Mathematical theology as source of mnemonic clues to global comprehension

Engaging with Hyperreality through Demonique and Angelique? (Part #6)

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As noted above, mathematical theology embodies to a suitably extreme degree the cognitive incommensurabilities by which current global decision-making could be said to be effectively "bedevilled". Its potential significance has been highlighted separately (Mathematical Theology: Future Science of Confidence in Belief -- self-reflexive global reframing to enable faith-based governance, 2011) with respect to a proposed International Institute of Advanced Studies in Mathematical Theology (2011).

Clearly extreme importance continues to be associated with faith-based perspectives in relation to global governance -- exemplified by the conflicts that they inspire, inform and are held to justify. This is despite extreme deprecation of any such framing from a scientific perspective (Richard Dawkins, The God Delusion, 2006; Christopher Hitchens, God is Not Great: how religion poisons everything, 2009). Set against this is the remarkable ability of the sciences, most notably mathematics, to articulate new ways of understanding the subtleties of extreme complexity. (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).

Comprehension of uncommon ground: More remarkable, however, is the complete lack of capacity of the sciences to enable modes of comprehension adequate to the crises of governance -- exacerbated as they are by competing belief systems -- including those of the sciences and philosophy more generally (Nicholas Rescher, The Strife of Systems: an essay on the grounds and implications of philosophical diversity, 1985). It is in this sense that the argument of Dawkins could be reframed in terms of any prospect for global consensus (The Consensus Delusion: mysterious attractor undermining global civilization as currently imagined, 2011).

By combining incommensurables -- as exemplifying requisite variety -- mathematical theology frames the challenging quest for "uncommon ground" (In Quest of Uncommon Ground: beyond impoverished metaphor and the impotence of words of power, 1997). It draws on the fundamental importance of number in the theology of many religions, as well as in the sciences (and most notably mathematics). The fundamental issue is how any form of unity is to be comprehended and articulated, whether as an inspiration for belief or in its primary role in the logic on which the sciences are based.

Transcendental unity: Clearly religions encourage a mystical belief in a transcendental unity of some kind -- purportedly accessible to experience in some measure, as appreciated in the mystics held to embody it to a degree. Their articulation is however almost completely divorced from that of mathematicians otherwise purportedly preoccupied with fundamental comprehension of the infinite in some form. A degree of compatibility is only occasionally recognized, as reviewed in the work of Sarah Voss (What Number Is God? Metaphors, Metaphysics, Metamathematics, and the Nature of Things, 1995). How might understandings of "heaven" be compared with the fundamental framings offered by mathematicians -- notably given the discussion by Voss of the infinite sets of Georg Cantor? To Cantor, his mathematical views were intrinsically linked to their philosophical and theological implications - he identified the Absolute Infinite with God.

Curiously, as has been an inspiration to some mathematicians, that discipline enables the articulation of fundamental insights which mystics are challenged to match. However the latter claim an experiential engagement with their belief which is seemingly meaningless to mathematicians, despite any reference to intuitive comprehension (Philip J. Davis and Reuben Hersh, The Mathematical Experience, 1981). Arguably, however, it is mystics that inspire a greater number of followers through the manner in which they embody their belief.

Angels and the transfinite? As summarized by Joad Raymond (Protestant Culture: Milton's Angels, History Today, 60, December 2010), though Protestants sought to distance themselves from Roman Catholics on the subject, angels played a key role in Protestant culture as a means by which to understand humans and their place in the universe. In the commentary of Peter Collins, however, angels in a sense represented a mythical way of representing the unconscious layers of the psyche, with the "bad" angels or demons pointing -- by contrast -- to the deep shadow elements (of the unreformed psyche). That "shadow" side is then to be understood as being increasingly exposed in demonic fashion throughout the world.

Collins considers that a substantial transformation in consciousness will eventually emerge, but not before much greater crises eventually convince us of the genuine poverty of our present responses. He argues in a chapter on Angels on a Pinhead (1994) that -- when rightly appreciated -- the burning issue in medieval theology of how many angels can dance on a pinhead? -- is far from trivial. He argues that:

In fact it is exactly the same issue that Cantor addressed with respect to "how many numbers exist within a small interval of the number system?". This of course led to his discovery of different orders of transfinite numbers and culminated in the "Continuum Hypothesis", which was the very first on Hilbert's list of important unsolved mathematical problems (at that famous conference in 1900). ( The Number Paradigms: the remarkable complementarity of mathematics and transpersonal psychology , 1994)

With respect to a section on Qualitative Numbers: transfinite, Collins introduces that chapter as follows:

Though their relevance has now greatly faded, angels in the past played an extremely important part in religious experience. There are in fact over 300 references in the Bible to angels. Also, it is clear that Angelology was an indispensable component of medieval theology finding its most developed expression in the system of St. Thomas Aquinas. From a psychological perspective it is quite clear that angels were essentially religious projections of profound archetypal significance providing a convenient figurative device for portraying the vital role of the unconscious mind. Thus the biblical war as between good and bad angels can be seen as a metaphor for the ongoing struggle between opposing forces in the unconscious mind....his In the Bible angels were frequently used to deliver important messages of great spiritual significance. Again this relates well to how so often, especially at critical periods in life, intuitively inspired inspirations - springing from the unconscious - mysteriously support people in the taking of key decisions.

Collins cites Etienne Gilson in a chapter on The Philosophy of St. Thomas Aquinas, to the effect that

The angels are creatures whose existence can be proved and, in exceptional cases, observed; their suppression would render the universe, taken as a whole, unintelligible; and lastly the operations of inferior creatures such as man can be perfectly understood only by comparison with, and often by opposition to, those of the angels.

For Collins, with an appropriate change of a few key words, this becomes a statement regarding the number system:

The transcendental numbers are quantities whose existence can be proved and in exceptional cases observed; their suppression would render the number system taken as a whole unintelligible; and lastly the operation of these "inferior" quantities such as rational (numbers) can be perfectly understood only by comparison with, and often by opposition to those that are transcendental.

The second hierarchy of angels best exemplify the dilemma of the medieval theologians in classifying angels. On the one hand such angels were a different species of creatures from rational humans and also - as they were not God - not fully infinite. Transcendental numbers correspond perfectly with this dilemma in mathematical terms.... The experience of unity, is essentially beyond reason altogether and purely intuitive. Indeed it represents a reality which is infinite. In like manner the "highest" order of number similarly transcends reason altogether and is purely intuitive. This relates of course in mathematical terms to infinite numbers....

Embodiment of metaphor: The argument above frames the relevance of the explorations of cognitive psychologists such as George Lakoff, especially given the challenge of women to theology ( Women, Fire, and Dangerous Things: What Categories Reveal About the Mind.1987; with Mark Johnson, Philosophy In The Flesh: the Embodied Mind and its Challenge to Western Thought, 2000; with Rafael Núñez. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, 2000) From that perspective it is questionable whether mathematicians are able to live fully by the metaphors they exploit so skillfully (George Lakoff and Mark Johnson. Metaphors We Live By, 1980) -- or derive significance from their understanding of limits and finality in the process of dying (Metaphors To Die By: correspondences between a collapsing civilization, culture or group, and a dying person, 2013)

** meta-maths

Questionable hierarchical determinism: This question is discussed below.

Avoiding premature closure: The methodological concern here is to avoid any form of definitional closure by using the challenge of comprehension as a means of ensuring appropriate cognitive distance from any premature conclusion. One question is therefore how belief with regard to what is comprehended is framed, especially when this is fundamental to an understanding of reality and identity within it. As an example, one inspiration for closure avoidance, in relation to cognitive fusion (however envisaged), is offered in metaphorical terms by the design requirements for nuclear fusion reactors. In that case it is vital that the nuclear plasma not come into contact with the walls of the toroidal container. (Enactivating a Cognitive Fusion Reactor, 2006)

Arguably it is premature closure on contrasting understandings which is most likely to engender and sustain conflict -- especially when these fail to reflect higher or more fundamental orders of comprehension, to the extent that these can be articulated and communicated meaningfully.

Requisite variety versus Contextual comprehension capacity: The focus here on comprehension of patterns of demons and angels -- understood as a demonique and an angelique -- therefore offers a means of considering the articulation of memorable distinctions in relation to what transcends conventional modes of comprehension.

As indicated in the main paper, if comprehension requires a grasp of more than 20, 50, or more factors (or dimensions), how is this to be achieved when cognitive capacity is constrained to less than 20, and possibly less than 12?

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