, “using cunning repartee.”

Indeed, after alienating astronomers, Jesuits, and the Pope himself with a controversial theory, he was tried by the Inquisition, found “vehemently suspect of heresy”, and forced to recant and spend the rest of his life under house arrest.

Galileo favored heliocentrism (the astronomical model in which the Earth and planets revolve around a relatively stationary Sun at the center of the Solar System) over geocentrism (the model in which the Earth is at the orbital center of all celestial bodies). He was right of course—but only half-right—as Einstein would have demonstrated using a logic (other than Aristotelian) that rested neither on Physical nor Mathematical constructs, but rather on imagination, proving once again his famous quote that Reality is merely an illusion, albeit a very persistent one.

What is irrefutable, as Einstein would clearly state, is that planets revolve around a central sun; suns within a galaxy revolve around some galactic central point; galaxies within a cluster revolve around some cluster-central point; clusters within a super-cluster revolve around some super-cluster-central point; super-clusters revolve around a group of spatially associated super-clusters…and son on and so forth, until we get to what would be termed the center of the Universe.

With every iteration, the theoretical—and at best approximate—central point begins to evade us until, for all intent, it becomes unknown. It is at this juncture that Einstein could have said that, if the center of the Universe remains unknown, it is ostensibly nowhere in particular, and anywhere he might choose—including the Earth. This distinction might have saved Galileo a lot of grief and spared himself the Church’s tyranny, without forfeiting his beliefs.

Religion, one of countless organized expressions of Aristotelian logic, has supported and still is supporting the first-order consequential reality, rooted in the logical operator OR (I am truthful OR I am a liar: the logic of OR). Having survived the test of time, largely by virtue of sustained indoctrination and of the absence of a challenging alternate logic, this reality is not just content to pull you in; it pushes you, bullies you into submission using Negative Reinforcement, an operant conditioning that strengthens a behavior or a thought because a negative reaction is stopped or avoided as a consequence of the behavior or thought.

Like all tyrannical bullies, the logic of OR suffers from low self-confidence and a fear of discovery of one’s failings. So, it battles without respite its arch nemesis: reasoning based on factual reality, which demonstrates time after time that the «I» can identify itself as one AND the other. And it does so by discrediting such identification and accusing it of fallacy so forcefully and convincingly as to invalidate experiential reality.

One wonders how such a sad state of affairs could have endured so long; how experience—a reality based on one’s interaction with one’s environment—could have been side tracked in favor of a limiting, circumscribing logic.

This becomes even more implausible when we interpret human states like the state of truth and the state of lie as abilities (the ability to tell the truth; to tell a lie). Within this context, we can naturally conclude that we are free from past choices, that we can wield these abilities at will, and that we can invent and reinvent ourselves at every moment, being neither one nor the other in particular, along any bipolar spectrum. We are no longer powerless or doomed to be like this or like that. We have the power to choose who we are for as long as we want. In the face of such preponderant evidence, logic prevailing over factual experience becomes by far the greatest paradox. And what is direly missing and needed is an advocate for the prosecution; one capable of harnessing the potency of the evidence and of debunking the paradox by its very nature.

However, any such advocate would allege that the nature of the paradox has been clouded by misguided and unsubstantiated precedence laced in circular argumentation, so repeatedly so as to create a wealth of Jurisprudence amply sufficient to elevate the logic of OR to the status of Law.

Plainly speaking, we’re faced with the ultimate case of the chicken and the egg. The logic of OR begot the world of OR as seen through a glass meticulously stained; and the colored world of OR begot the logic of OR. Case in point, when reality is inconvenient, almost any sect, religion or political group will legislate its creed into law and call it the truth. And no one can be against enforcing the truth.

The good news—because there is good news—is that, no matter what law guides our lives, we can agree there is no true paradox. Whether this belief is motivated by an avoidance of suffering, a power play, a philosophical consideration, or a gateway to higher consciousness, is immaterial. From it, you and I can lay the groundwork for a space in which the statement “There is no paradox” can exist without resistance. And with agreement on the effect, we can more easily open an exchange on the cause:

  1. There is no paradox since the world of OR and its defined Law of logic demonstrate that you and I cannot be one AND the other;
  2. There is no paradox since the world of AND and its undefined Law of logic prove that you and I can be one AND the other.

While the first argument will be readily acknowledged by most, it steers the thinker—uninitiated and educated alike—towards a recognition of the complimentary, reciprocal relationship between a world and its logic. One exists because of the other, and vice-versa.

This, in turn, leads to the concession that the world of AND (expressed through countless instances of fact-based reality) cannot be dismissed on the basis of no existing law, since the interdependent nature of World and Law has been conceded. Although currently undefined, this law must therefore exist, validating, at least in theory, the second argument, and demonstrating that a paradox is nothing more than the crutch of the close-minded.

In a nutshell, both the world of OR and the world of AND can co-exist, without prejudice to each other…just like the theory of parallel universes.

 

THINKING OUT OF THE BOX

So, how do we go about describing the Logic of AND?

One way, suggested earlier, is the removal of limitations plaguing the observer, or as the popular, and often bastardized, saying goes: thinking out of the box. This implies that: our way of thinking occurs in a metaphorical box whose boundaries determine and limit the breadth and depth of what can be thought; and that: our way of thinking would expand and transform outside the confines of this box. Just like the first fish that grew legs and left its watery domain, we would discover a whole new world that never could have been previously imagined—a whole new playground filled with wonderful new toys.

The obvious first step is to leave the box, just like we were leaving our own houses—we open the door, step out, close the door, walk a few yards, and turn around to look at the house.

To think and feel from this new vantage point, we must develop the ability to:

  1. Recognize the box (I can see my house, the doors, the windows, the bricks, the roof, etc.)
  2. Recognize its limits and power (I can only walk so far before hitting a wall, do a limited number of things, repeat customary behaviors like making love only in the bedroom or eating only in the kitchen, etc.)
  3. Know what’s outside the box (I can see the grass, the trees, the sky; hear the birds, feel the cool wind, the warmth of the sun etc.)
  4. Reason and think differently outside the box (I realize I can live very differently outside my house, do many other things, critically compare my house to my neighbors’, etc.)
  5. Recognize the benefits of reasoning outside the box (I have access to a whole new world of possibility; I have the power to choose).

By truly grasping these five abilities, we can move fluidly between Box #1 (world—or house—of OR + the logic of OR (Aristotelian logic), and Box #2 (world of AND + undefined logic of AND).

Note the reference to a second box. By induction, we can reasonably infer that if the box of OR is contained in the box of AND, then the latter must be contained in a third box, and that there are an infinite number of boxes (the nature of which lies outside the scope of this article). In short, if we were to break out of the OR box, we would invariably find ourselves in the AND box—yes! Another box!

So, it begs the question: why trade one box for another? Simply because of the abilities we learn in order to do so. By recognizing the box and its influence and restrictions, we draw a line in the sand that instantly delineates the box from the not-box (outside the box), compelling us to re-examine our education on what is logical, reasonable, possible and imaginable, and realize the might of the two-sided sword of OR—predetermining possible realities and excluding others as fallacious.

By removing the sword that hangs above our heads, a veritable danger to our survival, we effect a fundamental change in the context. Whereas the context of the OR box is separation and opposition (me OR you), generating conflict, antagonism and dissension that irrevocably lead to wins and losses (I win OR you win; I lose OR you lose); the context of the AND box (me AND you) is unity, reciprocity and partnership, leading to win-win outcomes.

It’s therefore not surprising the OR box and its workings have given rise to Millennia of conflicts between nations, tribes, families, couples; to discrimination, struggles for money, prestige, political stance, religious supremacy; to a world of control, dictatorships, famine and exploitation.

In business organizations, the OR box has given rise to abuses of power, isolation, constant opposition between unions and managements, power manipulation, prejudice, protectionism, injustice, lack of motivation and waste and loss of talent. At the personal level, we experience the same types of conflicts and struggles, embedded in severe lack of authenticity and transparency; in discrimination against race, color, sex and anything creating a differentiation that must be crushed; and in fear of being reduced to nothingness.

The OR box essentially results in a world of scarcity and danger where the only game in town is survival; a world in which we are prisoners of a singular reality that negates and opposes all other possible realities as fallacious, and whose challenge must be relegated to domain of allegedly insoluble paradoxes—a convenient dumping ground where everything is tainted as trash.

The OR box is insidious in maintaining its reality through transference of its structural identity from one civilization and culture to the next, ever reinforcing its conditioning of reasoning and perception into a so-called intolerant objective reality that is anything but.

By becoming able to see and travel from the OR box to the AND one; we gain the freedom and power to orient our way of thinking and reasoning, virtually at will. Nothing becomes impossible, unreasonable, unimaginable or illogical. By entering the AND box, we encounter a world of reciprocity and collaboration; a world where the concepts of Right or Wrong, Better or Worse, Win OR Lose become trivial, and exert no power.

And if we don’t like the box we’re playing in, we move to another one. If we want to play some more, we move to the next. The OR and the AND boxes, and all other boxes, are after all the product of our imagination—and we can store them, order them, fill them any way we want within the infinite warehouse of our minds.

By developing the logic of AND, and fostering the abilities that gain traction from this logic, we can create the world of AND, a world of wonders, resilient and impervious to the attacks of the world of OR that has yet to realize its existence could never be threatened by its sister world—that is simply not in the world of AND’s nature.

And so, after explaining the ins and outs of the world of AND to Aristotle, Einstein could well have made his friend realize that he had cheated his daughter and himself out of an authentic, non-judgmental relationship; that he had been oppressing her and forcing her into his image of the model daughter; and that he had denied himself precious moments of her utter badness—that were neither good or bad, but rather simply were. He and his daughter would have discovered the power to choose who and what they chose to be, the moment they chose to be it, and the life-affirming tranquility that comes with it.

The world of AND is within our grasp, and the time has never been riper for philosophers, mathematicians, scientists and thinkers alike to assemble and forge the logic key that will open the door to this exciting new world filled with new possibilities and new liberties.

The world of AND: the New Frontier.

 

 

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