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Mathematics and Religion - Templeton Press

Buy with confidence, excellent customer service!. Seller Inventory n. Javier Leach. Publisher: Templeton Press , This specific ISBN edition is currently not available. View all copies of this ISBN edition:. Richer insight into the nature and quality of wholth might be appropriately understood as the consummation of that intercourse.

The "embryonic" forms of wholth which have already become apparent may even be regretted as "abortive" -- cognitive "miscarriages" of various kinds. Engagement with society : This conclusion is consistent with the relative inability of both mathematics and theology to engage effectively with the experiential conditions of people at this time and with the problematic condition of society.

Both religion and science are increasingly challenged to justify themselves -- faced respectively with anti-religious and anti-science arguments. These controversies are exacerbated by the current challenges of religion to science and of science to religion, through forms of intercourse that are a credit to neither cf. Knowledge Processes Neglected by Science , Despite the specific nature of their appeal to quite distinct audiences, it is clear that, separately or together, they have little "new thinking" to offer in authentic response to the challenges of the times.

Succinctly stated, religion calls upon people to "have faith" and to "believe", ironically echoing the style of increasingly empty appeals by government authorities. Science mathematics selectively promotes its narrow discoveries, ignoring many of the more fundamental problems of connectivity faced by society as being "too complex". People are expected to marvel at the exploration of Mars by the few, and to ignore rising levels of poverty, conflict, unemployment, depression, and the like -- as experienced by the many. Ironically neither is able reframe disagreement creatively.

People do believe often despite religion and they do marvel often despite science , but experience of wholth is seemingly relatively rare. The offerings of " integral thinkers ", as notably cultivated by integrative studies, appear also to call for "belief", if only under pressure from their adherents and despite the challenge of communicating their insights meaningfully. Self-reflexivity : Curiously, from a psychosocial perspective, religious priesthoods bear a strange resemblance to the priesthoods of mathematics. Schools of thought and "denominations" may be distinguished in each case -- each with their "high priests" and dubious dynamics.

There are characteristic quarrels between them and amongst their members. These are treated as irrelevant to their larger undertakings and ambitions.

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Both initiatives are both essentially non-self-reflexive, with the exception of the preoccupation of isolated schools of thought in each case with their own difficulties. They are equally non-self-reflexive regarding the fragmentation of their disciplines. Put bluntly again, it is appropriate to ask, in each case, why it is they are unable to "get their act together" -- irrespective of their inability to engage fruitfully in intercourse with each other.

More fundamentally, given the integrative perspectives of each, how is it that they are unable to address these issues and fail to frame them as a fundamental challenge to the framing of their worldviews? In the case of religions, this is evident both with respect to failure in response to their violently schismatic tendencies and with respect to the inadequacies and tokenism of interfaith discourse.

In the case of mathematics, it is appropriate to ask whether mathematics has any sense of the order which its preoccupations represent, as discussed separately Towards a periodic organization of the Mathematics Subject Classification , Why would that be? Conceptual gerrymandering : There is a sense in which both religion and science have a blinkered view of wholeness -- a form of indulgence in tunnel vision.

This is evident in similarities in the response to complexity.

For religion, the complexity of reality is a characteristic of the mundane, necessarily to be transcended in the quest for the essential simplicity of truth -- however incommunicable. For mathematics and science , challenges are carefully selected to avoid those recognized to be too complex -- again in a quest for an essentially tidy truth. Unfortunately ordinary people are obliged to live immersed in complex mundanities, as separately discussed Living with Incomprehension and Uncertainty , They might even be described as obliged to live "betwixt and between" the axiomatically determined worldviews offered by theology and mathematics Living as an Imaginal Bridge between Worlds , A useful point of departure is the discipline suggestively named metamathematics.

This is the study of mathematics itself using mathematical methods. This study produces metatheories , which are mathematical theories about other mathematical theories. It is now considered synonymous with metalogic , and both have been substantially subsumed by mathematical logic. A seemingly relevant title in this respect is the work of Gregory Chaitin Meta Maths: the quest for omega , , which in passing makes comments of value to this argument.

He notes that maths like physics -- as a free creation of the human mind -- is an attempt by the mind to organize and make sense of human experience pp.


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And mathematics is far from static and perfect; it is constantly evolving, constantly changing, constantly morphing itself into new forms. New concepts are constantly transforming math and creating new fields, new viewpoints, new emphasis, and new questions to answer But history judges these creations by their enduring beauty and by the extent to which they illuminate other mathematical ideas of the physical universe, in a word, by their "fertility".

Integrating disagreement : Chaitin's account is usefully flawed for the purposes of this argument, both with respect to "meta maths" as the study of maths using mathematical methods, and in his reference to the highly problematic interactions between Gottfried Leibniz whom he strongly praises and Isaac Newton whom he strongly deprecates. With regard to the first, Chaitin's profile in Wikipedia notes that some philosophers and logicians strongly disagree with the philosophical conclusions that he has drawn from his theorems.

It is unclear how "disagreement" is predicted or contained by "meta maths" as a purportedly self-reflexive discipline -- and whether metamathematics is itself a preoccupation of metamathematics with all the paradoxes that may imply. With regard to unseemly disagreement between icons, it is then even less clear how two icons of science are to be framed together from a meta perspective, given his praise for one -- whom Chaitin contrasts "morally" with the other whom he deprecates pp.

Partial comprehension : Newton is recognized as a devout but unorthodox Christian, but one who refused to take holy orders as was expected of him. Leibniz was such an elevated soul that he found good in all philosophies, Catholic, Protestant, Cabala, medieval scholastics, the ancients, the Chinese Foe example, there's his remark that "music is the unconscious joy that the soul experiences on counting without realizing that it is counting" So you begin to see the problem: Leibniz is at too high an intellectual level. He's too difficult to understand and appreciate. In fact, you can only really appreciate Leibniz if you are at his level.

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You can only appreciate that Leibniz has anticipated you after you've invented a new field by yourself Voltaire was against one and in favor of the other, not based on an understanding of their work, but simply because Leibniz constantly mentions God, whereas Newton's work seems to fit in perfectly with an atheist, mechanistic worldview. Clearly Chaitin assumes he fully understands the preoccupations of Newton. Curiously metamathematics does not aspire to encompass the challenge of not understanding the insights of an icon, or the differences of perspectives between the icons of its own discipline.

Incomprehension is however a fundamental issue for many. Triumph of aridity : As Chaitin later notes with respect to the fundamental work of Leibniz on the quadrature of the circle , which he successfully addressed by transcendental methods p.

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Leibniz could not have failed to be aware that in using this term he was evoking the notion of God's transcendence of all things human, of human limitations, of human finiteness. As often happens, history has thrown away the philosophical ideas that inspired the creators and kept only a dry technical husk of what they thought they had achieved. What remains of Leibniz's idea of transcendental methods is merely the distinction between algebraic numbers and transcendental numbers.

Chaitin continues with respect to Georg Cantor :. Similarly, it was Cantor's obsession with God's infiniteness and transcendence that led him to create his spectacularly successful but extremely controversial theory of infinite sets and infinite numbers [ transfinite numbers ]. What began, at least in Cantor's mind, as a kind of madness, as a kind of mathematical theology full -- necessarily full -- of paradoxes In his conclusion, Chaitin affirms the view of Leibniz that mathematics and philosophy are inseparable as is claimed by theology of philosophy.

He argues that of the world's great philosophers only Pythagoras and Leibniz were great mathematicians p. After all, math deals with the world of ideas, which transcends the real world. And for "God" you can understand the laws of the universe, as Einstein did, or the entire world, as Spinoza did, that doesn't change the message.

Polyocular perspectives : Despite expressing admiration for complexity, Chaitin is frank in his conclusion that he himself is "monotheistic" rather than "polytheistic", explaining that p. I mean it only in the rather abstract sense: that I am always searching for simple unifying ideas, rather than glorying intellectually in "polytheistic" subjects like biology, in which there is a rich tapestry of extremely complicated facts that resists being reduced to a few simple ideas. More recently Chaitin has however sought to impose a degree of simplicity on biological systems Proving Darwin: making biology mathematical , This is of relevance to this argument in that the problematic dialogue between science and religion has also been explored in terms of models of creation and evolution A biologist's view of science and religion , Whilst a preference for "monotheism" may be appropriate for some, the challenge of any metamathematical endeavour would seem to be to allow for "polytheism" and to acknowledge the variety of forms this might take.

Again Chaitin fails to take up the challenge of self-reflexivity in relation to the polyocular argument of Magoroh Maruyama Polyocular Vision or Subunderstanding , Organization Studies , 25, Collapse of wholth : The focus of Chaitin's study in "questing for omega" now termed Chaitin's number , framed as the halting probability , could be caricatured as a mathematician's view of the religious preoccupation with " end times " and collapse.

More intriguingly it suggests a way of thinking of the collapse of any sense of wholth.


Of related relevance is his argument as to why mathematics has no Theory of Everything -- suggestive of the possibility that no such is feasible from any perspective Omega and Why Maths has no TOEs , Plus Magazine , 1 December The nature of this collapse recalls Bateson's phrase, cited above: Break the pattern which connects the items of learning and you necessarily destroy all quality There is scope for exploration of collapse through chaotic disruption of Chinese qi or Japanese wa as mentioned above , even through the alleged function of the Yellow Bell in imperial China cf Fred Fisher, The Yellow Bell of China and the Endless Search , Music Educators Journal , 59, 8, The legend of The Yellow Bell begins in the third century B.