Logic laughs at Logic


Section Headings

Is Logical Consistency more important than Direct Experience?

The preceding chapter suggested that it is far more useful to view the Cosmos as Paradoxical Polyverse, rather than a single monistic Material Universe. In fact, the second is a silly idea, which I would dismiss without discussion, except that it is the current dogma of the high ranking intelligentsia and their minions. They seem to have this bizarre obsession with both defending and maintaining the logical consistency of a single Material Universe. I hope to never revisit this absurd topic again. It seems somewhat ridiculous that I must address this ludicrous controversy at all. Yet this chapter calls to me. Let’s get it out of my system once and for all. 

The adherents of the single Material Universe paradigm, of which there are many, are convinced of the truth of their position because of logical reasons. Inescapable deductive logic leads inexorably to the conclusion that the entirety of existence is ultimately deterministic. Yet the day-to-day experience of these erstwhile logicians seems to be filled with choice, even to the extent that they make the logical decision to argue against the possibility of decision-making. For these super-rational individuals, logic trumps direct experience. What is wrong with this picture? How do we account for this major discrepancy between reason and conscious experience?

Rather than engaging the beast directly (he is too strong), we take an indirect approach. We tackle this tricky conundrum by teasing Logic – exposing him for the fraud he is. No philosopher I. Rather than engaging in esoteric word games, I will just reveal his hidden corners – the unsavory places that respectable members of society pretend to ignore or conveniently forget. Their domain dependent understanding seems at times to extend even unto their own disciplines. For a more complete understanding of reality, it is necessary to expand our Minds beyond narrow specialties without depth.

As I am a Logic worshipper myself, I am just poking fun at this proud god in my pantheon. He needs to be taken down a few notches. His arrogance is boorish and even offensive, causing great and unnecessarily hostile divisions in humankind. Why can’t we worship multiple gods rather than just one? What about the gods of Music, Art and Beauty; Love, Religion and the Divine? We can’t forget the sensual delights of the Body. Does Logic really think he can touch these mysterious ecstasies with his vaunted understanding? Time to deflate these naïve rationalists – take them off their pedestal.

But who am I fooling? They will never understand. Monists will rationalize anything I say with their fancy words. Confirmation bias is a powerful inclination – a built-in human trait that is hard to circumvent.

Why Intellectuals are Blinded by Logic

(√ 2.8 pgs)

Hard Science Community sneers at Choice

Considering that scientists have been unable to utilize Material Dynamics, both traditional and quantum, to either model or explain a vast body of evidence associated with living behavior, one would think that intelligent researchers would look for and even welcome an alternative model and/or explanation. And yet this is not true.

Tied, as if with an unbreakable chain, to the Material Dogma, the scientific community resists innovation and even shuns or ignores those who might suggest otherwise – dismissing them as crackpots or lunatics with a side wise glance and disparaging sneer. “It is amazing that these silly people still believe in Consciousness and Choice. How immature, ignorant and misguided they are to ignore what logic tells us.”

Humorous Questions: How maintain Scientific Determinism when Abundance of contradictory Evidence?

This rigid mindset raises some humorous questions. With such a huge body of evidence associated with living systems unaccounted for by Material Dynamics, why has the notion of scientific determinism infected so many otherwise brilliant individuals? How can these extraordinary people logically deny the existence of deliberate decision-making as they choose their words, chapter organizations and publisher of the books they write attempting to debunk the notion of Consciousness? How did they come up with the bizarre notion that Choice is an illusion? And how can they maintain a straight face when they attempt to persuade the rest of us to believe the same inane proposition?

Why? Suggest blinded by Logic

Of course, there could be a variety of reasons for this blind state of denial. Yet I would suggest that seemingly intelligent humans have a greater tendency than most to be blinded by Logic. Why?

Worship of Logic à Successful Career

Many have spent a lifetime worshipping and feeding at the trough of presumably dependable Deductive Logic. Career, livelihood, prestige and lifestyle are all dependent upon it.

Intelligent People Conflate Logic with Truth

Due to this constant exposure combined with self-interest, they became inculcated with the notion that deductive logic rules supreme, even trumping direct sensory experience. Mistaking the metaphor for reality, these otherwise intelligent individuals conflate a useful way of understanding the physical universe with absolute truth. Logic is mistakenly equated with Truth.

Logic ≠ Truth

Objectification of Process a common flaw that I must address for work to be accepted

This objectification of process is a common human flaw. I must address this misguided tendency if my work is to be accepted by the intelligentsia. They are really the only ones who might care about my themes of Choice, mental energy and Attention.

Tarski & Godel: Logic does not determine Truth

Let us first address the relationship between truth and logic. At the turn of the 20th century, logic reigned supreme. Wealthy philosophers offered a substantial prize to anyone who could employ logic to determine truth. The prize remained unclaimed for decades. Then in the 1930s, the work of Alfred Tarski and Gödel proved the opposite, namely that truth and logic are separate. Logic works on assumptions. The assumptions of any logical system, even though intuitive, can never be proved due to infinite regression.

Logic & Math have contradictions hidden in corners:

There are other problems. Super rationalists have a fondness for mathematics, as it is the ultimate form of deductive logic. It has provided the logical foundation for all the so-called hard sciences. Because of this nearly perfect fit with material phenomena, mathematics has a well-deserved status, especially amongst the type that worships science.  Strangely enough despite their reputation as upright citizens, logic along with mathematics actually have lots of contradictions and inconsistencies, even magic, hidden in their corners.

Science’s Mathe-magic: Imaginary numbers

Humph! The arrogance of the scientific community to assert that they don’t believe in miracles. Mathematics abounds with miracles, precisely defined logically consistent miracles, yet miracles nevertheless. For instance, Imaginary numbers are one common form of mathe-magic. The name says everything. They only exist in the imagination, not reality. We can have two artists or one quarter of a boysenberry pie, but we can’t have an imaginary number of anything in our world. Nothing equivalent to real numbers.

Imaginary Numbers x Real Numbers = Complex Numbers

Imaginary numbers are not a trivial mathematical construct. When this product of the mathematical imagination is combined with real numbers, the result is complex numbers. Complex numbers, the mixture of the real and the imaginary, are the true mathematical building blocks of engineering and science. Without them, this esteemed community would be paralyzed, unable to solve many elementary problems. Yet to have utility, the solutions must be purely real - no imaginary component.

Imaginary Numbers x Real Numbers = Complex Numbers

Imaginary Numbers: A Logical Impossibility

Engineers rely on the imaginary numbers of mathematics in their equations to arrive at very practical results. As the square roots of negative numbers, imaginary numbers are a logical impossibility. At first considered a mathematical curiosity, these paradoxical entities are now a standard feature of any scientific education due to their utility. Logicians that look for absolute consistency seem to have forgotten about these strange creatures of the imagination.

Calculus Mathe-magic: Nothing x Infinity = Something

Magic is also at the heart of calculus, the primary mathematical system of the hard sciences. An infinite number of points with no dimension, i.e. infinitesimals, accumulate into a finite line segment. Nothing is multiplied by infinity to get something. Integrals and differentials, the primary functions of calculus, rely on this magical process to generate practical results. 

Zeno’s Logic shows that motion is impossible

And then there are Zeno’s logical paradoxes, which show that motion is impossible. We must first move half way to our destination. But before that we must move half way to the halfway point. An infinite regression leads to never getting anywhere because we must first get half way there. Of course, nobody is deterred by this logical impossibility of motion and continue moving from place to place.

Despite paradox & Logical impossibilities; Philosophers deny Choice on Logical Grounds

How can Logic take himself seriously when he hangs out with such bizarre creatures as imaginary numbers, infinitesimals and Zeno’s paradoxes? Yet despite all these paradoxical processes and impossible logical conclusions that lay at the heart of mathematics, science and logic, erstwhile philosophers confidently tell us that choice is an illusion for logical reasons. Of course, everyone, including those writing the books against the possibility of choice, go about their daily business attempting to make the best decisions regarding a virtual infinity of factors, e.g. health, emotions, relationships, spirituality, child-rearing, and careers.

If Tarski can prove that logic can’t determine truth, if Zeno can logically prove that motion is impossible, if mathematicians and engineers regularly employ imaginary numbers to make useful computations, if calculus is based in adding up an infinity of nothings to yield something, why do intelligent people desperately grasp onto logical consistency as if onto a raft in the middle of the ocean? Can’t they see with all these strange and peculiar examples that logic is a useful tool in many, but not all, circumstances. Due to these limitations, logic must be employed very carefully to evaluate propositions, especially when its conclusions are contradicted by real life experience.

The Fallacy of Logical Consistency

 (√ 4.2 pgs)

Logical Consistency: an amusing concept

Logical consistency is an amusing concept. Why?

Prior: Paradoxical but useful constructs: Imaginary Numbers & Infinitesimals

The rigid logic of physics and even mathematics is mired in logical impossibilities, e.g. imaginary numbers and infinitesimals (developed in a previous section). Logicians and scientists do not reject these impossible propositions outright because of their utilitarian value. Imaginary numbers and points without dimension are essential components of the computational tools for solving real world problems. It seems that paradox, i.e. propositions that seem to be contradictory or absurd, are a necessary feature of mathematical and scientific truth.

Abstraction based in Metaphorical Blends à Fuzzy at he edges

Innate Paradox, i.e. the utility of the absurd, is not the primary reason that those that advocate or even worship logical consistency amuse me – maybe even eliciting a grin, a broad smile, or even an outright chuckle. Cognitive linguists as a group are in broad accord that complex abstractions including mathematical constructs and philosophical propositions are based in metaphorical blends. Metaphors themselves are never exact. However when metaphors are blended to build and derive even greater truths, the edges become even fuzzier.

Quest for Rigor & Elimination of Logical Problems: Strips math of visual component

For instance, in the quest for absolute rigor, mathematicians in the late 19th century stripped mathematics of the visual sense of geometry. This strategy was taken partially to rid math of the inherent subjectivity of sensual experience and more specifically to resolve some logical paradoxes that arose from the geometric propositions. This reformulation of math’s basic tenets definitely resolved the paradoxical inconsistencies that arose from the geometrical approach.

System adjustments leads to other logical inconsistencies

However, this advanced logical rigor simultaneously introduced new paradoxical propositions. Try as they might, these theoreticians could not completely eliminate all contradictions no matter how much they tweaked the system. Each new adjustment, while resolving one questionable proposition, would always introduce another problematic proposition. They could not develop a system without a glitch at the corners.

Math’s Metaphorical blends: Whole Numbers for counting; Real Numbers for Measurements

Why? Despite its apparent monolithic nature, complex mathematical systems are also metaphorical blends. For instance, discrete whole numbers have some distinctly different characteristics than rational numbers even though they are seemingly contained in the set. Counting numbers are employed to enumerate unitary indivisible objects like humans or any living system. In contrast, rational numbers are used to measure non-unitary quantities like distance, mass or time.

Counting Logic ≠ Measuring Logic

The logic of counting and measuring, while similar in that they are both mathematical, also have some significant differences. One is discrete and forever separate while the other is continuous and forever connected. Blending the two types of logic has some utility, but also has some inherent inconsistencies at the corners, i.e. extreme examples or special circumstances.

Counting Logic ≠ Measuring Logic

Example: Whole Numbers Indivisible, Fractions Divisible

For instance, all whole numbers can be written as a fraction, i.e. a rational number. However the logic of fractions does not apply uniformly to whole numbers. The logic of whole numbers includes indivisibility. No fractional humans. Dividing living systems is a laughable notion. Conversely distances can be divided and subdivided almost endlessly. Quantities of this type are not unitary in any way. The logic of fractions can only be applied to unitary entities with great care.

Specific: Fractional Logic Woman’s Height

Fractional logic applies to a woman’s height. Most are in a continuous range somewhere between 5 feet and 6 feet tall. There are no restrictions on the exact number of inches. Perhaps her height even grows when young and shrinks when old.

Whole Numbers:  # of Women

However, there is exactly one of her, no more no less. The number of women in a group is precise with no room for variation. No such thing as five and half women. Whole number logic applies in this case.

Fractional Logic ≈ Molecular Realm; Whole Number Logic ≈ Subatomic Realm

One type of logic applies to ultimately divisible measurements, while the other to indivisible units. Indeed the logic of whole numbers and fractions is so fundamentally different as to be applicable to unique realms of existence. The logic of discrete whole numbers can be applied to the Subatomic Realm with its individual electrons, photons, energy quanta etc. Similarly, the logic of continuous fractions is more applicable to the Molecular Realm where objects move continuously through the aptly named space-time continuum.

Fractional Logic ≈ Molecular Realm

Whole Number Logic ≈ Subatomic Realm

2 Maths: Continuous & Quantized Functions

Scientists were even forced to develop unique mathematical systems to address these qualitative differences between the realms associated with counting numbers and fractions. Newton developed the mathematics of continuous functions (calculus) to model the Molecular Realm. Dirac developed the mathematics of quantized functions (Quantum Mechanics) to model the Subatomic Realm.

Attention Realm: Metaphorical blend of counting & fractional logic

The Attention Realm requires a blend of both types of logic. Attention’s iterations are unitary like whole numbers. The iterative process happens or it doesn’t. Although the iterations are indivisible, the LA’s computational process yields fractional results.

3 Maths: Continuous, Quantized & Reflexive Functions

Just as the Molecular and Subatomic Realms required their own mathematics, I developed the mathematics of reflexive functions to address the monitor and adjust feedback loops associated with the Attention Realm. Each type of function is based in a different type of logic. Each Realm requires its own logic. This is why it is more useful to view them as distinct realms of existence rather than as a unified whole.

Molecular Realm ≈ Continuous Functions

Subatomic Realm ≈ Quantized Functions

Attention Realm ≈ Reflexive Functions.   

Eliminating Metaphorical blend = Eliminating Feature of Reality

To resolve the inherent logical inconsistencies of the metaphorical blend, mathematicians inadvertently attempt to eliminate the blend. It is definitely possible to remove these logical glitches by eliminating one of the mathematical metaphors from the blend. However, this strategy simultaneously eliminates a feature of reality from consideration.

Eliminating Metaphorical blend = Eliminates Feature of Reality

An exclusively Digital World: AI and Computers

For instance, many theoreticians have attempted to employ an exclusively digital system to characterize the real world. The precision of 1s and 0s is very appealing to the rigorists especially in comparison with the alternative – the imprecision of analog. The adherents of artificial intelligence are especially adamant on the possibility of a digital Universe. According to this perspective, computers with their ones and zeros will eventually rule the world. 

Digital (1 & 0s) Logic ≠ Touching Logic ≈ Analog Logic

However eliminating the messy continuity of analog from mathematics also eliminates touch from consideration. As digital ones and zeros can never touch and are always isolated, binary logic is inappropriate for snuggles. Analog logic is required to characterize the warmth of a hug or the ecstasy of sex. Digital logic is also helpless before living meaning and interaction, as they are also forms of touching. The individual monitors the environmental touch and then makes an adjustment by touching the environment.

Digital (1 & 0s) Logic ≠ Touching Logic ≈ Analog Logic

Price of Logical Consistency: Incomplete

Logical consistency comes with a price. It is necessarily incomplete. Multiple systems are necessary to encompass a greater reality. One is not enough. We require both counting numbers and rational numbers to characterize our everyday lives.

Metaphorical blends sacrifice consistency to gain complexity

Metaphorical blends sacrifice logical consistency (by necessity) to gain complexity. The loss is secondary to the growth of complexity and utility of conception. Just stay away from the edges and everything will be all right. 

Gödel: Logically consistent systems self enclosed: Something always outside

There is another problem with logically consistent systems. They are frequently insulated from other logically consistent systems. Gödel again. Logically consistent systems are self-enclosed and incomplete. More specifically, there will always be logical propositions that are outside the system. These propositions can’t be evaluated as to their truth or falsehood within the system. While it can approximate, digital logic can’t possibly model the logic of touch, meaning or music.

Mathematical & Verbal Logic as Metaphoric Blends = Fuzzy at corners

These examples indicate that even mathematical logic is fuzzy at the corners, i.e. logically inconsistent. This is because complex mathematical systems are always, yet inadvertently, based in metaphorical blends, rather than a monistic logic. Even mathematical logic breaks down under extreme examples. As complex verbal abstractions are also based in metaphorical blends, they also have some inherently paradoxical elements.

Quest for Logical Consistency amusing as it is missing something

This is why it amuses me when philosophers claim that they are aiming at absolute logical consistency. Either their quest is hopeless or it is missing something. Most likely the second.

Material Logic misses Choice

When someone, usually the super logical rationalist, asserts that Choice doesn’t make any logical sense, it makes me laugh. Why? Of course, it is impossible from the logically consistent perspectives of the Molecular and even the Subatomic Realms. Yet an abundance of everyday identifiable, living processes exposes the glaring incompleteness of this vision. Simply speaking, Matter’s deterministic logic can’t encompass Choice. The mismatch renders it impossible.

Grasping logical consistency in face of such evidence like monkey with hand in jar

 Grasping logical consistency in face of such evidence is like the monkey who is captured because he can’t let go of the bananas in the jar. Medieval scholars hold onto Ptolemy’s earth based system despite evidence to the contrary – claiming it is more logical. Naively rejecting continental drift because it just doesn’t make sense. Einstein denying the probabilistic nature of the quantum world because ‘God doesn’t play dice’. A Born Again fundamentalist attempting to convert me to his belief system.

“Blinded by the obsession with logical consistency.”

When they ask why I laugh at their seemingly serious objection to my system, I just smile, having learned from previous experiences that explanations usually cloud, rather than clarify, the water. Rather than responding directly, perhaps a simple response is best. “Blinded by the obsession with logical consistency.”

No Explanatory Power, No Evidence, Impossible to Negate?

(√ 2.0 pages)

Phillip Goff wrote an incredible book called Galileo’s Error. In it, he exposes the major flaw in scientific determinism. This philosophy derives from the unequivocal results of modern science regarding Matter. Physics epitomizes this scientific approach.

While Physics et al is able to account for material behavior, it has never been able to address the special features of Consciousness. Physics specializes in quantifiable phenomena, especially objects that have mass and move through time and space. Goff argues convincingly that Galileo is the originator of this wildly successful methodology.

However, a lemon, for instance, has features like taste, smell and color that cannot be quantified. These features do not exist independent of Consciousness. The sensual delights are an irrefutable part of conscious experience. Because Galileo’s scientific method cannot account them, Goff poetically calls it ‘his error’.

Ultimately the materialist perspective is unable to deal with Conscious Experience. Thus the question becomes: How to deal with Consciousness?

Goff breaks down the approaches to this question into three general categories: materialism, dualism and panpsychism.

Materialism, i.e. scientific determinism, generally denies the independent existence of consciousness, claiming that it is just an emergent feature of material behavior. With enough time, the current scientific approach will eventually get a handle upon this elusive feature of existence.

Dualism, originating from Descartes, holds that Mind (Consciousness) and Body (Matter) are forever separate. While Body obeys the deterministic laws of Matter, Mind obeys a different set of laws. In other words, Life has an immaterial component that is independent of Matter.

Panpsychism is the belief that matter possesses consciousness. Under this perspective, the special features of consciousness are somehow integrally connected with matter, yet inaccessible to the scientific methodology that began with Galileo. A new methodology is required to address consciousness. Goff is a proponent of panpsychism. 

Having developed a new methodology that effectively addresses conscious experience, I decided to contact the esteemed Dr. Goff. As he is only available to the general public via Twitter, I set up an account and tweeted him. Although mostly ignored (not a professional academic?), we did engage in the following series of tweets late March 2020.

Me: “Any reasonable proposition must have the possibility of being negated. Else it is a proposition like God or Providence. How do you negate panpsychism?”

Dead silence. (My model of Attention can be negated by showing that conscious behavior is different than what the model predicts.)

Me: “Science provides explanatory power for material behavior. The Attention Matrix provides the same for conscious behavior. Does panpsychism provide explanatory power for any data?”

Ghosted again.

Me: “Science require evidence to support their theories. An abundance of evidence supports my theory of conscious experience. What evidence supports panpsychism?”

Finally a response, Goff: “This is the most frequently asked question regarding panpsychism.” He then provided me with a link to an article he had written. The article provided a philosophical justification for why no evidence was needed.

Me: “Your panpsychism requires no evidence, provides no explanatory power for any empirical data, and can’t be disproved. Sounds like an impregnable proposition. Where’s the relevance?”

Goff: “It’s the same for materialism, dualism or any other theory of consciousness.”

It is ironic that I must defend the Attention Matrix, which is supported by an abundance of evidence, provides explanatory power for Conscious Experience, and can be negated, against the predominant philosophy of materialism, which provides none of these. Why? The intelligentsia is either blinded by dogma or afraid to stand alone against the crowd. Actually probably a combination of ingredients. Like Copernicus et al, I must await the death of the old guard and hope for a member of the younger generation to take up my torch.

The Dreaded Duality

(√ 3.5 pgs)

You might wonder why the esteemed philosopher Phillip Goff embraced and has even become the modern champion of panpsychism, i.e. the notion that matter has consciousness. After all, a table seems quite different than you or me. While we seem to monitor and then adjust to our environment, our inanimate table just sits there. It never resists when we move it this way or that. Likening the dull predictable behavior of an inanimate object to the continual demands of a young child seems somewhat absurd.  

Life and Matter seem to be poles apart. A rock and a tree have decidedly different trajectories. The one gradually disintegrates, while the other grows. The one has no loyalty to its existence, while the other is continually attempting to maintain its personal integrity.

So what is behind the growing appeal, according to Goff, of this seemingly fanciful belief system? You are going to laugh when I tell you. Again those logic worshippers are blinded by their own brilliance.  But in this case, they escape one dogma only to be trapped by another.

Panpsychists accurately and admirably reject scientific determinism, a prevalent dogma of the intelligentsia. Goff boldly acknowledged and even wrote a book claiming that Consciousness has characteristics that science has not and cannot address. He argues convincingly that conscious experience should be included in the scientific dialogue perhaps with another type of language. His desperate purpose is to provide a philosophical framework for the discussion.

The Common Man:  “Simple solution. Conscious Life is alive and Unconscious Matter is dead. An obvious duality.”

Yikes! Academia dismisses Descartes’ Mind-Body dualism as an outmoded, antiquated, even intellectually immature belief. Why? It implies that Life has an immaterial component. Horrors!? We’re stepping on academic dogmas right and left, wherever we turn.

So trapped are they in the materialist perspective that even suggesting an immaterial component evokes patronizing smiles as if they are talking with young children. “How immature they are to still believe that the Universe contains something besides Matter. How silly. Why we left that old-fashioned concept behind a century ago, along with the archaic, superstitious belief in religion, gods and spirituality. Thank Science for revealing the truth. The educated have finally left those childish beliefs behind.”  

Wanting to avoid censure and shunning by their colleagues, academics must keep their contrary beliefs to themselves, especially those associated with free will and the immaterial. Goff didn’t actually challenge these dogmas, but he did have the courage to stand against the scholarly crowd and provide a cogent philosophical argument for the existence of Consciousness. Yet he was still trapped by the anti-duality dogma.

“Hmmm? Logical conundrum. Have proved the existence of conscious experience independent of the current scientific endeavor. Rightfully proud of myself for bucking extreme materialism. But how to avoid the dreaded dualism? Would be the laughing stock of my colleagues, if I even suggested it. Ah! Eureka, I’ve got it! All matter is invested with consciousness. Even a rock has conscious experience, but only on a minimal level. This way consciousness exists, but no duality, as it is an integral feature of matter. Hip Hip Hoorah!”

But he had to justify his peculiar position by acknowledging other positions, for instance duality with its ‘to be avoided at all costs’ immaterial component. “Coming out for consciousness was already risky; but standing for the duality, no matter how reasonable, is over the top. I would be ostracized from conferences. Might even jeopardize my career.”

Brilliant worshipper of logical consistency, Goff came up with a critique of dualism that satisfied him and his colleagues. Dualism is too complex. Occam’s razor, an effective scientific and mathematical criterion, holds that simple beats complex, if all other considerations are equal. In other words, if two competing theories both account for the facts equally well, the simplest wins out.  A great and even intuitive standard. Nature too likes simplicity.

Employing Occam’s razor, Goff rejects dualistic thinking as unnecessarily complex. He argues that the monistic philosophies of materialism and panpsychism are necessarily simpler than dualism because there is one rather than two. Definitely true.

However, Occam’s razor can only be applied when ‘all other considerations are equal’ between the two hypotheses. Are they really equal? Do our three systems really account for phenomenal existence, especially the Consciousness/Matter relationship?

Let us consider living and non-living matter. Dualists (a.k.a. vitalists) say that a tree and a rock have some qualitative differences, while panpsychists and materialists claim that they are qualitatively the same. Which do you believe? Conscious Experience or Logic? Only the super-rational could possibly hold the position that the two are equivalent. Thinking that they are the same glosses over some significant differences, e.g. growth vs. reaction. Most of us would laugh heartedly at this ridiculous logically consistent conclusion.

Frequently, if not always, monistic thinking, while simple, misses a huge swatch of reality. Monism is marvelous in its particular arena, but neglects to account for other significant phenomena. Sometimes dualistic thinking is required to incorporate a greater field of action – other realms of existence.

Mathematics, as mentioned, consists of many incredibly useful dualisms. On the most basic level, the duality of whole numbers and fractions is incredibly productive. To demean the differences between the two types of numbers would be like saying that there were 3 and a half people at the party. Humans, indeed all living systems including cells, are never fractional.

We can’t forget the mathematical duality created between imaginary and real numbers. One type of number is impossible, while the other applies to real events, as their names indicate. Yet the interaction between this duality lays the foundation for the complex numbers, a necessary building block of scientific progress.

And then how about the electricity-magnetism dualism? The scientific community was stumbling about in the dark, until Maxwell developed his famous equations that incorporated the two sets of data into one set of dualistic equations. Maxwell’s dualistic thinking was so fruitful that it inspired a way of conceptualizing the material Universe that lies at the heart of physics.

Considering that our Cosmos, our very existence, is filled with dualisms, it seems odd that Goff would reject dualistic thinking as too complicated. The Material Realm itself consists of a dualism – the Subatomic and Molecular Realms. If anyone suggested that the addition of the Subatomic Realm was unnecessarily complicated, the entire scientific community would laugh. Why? The Subatomic Realm incorporates a vast amount of data and phenomena that was previously unavailable to traditional approaches.

In similar fashion to Subatomic Realm, the Realm of Attention provides a unique mathematical language for a huge set of phenomena related to conscious experience that continues to baffle traditional material approaches and explanations. Just as the Molecular and Subatomic Realms form the Material Dualism, the Material Dualism combined with the Attention Realm forms the Living Dualism. Mind and Body have different mathematical languages, as Descartes suspected.

To say that adding this additional realm is unnecessarily complicated due to its implied dualism is to ignore an entire phenomenal network. It is a curious claim that materialism and panpsychism can incorporate these phenomena into their monistic systems. How does the belief in an exclusively material world or a universe filled with conscious matter help me to write this paper and finish my book?

If the materialists and rationalists want to believe that all their choices are automatic and there is no difference between a rock and a tree, so be it. If it seems useful to believe that conscious decision-making is an illusion or that sand has conscious experiences, more power to them. Who am I to argue with logical consistency, no matter how ridiculous its conclusions?


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