Numbers Prove God

New Science / Friday, April 15th, 2016

Tatiana Plakhova_third eye

art by Tatiana Plakhova

By: Jay Dyer

When considering the question of “proofs” for the existence of God, the history of argumentation has often been lacking.  The dialectical relationship of the empirical/materialist tradition debating with the idealist/Platonic tradition is a perennial feature of the history of western philosophy.  Modern “New Atheists,” for example, are eager to pounce on flaws in the so-called “classical proofs,” as if these were the b-all, end-all of the question of rational certainty for the divine.

The chief problems with the “classical proofs” are that: 1) They do not prove what they set out to prove insofar as they are (classically) based on an empirical theological method that stems primarily from Aquinas, 2) The arguments themselves are non sequitur, where the starting points of the proofs do not logically necessitate the conclusions, and 3) The philosophical and theological assumptions implicit in the arguments are not consistent with the theological beliefs about God in the biblical system.  These three majors flaws have led to centuries of debates that were often fruitless and have allowed overly confident pseudo-philosophers and “scientists” to presume that these matters are bound up with medieval superstitions that were heroically suppressed and refuted by the rationalists of the Enlightenment era.

Ironically, this narrative itself is a modern mythos presented by the “New Atheists” and the average run-of-the-mill academicians.  The modern materialist apologists are themselves buried in a faux dialectic that ignores, suppresses and misses the real issues at hand.   It should also be remembered that ancient and medieval thinkers had not asked questions that would later be raised, and in particular, I’m thinking of more foundational philosophical questions that never entered the mind of the medieval man.  Areas of philosophy and physics that developed in the modern world, like subatomic research, phenomenology and linguistic and semiotic research were not within their purview (obviously).

With such being the case, we can assess that the classical proofs are not necessarily terrible, but flawed due to the fact that they were posited with certain presuppositions.  But what happens when, over time, philosophy and science (and theology) questions those assumptions, and asks how do we make sense of these principles themselves.   For example, all medieval thinkers utilized Ancient Greek principles of logic and geometry.   Numbers, logic, and geometric forms were assumed to be the case: It never entered Roger Bacon’s or Photios of Constantinople’s mind to ask, “How is it possible for logic and numbers to be.”

In other words, the medieval mind didn’t consider things from a meta perspective.  There is logic, but what about metalogic?  Logic functions, but is there a higher level logic to logic?  What are the necessary conditions for the possibility of logic to be at all?  One could probably trace out a deeper connection between the artistic forms that were created in different periods and the development of 3d perspectivalism on a 2d surface, compared with the philosophical and scientific questions that began to be asked in that period.  Were the developments in optics and the study of light influential on the Renaissance portrayal of 3d perspectives?  I’m sure they were.   However, it had not entered the mind of medieval man to think in meta or transcendental categories.

It is true that ancient and medieval man posited transcendental arguments: Aristotle presents one for the law of non-contradiction, as well as filling out a more specific consideration of the different categories, which do match up in certain ways to Kant’s categories, so it’s not correct to say the medievals had no idea of what a “transcendental” was, or what a transcendental kind of argument was.   It is correct to say they did not consider the various sciences and arts from the perspective of how they are possible – what the necessary conditions for the possibility of those things to be were.  When the secular scientistic revolution occurred asking a lot of these questions, western Theism marched confidently along professing the same old, tired arguments that were unprepared to meet the level of questioning the revolutionaries were asking.  Western theology was ill-equipped due to its own assumptions about God’s existence being strictly the same as His essence, Actus Purus, an absolutely simple monad, with all human predicates equalling the divine ousia itself.

Given those kinds of theological presuppositions, it was impossible to meet the onslaught of Humes and philosophesthat were merely forcing the western theological assumptions to be consistent.  If God is an absolutely simple First Cause, and this (and the other “proofs”) is the extent of the “rational” evidence for His existence, then it doesn’t follow from that premise that the God presented in the Bible is that Deity.  Perhaps the First Cause is the impersonal Being of Greek thought.  Perhaps the First Cause is the theism presented in Mohammedanism.  Perhaps it is an unknown First Cause of the Enlightenment deists.  It should be evident that this argumentation as presented is useless (and actually harmful) to anyone who professes the Bible in whatever capacity, since these views are not the Biblical view, especially since Thomists, Muslims, Deists and Greek philosophers have all used this  bad argumentation.

When Etienne Gilson, the famous medievalist expounds the “I AM” of Exodus in Thomistic fashion, it is explained according to Greek philosophy, where God is revealing Himself as “Pure Being.”  Eastern patristics had similar statements, but never went on to conclude that meant God was synonymous with His existence.  And they refrained from that precisely because they knew that equating the divine essence with the absolutely simple Monad of Platonism resulted in all the same difficulties of Platonism.  So with that background, I’d like to proceed to my own reformulation of the transcendental argument in terms of the question of numbers and predication.

Delving into ancient mathematics in my graduate class on Aristotle’s metaphysics, the question of number was a crucial theme.  Both Aristotle and Plato have an important place for mathematics, and both give two famously different approaches to how invariant numerical entities relate to the objects in our realm of time and flux.  Thus, the question of numerical entities was of peculiar interest to the ancient Greeks who, according to Plato’s Timaeus, inherited their mystical and Pythagorean notions from Egyptian esoterism.  It is also in the Timaeus that we are presented with an almost miraculous knowledge of the structure of miniscule reality (Platonic solids), seemingly impossible, given the technology of that time!  Back to the argument – it occurred to me that in considering the transcendental argument for God, an overlooked, yet crucial component of this approach is the issue of numbers themselves.   For those that are well-read in Maximos the Confessor and Philip Sherrard, an even deeper insight comes to the fore.

Any time we predicate something of an object, we utilize principles and categories.  This is unavoidable and one of the things we assume is mathematical entities.  All created reality can be categorized according to unity and difference.  Thus, one and many are assumed in anything and everything.  When I say, “That table,” I am assuming a special unity of a specific object in my experience that is distinguished in that act by all other objects of perception.  One is therefore assumed in any act of predication or communication.  But “1” itself is not just a token symbol or sociological development, it is an actual objective principle, which is made evident by the fact that predication, communication and mathematics can be done across cultures and over time.  If it were not invariant and objective, it would be subject to change like all material things.

“1” is not just 1.  1 is also infinitely divisible.  Even Xeno was aware of the possibility that space could potentially be divided infinitely, and the result of this is that infinity is actually present at every point.  When I say “point” here, I am referring to the Pythagorean and Platonic idea of the monad or point in geometric space and/or time.   The 1 is therefore not merely 1, since it can be divided infinitely, it also encompasses an infinite potentiality within itself, as well as infinite potential relations to all other unities or objects.  This is a peculiar problem for materialists especially, because for a materialist with the standard empiricist assumptions, the only “rational” thing to acknowledge is whatever can be (supposedly) retained from immediate sense experience.  But even back to Berkeley’s time, it was posited that infinity is surely a mathematical reality, yet no one has a direct sensuous experience of anything infinite.

So how can we assume something that is present at every point, as well as in every act of predication, that is completely a fiction?  In other words, not only is there a transcendental unity of an object that must be assumed for anything in our world to make sense or for communication to be possible, 1 itself necessitates the infinity of other numbers.  Does not 1 contain .1, .2, etc?  Of course it does, and as I showed in my Egyptian metaphysics paper, the basic energetic structure of our world seems to operate on that binary mathematical principle of I, 0, or energy/being and non-being.  This means that predication necessitates 1, which necessitates not only that “1,” but all other numbers, too, unless someone wanted to be so absurd as to say that only “1” exists, while 2, 3, etc., are illusory (which would be impossible, since 2, 3, etc., are made up of combined 1s: 1 + 1 = 2).

Mathematically, then, 1 is present at every point (1 is the monad/point), and contains within itself infinity.   But infinity is not something directly perceived by any finite mind, it is only known apophatically, or negatively as we say, being compared to what it is not.  Infinity is not bound by space, not bound by time, etc.  Infinity also cannot be a mere number, since it does not obey the rules of normal arithmetic, as the BBC video below shows.  All the more absurd for the “classical proofs,” which attempted to deal with this topic according to empirical theology!  But it’s also absurd for the materialists in this regard, since infinity does not obey the rules of any set, as Godel showed.  So the fools who think they can excise anything non-material and sensous from existence cannot even predicate!

Reality, at every single point, and in every single act of predication, requires infinity.  That itself is a huge mystery, but no one would be so ridiculous as to say that mystery means we cannot know anything.  What philosophy or theology can make sense of how infinity is present and necessary at each point?  How does a finite, created mind access or touch upon infinity, if infinity is something only present to, and confined in, our realm of existence?  It would seem to be impossible on any kind of materialist grounds, but even beyond that, other religions would have the same question to grapple with.  Where has this even been proposed or considered?  To be sure, many mathematicians and philosophers and theologians have considered similar questions, which ultimately boil down to the question of how God relates to and interacts with our world.  If infinity is ever-present and necessary, there needs to be some way to connect this infinity or these infinities to finite reality, and for them to be accessed or known or touched in some way.

In my analysis, western theology is wholly unequipped in this task.  Because God is an absolutely simple essence with no direct relation to our world apart from another created mediation, finite reality is basically encapsulated and shut off from God.   In eastern theology, there is a different view, which has tremendous implications for anthropology and how God interacts with the world.  In Eastern theology, man is not just a body and a mind/soul, where the intellect is the highest faculty, but also a spirit, where there is a direct point of contact with God.  This spirit is man’s “nous,” where he directly perceives the logoi, or the uncreated principles that are the archetype and pattern of all created things.  Man encounters the logoi even if he is unaware of it, because he is created with a faculty for knowing God.  Beause man is fallen, this nous is buried under false beliefs and lies man has chosen to believe, but because God is ever-present and is ever-present in His infinity, it is impossible for man to escape this or utterly stamp it out.

Only in Eastern theology does man’s nous directly perceive and touch the uncreated reality, and this is made evident from what I argued above.   It is clear that infinity is present, and even created things that are seemingly finite, also possess an infinite aspect to them.  Their infinite aspect is that logoi, situated “in” the uncreated Logos of God.  This is revolutionary for epistemology, because it means only with the right metaphysic and theology is predication and knowledge possible, and only with a robust view of the many logoi being united in the one Logos is there any explanation of how this can be.    Dr. Philip Sherrard explains of the nous touching the uncreated logoi:

“At the same time, man is not οnly soul and body, for he is also endowed with a third faculty or power, which is both the image of God, or spiritual principle, in him, and the ‘uncreated’ centre of his created nature. This centre, man, like every finite form, possesses in him ‘from the beginning’ through the very fact of being created at all, and it remains with him, however it may be obscured, through all his temporal transformations.(1) The Incarnation of the eternal Logos in Christ is not thus an exception to, but a confirmation of, what man is;(2) and the same may be said of the Resurrection, for it is οnly in the effective ‘realization’ of his οwn uncreated logos that man achieves his deification and, through it, that deliverance (from the death and corruption of his merely temporal existence) in which his purpose is fulfilled.

The realization itself by man of his οwn uncreated and indwelling logos is something beyond the reach of all natural powers of soul and body, reason and sense:

It is truly impossible to be united to God unless, besides purifying ourselves, we come to be outside or, rather, above ourselves, having left all that which pertains to the sensible world and risen above all ideas, reasonings, and even all knowledge and above reason itself, being entirely under the influence of the intellectual sense and having reached that ignorance which is above knowledge and (what is the same) above every kind of philosophy.

This ‘intellectual sense’ (αίσθησιs νοερά) is not, therefore, the consequence of any theoretical and abstract speculation; it is, οn the contrary, the consequence of a long process of purification and prayer in which God is revealed in the heart. The intellect (νους) is not in this context the equivalent of the mind or of any mental or rational faculty; it is of another order altogether, being, indeed, precisely the spiritual image of God in man and naturally deiform, and having its seat not in the mind but in the heart. It is the heart which is the intellectual, or spiritual, centre of the whole psychophysical nature of man, and the intellectual sense spoken of above, and the spiritual discernment and enlightenment which go with it, can οnly be achieved through a bringing of the mind itself into the heart; for it is οnly in this ‘treasury of thought’ that the intellect ‘purified and illuminated, having manifestly entered into the possession of the grace of God and perceiving itself . . . does not contemplate only its οwn image, but the clarity formed in the image by the grace of God . . . that which accomplishes the incomprehensible union with the Supreme, through which the intellect, surpassing human capacities, sees God in the Spirit’.

Μan then ‘being himself light, sees the light with the light; if he regards himself, he sees the light, and if he regards the object of his vision, he finds the light there again, and the means that he employs for seeing is the light; and it is in this that union consists, for all this is but one’.(5) Ιn such a union, man does not merely contemplate what is outside and beyond himself; he becomes himself what he contemplates, the uncreated ground of his οwn proper being in which the whole of himself body and soul, participates, and through which he is deified, ‘not by the way of ascending from reason or from the visible world by the guesswork of analogy’, but by mingling ‘unutterably with the light which is above sense and thought’ and by seeing ‘God in himself as in α mirror’.”

We have here an answer to the question at hand.  Man is never “away” from God or the infinite, as God is presupposed in every act of predication.   Anytime the “infinite” is considered, we are not and cannot be dealing with merely some impersonal force or meaningless void, but rather a personal Being.  This crucial aspect is important for distinguishing the position being argued here from Platonism.  Platonism might agree with the argumentation so far, yet for Platonism, the ultimate Monad or Mind is not personal.  It is not hypostatic and it is not directly related to the world of flux in which we dwell.   It is inaccessible and wholly other, and incapable of explaining how or why there are “many” things at all, and not just “One.”  If the uncreated logoi are posited then, it is necessary that they are “contained” or related and associated together in an omniscient Mind that is able to connect and relate these infinite potentialities and relations.  But this divine Mind cannot be cut off from our realm, as it is in western theism and Thomism, it must directly interpenetrate our world.

It is at this point that Maximus the Confessor brings an enlightening argument to the question of the divine Mind, the logoi and the created realm.  Maximos scholar Stephen Clark writes:

“This is bound to sound un-Plotinian – but perhaps it is less un-Plotinian than it sounds, even though Plotinus himself does not endorse it. The particular way that I have expressed the issue may be significant. In speaking of ‘possible worlds’ have I suggested that all such worlds are real, that the infinite possibilities of creation are all realized somewhere (very much in the style of modern physics, with its talk of the multiverse)? Tollefsen has suggested that it is here that we can see a real distinction between pagan and Christian metaphysics: for the pagan Neo-Platonist all the ideas contained in the divine Intellect are mirrored in phenomenal reality (though not necessarily all at the same time, nor in the same region). For the Christian only some are realized here, the ones somehow selected to be companions and associates of the Incarnate Logos.

Maybe so, though it does not seem that there are explicit statements of either possibility in the available texts. My question is: would Plotinus have definitely rejected the thought attributed to Maximus? And my answer is that he would not. To put the point another way: there is no reason for Plotinus to suppose that all the souls who dance around the One (so to speak) have descended into phenomena to assist in the grand creative act that mirrors the divine. Nor does he have to suppose that all have fallen far. The phenomenal world is only a partial mirror, a partial selection from the infinite, and there is no need to suppose that every Idea is imitated here. Not all souls, even if they enter here, come further ‘down’ than the stars. This is not to say that those Ideas that are not imitated here have been held back, as not deserving of phenomenal reality! So maybe there is an interesting change between the pagan and the Christian thought.

This world here is a selection – but for that very reason, so the pagan may suppose, it is an incomplete, an imperfect copy; those Ideas, those souls, that have not entered here are immeasurably our superiors. But if the Christians are correct, it is rather the other way round: it is we who have somehow dared to enter who are to be the true companions of the Logos. It is the Incarnate Logos – incarnate by Maximus’s account in the ‘natural order’, in Scripture and finally as the man Jesus – which is to be the focus of all endeavour, not simply a God with whom we are to be acquainted just by intellect. Once again, I am not altogether persuaded that even this thought is completely non-Plotinian, but it may be a likelier candidate than most. Note that I am not suggesting that Maximus differed from pagan Neo-Platonists in holding, in Tollefsen’s summary, that ‘Christ as the Logos is not a universal at all, but is the personal divine center of all creation’, because I don’t think that the Neo-Platonic Logos is a universal either (and neither are the logoi it contains – as even Balthasar realized!). Paradigms aren’t universals.

My own – very tentative – suggestion is rather that for Maximus the divine centre is made manifest within the phenomenal world, that this is why there is a phenomenal world at all, and that what is not thus manifest (in the natural order, in Scripture and in the Incarnate Christ) is of less significance for us than – maybe – Plotinus would have thought. On the one hand, Plotinus would have been wrong to suppose (as he supposes of other sects in his treatise Against the Gnostics: Ennead II. 9 [33]) that Christians despised this world here: on the contrary, it is in this world here that the centre of creation is to be known. On the other hand, he would have been right to think that Christians reckoned animal humanity of more importance than the stars above us: those stars, as it were, are the signs and habitation of souls too delicate to risk contamination. The angels’ fall, so tradition tells us, began in Satan’s outrage that he could be expected to bow down before an animal!”

Clark begins to consider the possibility of an Incarnate omniscience, citing Maximus, as he proceeds, but what read here is relevant, too.  The similarity to Plotinus is undeniable, but there are definite differences.  No finite mind in the biblical view can be omniscient.  For the logoi to be contained in the Logos, and for the structure of reality to hold constant as it does, There needs to be an infinite, omniscient Mind to relate these uncreated logoi and the created realm.  Our finite minds clearly cannot hold or contain or recall the Infinite and uncreated, apart from scant fragments of vague notions, as we “see through a glass darkly.”  We can use symbols and terms that stand for the Infinite, but it is really something mysterious, yet necessary, that is assumed in each act of predication.  And the infinite monadic points and the infinities which they contain within themselves are directly connected to the uncreated logoi.  Clark finished with a key argument that directly speaks to my argument, in regard to numbers:

What do we change by seeing or saying that it is Christ who plays in everything? To be is always to be, or to be beginning to be, something, in virtue of some single call to being. And being something is always, for us, to be a member of the whole: failing in that, we fail in being at all. But where are we to look? In the pagan cosmos we can be guided only by memories and imagination, looking towards the ordered beauty of the stars, or mathematics, or such images of virtues as we can internalize. But perhaps there is a problem: on the one hand, there is nowhere short of the whole world to serve as a guiding image for each and all of us, but on the other, that whole world, though we speak of it as if it were wholly unified, a single beautiful cosmos, does not in fact exist save in the fragmented, barely sociable mirror of the many souls seemingly caught up in it.

Without soul there is only darkness. If we are to believe that there is indeed a single, unified cosmos, it must be that this cosmos is contained in a single soul. If there is to be a way of seeing things right, there must be an Intellect indeed that contains and decrees right answers, but if there is no equivalent single Soul then the phenomenal world is always far astray. Our experience is always delusory by comparison, and delusory in multiple, transient ways. If we are to believe not only that there are right answers, but that we can discover them, it must at least be possible for Zeus himself to be incarnate, for there to be someone, somewhere, who has not only the Mind of God, but His actual life. For Plotinus, that incarnation was in the World Soul herself: at once our elder sister and the fullest possible expression of Soul Herself. But maybe there has to be a more particularized embodiment, and one that can be grasped from within the pagan synthesis.

That man – each man – is a microcosm of the larger cosmos is not to be understood as saying that the cosmos has arms or legs or eyes. What good would such limbs or organs be? The point is rather that for each of us there is an experienced world, our world, our being, that is a copy or mirror image of Reality. But how could we ever know that any of these copies were even partially correct unless there was someone, somewhere, whose experienced world just was the real world, whose experience and not just his intellectual insight, provided the model for us all, someone who is indeed the centre? And the orthodox Christian claim, turning from all the easy answers, has been that there is such a one.

The template for human, and indeed for all animate life, is the man Jesus: it is his life that provides the model, and the power, for us to live by, not because he was moulded to resemble the One’s life (that would merely reintroduce the problem) and might, as before, have lived as an atheistical, jobbing carpenter, but because the One’s productive power took shape, from the beginning, as that very individual. Nor is it that the eternal Word took on a pre-existent human or animal nature, as a cloak on its identity: to be human, to be alive at all, is to be little like that actual, historical individual – or like enough, at any rate, to be able to join, as it were, his party. It is in Jesus that God invented human nature! It is there, in Christ’s world, so Maximus tells us, that all divisions and differences are overcome. It is a notion endorsed elsewhere in the Orthodox tradition, and largely – though not entirely – forgotten in ‘the West’.

Rather than seeing Jesus Christ as a trinitarian person who erupted into linear history 2,000 years ago, the patristic and apostolic perspective is that of Jesus Christ as the foundation of all history (‘by whom all things were made’), the centre of creation, and the image of God (Heb.1.3; Col.1.15), according to whose image we are made – and not just as a ‘pre-existent Logos’, but eternally as the crucified one, the ‘Lamb slain from the foundation of the world’ (cf. Rev.13.8), destined before the foundation of the world but made manifest at the end of the times for your sake (I Peter 18.20).

This is of course an extraordinarily grand claim, both metaphysically and ethically. It is hardly surprising that even many fellow-travelers have preferred some more intellectualist approach, choosing to see the Logos as embodied, at best, within a book or a theory or an architectural marvel, but as remaining essentially distinct from all its representations in the phenomenal world. It is not the part of a jobbing philosopher to show that Christian orthodoxy is correct, nor to pretend to any special insight into how exactly to live with an eye to the Incarnate Logos rather than just to our own best theory of the divine reality (however we may identify that ‘best’). It is, I suppose, my part to try at least to get some idea of what disagreements there may be about the one true path to excellence. And as Maximus also said, with more courage than, fortunately for me, I need now display: if I am wrong, refute me!”

Apply this to numbers and infinities.  We know that 1 contains infinity infinities within itself.  We know that one presupposes the whole set of numbers.  We know that one is necessary for any act of predication, as a transcendental unity.  We know that man must have access or a point of contact with these infinities, and here is the answer to how that happens.  Numbers are therefore a transcendental argument for the necessity of God.  If the referent for the symbol for infinity or the word “infinity” is not real, or is merely a token linguistic symbol, then predication is impossible, and so is knowledge.

Related: Cantor and Multiple Infinities


Numbers Prove God

++ Numbers ~~ Nassim Haramein [updated]

++ Infinity in the Finite ~ Nassim Haramein

++ That which is infinite cannot be many, for many-ness is a finite concept.

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