Methods, Muses and Mannheim – Xenophanes’ Paradox, Godel’s Theorem of Incompleteness, St Gregory of Nyssa w/ the “Impossible” Penrose Triangle

Abstract: As St Gregory of Nyssa, an early Christian mystic observed long ago, “Concepts create idols; only wonder comprehends anything. People kill one another over idols. Wonder makes us fall to our knees.” Understanding the principles of logic and rational analysis can be very helpful. The Nobel prize winning quantum physicist astutely observed .“It is only a narrow passage of truth (no matter whether scientific or other truth) that passes between the Scylla of a blue fog of mysticism and the Charybdis of a sterile rationalism. This will always be full of pitfalls and one can fall down on both sides.” Iain McGilChrist states the most frequent mistake is likely the lack of “real-world context”. Plus a close look at academia reveals a number of rather obvious oversimplifications. Neuroscientists emphasize the different processes in the mind are intimately interconnected. An important question for true understanding is realizing the limits of consciousness and rational analysis. as Philo the Jew observed “The mind is able to comprehend all other things, but not of understanding itself. The mind which is in each of us is able to comprehend all other things, but has not the capability of understanding itself. For as the eye sees all other things, but cannot see itself, so also the mind perceives the nature of other things but cannot understand itself.” (Allegorical Interpretations I) It stands to reason that, in principle, human consciousness can only understand itself through a “frame of reference’ that is itself a mindset of sorts within human consciousness. Mannheim’s Paradox states that ideologies because of their limited perspective skew the understanding of other ideologies, making objective analysis difficult. Long before Mannheim, Xenophanes observed that human ways of thinking can shape perspectives and judgments conclusions, and that people view God through their own frame of reference. Modern science has demonstrated that the Default Mode Network operates to analyze and view intentions of others – and often the world..Furthermore, Mannheim’s Paradigm states that “socio-historical” location and political aspirations influence thought, potentially leading to distorted and false ideologies. In that context materialism is a value-laden ideology that excludes aspects of human experience like art and music.

Perspective on Social Science

• If ever there was a social-political movement that was centered on ideas, the Enlightenment would be it. The Enlightenment, or Age of Reason, which began in Europe during the 17th and 18th centuries were an intellectual and philosophical force created by social-political-religious ideas that dominated the world of ideas in Europe and generated major changes in the culture of Western Civilization. Consciousness as drive and force is a theme throughout my writing which involves diverse topics such as spiritual actualities with intricate interconnections including compassion, grieving, stone worship, myths, and musical spirituality – and compare that to the vagaries of psychoanalytic theory. I contrast rational individualism and free will with social consciousness, relational will, especially in context of cross-cultural understanding (e.g., Filipino values like Bayanihan, Kapwa, loob). In Myths as Symbolic Maps of Social-Moral Order, I stress the historical connection and correlation between spiritual beliefs and social-moral order – supporting Emile Durkheim’s view of religion as the foundation of morality, arguing that religious experiences generate shared values and beliefs that bind society together.
• I critique materialism as value laden ideology (Mannheim, Talcott Parson, Iain McGilChrist, Rene Guenon, Rupert Sheldrake, Jeremiah Reyes, Arran Gare) and materialist methods. The “materialist model” of spirituality is “All spirituality is unreal” – based on the materialist maxim that spirituality is “intangible and beyond the senses”. First, that is a fallacy – the Definist Fallacy to be exact. For instance, take the concept of “Death”. Death, of course is “intangible and beyond the senses, so following the materialist argument Death becomes a figment of your imagination – which is absurd of course. Furthermore, there are a number of “tangible” types of spirituality such as compassion, grieving, musical spirituality and art. A derivative of the materialist maxim is the concept of the “supernatural” – which by definition is outside the scope of science and thus lacks any real-world context-evidence necessary for a valid scientific theory (Kant, McGilChrist, Muzafer Sherif) – which makes the “supernatural and artificial abstraction which scientifically and academically worthless.

Keywords: Mannheim, Mannheim’s Paradox, Godel, Theorem of Incompleteness, logic, rational analysis, Xenophanes, Philo the Jew, St Gregory of Nyssa, Wolfgang Pauli, Real-world context, Iain McGilChrist, Kenneth Gergen, Muzafer Sherif,

The mind is able to comprehend all other things, but not of understanding itself.

“The mind which is in each of us is able to comprehend all other things, but has not the capability of understanding itself. For as the eye sees all other things, but cannot see itself, so also the mind perceives the nature of other things but cannot understand itself.” ~Philo the Jew; (Allegorical Interpretations I) It stands to reason that, in principle, human consciousness can only understand itself through a “frame of reference’ or mindset within human consciousness. Several scientists have observed that the only way for science to evaluate human consciousness is by using a mirror in one sense or another.

Karl Mannheim, (1893 – 1947), a founding father of sociology stated that “we must realize once and for all that the meanings which make up our world are simply an historically determined and continuously developing structure in which man develops, and are in no sense absolute”. Mannheim also emphasized “As long as one does not call his own position into question but regards it as absolute, while interpreting his opponents’ ideas as a mere function of the social positions they occupy, the decisive step forward has not yet been taken.” Several Christian psychologists have noted that materialists regard their materialist beliefs as absolute and often are “impervious to mere evidence” – which I concur with. Mannheim is perhaps best known for the Mannheim Paradox. Mannheim argued that essentially ideologies and the values built into those ideologies underlie social norms and beliefs. Furthermore, that these ideologies have a profound effect on philosophical, artistic, humanitarian expressions and theories. The Mannheim Paradox stated that the ideological views of the political scientist or sociologist will skew the views and understandings of other ideologies to the point that objective analysis would be impossible. 

Karl Mannheim (1893 – 1947), a founding sociologist stated that “It has become extremely questionable whether, in the flux of life, it is a genuinely worthwhile intellectual problem to seek to discover fixed and immutable ideas or absolutes. It is a more worthy intellectual task perhaps to learn to think dynamically and relationally rather than statically.” While Ian McGilChrist, echoed by Guenon, points out that the materialist “rigid adherence to arbitrary quantification” “limits and restricts” analyses, perhaps Jeremiah Reuyes described it best when he said:  Perhaps Jeremiah Reyes has the best “description” of the materialist problem. Jeremiah Lasquety-Reyes, author & widely quoted expert on Filipino ethics I quote quite often said, “Hi Charles, I completely agree with you that this extreme adherence to materialism is too restrictive and limiting, and frankly fails to capture so many richer aspects of human experience and psychology. It leaves the field of psychology all the poorer. I am myself looking for a framework that helps me confront it. Partly, I think an alternative metaphysics is needed, one that respects the reality and meaning of things like love, relationships, and the profound reality of other people as people and not just as a compound of atoms, chemicals, and neurons firing. Glad that we’re on the same page!”

Half of human consciousness is not strictly quantifiable: art, music, dancing, dreams, ideals, and of course, death. Furthermore, as Elzbieta Halas states, symbols “condense numerous meanings” and point to realities beyond their literal representation. Balaganapath emphasizes that “The meanings that these symbolic forms transmit are complex. Instead of standing for a single referent, they evoke a variety of meanings, some of which may be ambiguous.” – which place symbolism outside the strict materialist quantification methods. In fact, Kant pointed out that “freedom” is a complex symbol which will forever remain unknown. Yet, as Confucius, a Chinese philosopher and spiritual leader who lived from 551 to 479 BCE, observed long ago, “Signs and symbols rule the world, not words or laws!” Modern politics and religion have proved Confucius right. Ralph Waldo Emerson said, “We are symbols, and inhabit symbols.” 

Lastly, there are certain built in ideo-synchronicities in the human mind: Xenophanes Paradox, The Penrose triangle, Einstein, Godel’s theorem, Mannheim’s paradox, and the limits of logic and rational analysis. Some visual illusions are built into the human brain. The Penrose triangle, also known as the Penrose tribar or impossible triangle, is an optical illusion that depicts a three-dimensional object that appears to be impossible to create in reality. It’s a triangular structure where each corner appears to connect logically, but the shape violates Euclidean geometry.

Wolfgang Pauli “To me it seems the most important and exceedingly difficult task of our time is to work on the construction of a new idea of reality.”  

It would seem “our reality” isn’t working all that well.

Albert Einstein: We cannot solve our problems with the same thinking we used when we created them

Xenophanes Paradox & Frame of reference vs. Mannheim’s Paradox 

Xenophanes (believed to have been born roughly 570-560 BC.) did advocate that a “truth of reality” did exist but – like St Augustine, St Gregory of Nyssa, and many other Christian spiritual leaders – held that absolute truth is beyond mortal human capabilities. It is said that Xenophanes was the first philosopher to distinguish between belief and knowledge. I should highlight in my research I came across an article which emphasized how the rational bias of Greek Philosophy had altered the original understanding of “knowledge” as being up close and personal – as opposed to a rational argument.

Xenophanes argument – human ways of thinking can unduly shape conclusions arrived that people make. 

But if horses or oxen or lions had hands

or could draw with their hands and accomplish such works as men,

horses would draw the figures of the gods as similar to horses,

and the oxen as similar to oxen,

and they would make the bodies of the sort

which each of them had. — Fragment 15

Roughly 800 years later, St Augustine of Hippo, – Saint Augustine, (354 AD – 430 AD), a theologian and philosopher, made the same observation that people – human beings tend to view God in terms of their own human frame of reference. Hume made the same exact observation. Of course, now modern science has identified the Default Mode Network – which functions to envision others and derive their intentions from observations. It is also called the “Theory of Mind” process. It is well known that most autistics (not all) – who have a deficit in social skills and the Default mode Network processes have difficulty envisioning God as a being. 

Xenophanes observation that a person’s frame of reference can at times unduly shape their worldviews is a precursor by several millennia of Mannheim’s Paradox. Mannheim’s Paradox has a similar point – that every system of thought is a frame of reference has limits because every system has assumptions and therefore biases of one sort or another.

Insights from Xenophanes from “Thought Itself: The History of Philosophy, Logic & The Mind” with Eric Gerlach Greek Philosophy Xenophanes

“Many have argued that in modern times, since the 1800s, the growth of technology has changed human thought such that we now understand our world and ourselves metaphorically in terms of mechanics rather than living spirits.  Rational is understood to be a series of operations rather than balance and justice, and truth is said to be objective, like an object without purpose or intention.  Some such as the French philosopher and sociologist Bruno Latour, have argued that it is our tribe, the Moderns, who are the most mythological and the least aware of our metaphors.  Because we increasingly view our reality through machines, much as we have always heard about it from the voices and writings of others, we forget that we construct our reality.  We believe that the ancients carved their beliefs in wood and stone, much as Xenophanes says oxen and horses would if they could, but that we Moderns find rather than build our beliefs.  As Xenophanes says, we give reality, truth and meaning the same shape as ourselves, as we are increasingly shaped by technology.” That is not a bad “overview” of Mannheim’s views as well.

Mannheim’s Paradox

Mannheim holds that historical and political thought is determined by the socio-historical location of the thinker and the political aspirations and material ambitions of the group or groups to which he belongs. Such thought is inherently value-laden, one-sided, distorted, and therefore false. In short, all systems of historical-social-political thought are ideologies. And this leads to Mannheim’s famous paradox: if all such perspectives are ideologies, an objective and valid social science is impossible, and Mannheim’s own reflections on the historical process are “self-refuting” – for his perspective can claim no more objective validity than can other perspectives.8 (p.143 Truth and Ideology: Reflections on Mannheim’s Paradox by Willard A. Mullins, History and Theory, Vol. 18, No. 2 (May, 1979), pp. 141-154)

Christina Maimone observes, “Ideology is, as Mannheim uses the term, a mode of thought that obscures the real condition of society to the group holding the thought, thereby stabilizing the shared social reality of the mode of thought.  Groups are simply unable to see particular facts that would undermine their conception of the world, that would show their collective perception of the social situation to be a misapplication of thought to experience.  Ideology is most strongly associated with groups that have a dominant position in society.  Their ideology serves to secure their place in the social order, although the development of their mode of thought was not consciously controlled in this direction.” 

So, what Mannheim is saying is that ideologies are mindsets or modes of thought that filter information – seek certain types of information and filter out other types of information. That is consistent with modern neuroscience research on selective attention. The model of mindsets that filter information applies then to ideologies such as capitalism or communism. It would also apply to religious, spiritual and social science ideologies as well.

Selective Attention and the Materialist Ideology

As Claudia Nielsen pointed out, the psychiatrist McGilChrist states: “The scope of inquiry and understanding of the Materialist Doctrine with its rigid adherence to the actually arbitrary principle of quantification and over-emphasis on physiological characteristics [and laboratory experiments – Kay Deaux] is severely restricted and limited in the analyses that can be performed.” Rene Guenon also notes that “rationalism” “asserts itself chiefly by the suppression of the entire supra-individual domain.”

1.        “Selective attention,” also called “selectivity bias”—the tendency to orient oneself toward and process information from only one part of our environment to the exclusion of other parts, no matter how obvious those parts may be.”  – David DiSalvo

2.       “Selective attention is often described as the ability to focus on and prioritize relevant information while filtering out irrelevant information. This prioritization transpires in attending only to a given channel in dichotic listening tasks – D Plebanek & V Sloutsky state that

3.       “Attention may sound dull, but it is an essential aspect of consciousness. In fact, it governs what it is that we turn out to be conscious of, and therefore plays a part in the coming into being of whatever exists for us “We bring about a world in consciousness that is partly what is given, and partly what we bring, something that comes into being through this particular conjunction and no other. And the key to this is the kind of attention we pay to the world.”   Iain McGilchrist

4.       Filtering & selective attention: William James stated that attention “implies a withdrawal from some things in order to deal effectively with others.” “[interaction with stimuli] is indeed accomplished, quite literally, within the approach circuit of the rostral tectum…these simple circuits are indeed the precursors to the mechanisms that control what has been called “selective attention.” 

5.       “Tell me to what you pay attention and I will tell you who you are!”  – Ortega y Gasset

6.       Selective Attention in Neuroscience: “It is argued that selectivity in processing has emerged through evolution as a design feature of a complex multi-channel sensorimotor system, which generates selective phenomena of “attention” as one of many by-products.” 

Rene Guenon: Denial of everything Supra-Individual

Rebe Guenon observes that rationalism is “defined by a belief in the supremacy of reason, proclaimed as a veritable ‘dogma’, and implying the denial of everything that is of a supra-individual order, notably of pure intellectual intuition, and this carries with it logically the exclusion of all true metaphysical knowledge….[and] the rejection of all spiritual authority, rationalism and individualism are thus so closely linked together that they are usually confused,”  (p.90)

Guenon’s assessment is correct. Kenneth Gergen, David Hay and Virgilio Enriquez agree that Rational Individualism (a political ideal) has morphed (from the Age of Reason to the Materialist Age) into a form of extreme individualism. Wikipedia has only three references to social consciousness – the most salient being Karl Marx. In western academia, the Rational Individualism norm holds sway. As a point of information, the English language has no words for the Filipino words, Bayanihan (helping others in a community context), Kapwa (shared identity), or loob (relational will – equality)

So, in context of Mannheim’s Paradigm, materialism is not objective at all and is perhaps the most value laden ideology in the history of humanity. The stereotype that “quantification” unequivocally equates to “science” is widespread.  Strict quantification excludes art, music, hope, dreaming, dancing, creativity, poetry, true love, idealism, freedom, as well as justice and even imagination

While I have come across several materialists who believe that quantification gives them absolute kno9wledge, the Absolute Truth [God – Transcendental Intelligence] is beyond human comprehension Early Christian Mystics, St. Gregory of Nyssa, St. Augustine – Humility & Wisdom without Arrogance “According to the true words of the Lord [Mt 5.8], the pure of heart will see God. They will receive as much as their minds can comprehend. However, the unbounded, incomprehensible divinity remains beyond all comprehension.” (St Gregory of Nyssa p.161 Song of songs)

Godel’s theorem of incompleteness: “[T]he meaning of a system cannot be determined by the logical arguments within the system.”

Kurt Godel, the Austrian mathematician, proved in 1931 that any mathematical system would be incomplete, which, curiously, is called the incomplete theorem. Gödel’s theorem of incompleteness has proven that all formal systems will be either incomplete or incoherent. That is to say that there will always be questions that we will not be able to answer, using a certain set of axioms, and you will not be able to prove that a system of axioms is coherent, unless You did not use another set of axioms. In addition, Gödel has mathematically demonstrated that in all effective systems (as in a computerized program) of natural numbers which are coherent, these systems will contain true declarations which cannot be proven. A philosophical involvement is that the truth of a rational thinking system cannot be reduced to a logical system of symbols.

Palle Yourgrou writes: “One of the most spectacular results of the Gödel incompleteness theorem is precisely to establish that one cannot reduce the (semantic) notion of mathematical truth in that of (syntactic) concept of proof within a given formal system” (p. 146). That is to say that the meaning of a system cannot be determined by the logical arguments within the system. The proof cannot “simulate the truth”. Any thinking system, as complete as it may be, will ultimately be incomplete. In the final analysis, “(the) logic” is not synonymous with “(the) truth”.

Einstein has an excellent synopsis of the limits of science • Albert Einstein: “Try and penetrate with our limited means the secrets of nature and you will find that, behind all the discernible laws and connections, there remains something subtle, intangible and inexplicable. Veneration of this force beyond anything that we can comprehend is my religion!”

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