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volume II: Synopsis

part IV: Divine Dynamics

page 25: God

Can God make a stone bigger than he can lift? This ancient conundrum points to the only possible restriction on the nature of God: consistency. Here, by God, we mean the whole of reality, everything. Is reality divided into two, God and the Universe? or is it one, simply God? We take the latter view, and ask all the classical questions about God, what is God's size, power, knowledge, durability, and so on? God - Catholic Encyclopedia, God - Wikipedia,

Our working definition is that God is everything, the way things are. God is as big as can be. Thomas Aquinas produced a number of proofs for the existence of God which all boil down to a similar argument: the visible world of human experience is not everything. It cannot account for itself, therefore there must be some invisible entity, called God, which creates and sustains it. These proofs all depend on the models of God (the Unmoved Mover) and the World that Thomas had derived from Aristotle. Aristotle: Metaphyiscs Book XII, Aquinas 13

Bernard Lonergan set out to update Aquinas' thirteenth century arguments to the twentieth century. In my opinion, Lonergan's approach fails. His work was instrumental in my leaving the Catholic Church and continuing to work on the alternative hypothesis: that God and the Universe are one. Bernard Lonergan - Wikipedia

Lonergan argued (in his book Insight) that the divinity must be fully intelligible. He claimed that this is not the case for the Universe, because it contains 'empirical residue'. 'The empirical residue . . . consists of positive empirical data, . . . which is to be denied any immanent intelligibility of its own . . . .' Lonergan approaches the empirical residue through 'inverse insight: . . . while direct insight meets the spontaneous effort of intelligence to understand, inverse insight responds to a more subtle and critical attitude that distinguishes different degrees or levels or kinds of intelligibility. While direct insight grasps the point, or see the solution, or comes to know the reason, inverse insight apprehends that in some fashion the point is that there is no point . . . the conceptual formulation of an inverse insight affirms empirical elements only to deny an expected intelligibility.

An example of an inverse insight is Newton’s conceptualisation and formulation of the first law of motion: . . . a body continues in its existing state of uniform motion in a straight line unless that state is changed by an external force. It seemed to me that Lonergan was mistaken about the presence of empirical residue in the Universe. I was not aware of the quantum no cloning theorem then, but I feel that my instinct was good. No cloning theorem - Wikipedia

Lonergan’s misunderstanding is at least as old as Parmenides: he mistakes an abstraction for reality. In an abstract way it is true, as Lonergan says . . . that (1) particular places and particular times differ as a matter of fact, and (2) there is no immanent intelligibility to be grasped by direct insight into that fact. Parmenides - Wikipedia

The physical models which we use to summarise the relationships of events in the Universe are formal constructs capturing invariant symmetries. They do not imply that there is no intelligibility in the relationships of real events, which break symmetry, such as the impact of a particular hammer on a particular nail at a particular time and place in the construction of a particular house.

There seems to be no reason to believe that the world is not completely intelligible. It just happens that neither Lonergan nor any other person understands it in its entirety. If the attempt to prove that God is other than the Universe falls down then there is no reason to believe that the Universe is not divine. Nor is there any reason to believe that there is a real distinction between the entities symbolised by matter and spirit, sense and intellect or soul and body. These distinctions are simply elements of a model used to elucidate a seamless world. Lonergan Insight, pp 19-26

Our hypothesis is that the Universe is self sufficient, can explain its own existence, and is therefore fittingly called God. From his proofs for the existence of God, Aquinas concluded that God is 'pure activity' (actus purus). From this model of God he went on the derive the classical properties of God. Actus purus - Wikipedia

Here also we start with the idea that God is pure activity. We know that there are quanta of action that blend seamlessly to produce larger actions. Further we know that energy is the rate of action, so that the total energy of the Universe determines the total rate of action in the Universe. Furthermore, energy is conserved, leading us to conclude that the rate of action is constant through time. Conservation of energy - Wikipedia

The next ingredients in our model are fixed point theorems (eg Brouwers), that tell us that subject to certain conditions, maps of a set onto itself (as when the Universe moves) have at least one fixed point where f(x) = x. There is thus no reason why a purely dynamic system should not have points which do not move. This overcomes the objection that the Universe is not actus purus because it complex rather than absolutely simple. Further, it seems consistent that a purely dynamic system contain a very complex set of fixed points. One need think only of the dynamics of one's own physiology. Brouwer fixed point theorem - Wikipedia, Aquinas 20

Science, as Parmenides recognised, can only make true statements about relatively fixed points of the Universe. In the physical world these statements often take the form of differential equations, like Newton's famous formula F = ma = d2s / dt2 where f represents force, m mass, a acceleration, s distance and t time. In classical mechanics this formula is believed to be true everywhere for all time. It is an ubiquitous and eternal feature of a classical model of God. Differential equation - Wikipedia

Quantum mechanics reveals that the Universe appears to have a countable infinity of fixed points, the eigenfunctions of the quantum operators that represent motion. These fixed points are the fixed foundations upon which the stable elements of the Universe are built. On this site, we guess that these these eigenfunctions are the set of computable functions represented by halting Turing machines. Eigenfunction - Wikipedia, Turing machine - Wikipedia

Cantor built the space of transfinite cardinal and ordinal numbers from combinations and permutations of the natural numbers. The transfinite Universe thus provides a model for the elaboration of more complex fixed structures that we observe, like ourselves. I am a huge ordered set of ordered sets . . . of elementary actions.

The twentieth century saw an explosion in mathematics arising from Cantor's work. Cantor showed that given any set, there exists a set with a greater cardinal number. We understand Cantor's proof as the formal basis for the creativity of the world. Without understanding in detail how God creates itself, we can nevertheless see that from a formal point of view (that is in terms of its fixed points) a dynamic Universe that did not create more stationary points would be self-contradictory. Cantor's diagonal argument - Wikipedia

Christianity claims that God created us to show off his glory. Natural theology, if this idea is correct, shows that the divine Universe (= God) creates new fixed points (while maintaining its dynamic unity) because it cannot do otherwise. This creative force we might call the Cantor force, a formal representation of the force driving creation, the pure activity of God.

(revised 24 May 2013)

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Further reading

Books

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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '... Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Miles, Jack, God : A Biography, Vintage Books 1996 Jacket: 'Jack Miles's remarkable work examines the hero of the Old Testament ... from his first appearance as Creator to his last as Ancient of Days. ... We see God torn by conflicting urges. To his own sorrow, he is by turns destructive and creative, vain and modest, subtle and naive, ruthless and tender, lawful and lawless, powerful yet powerless, omniscient and blind.' 
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Links
Actus purus - Wikipedia Actus purus - Wikipedia, the free encyclopedia 'Actus Purus is a term employed in scholastic philosophy to express the absolute perfection of God. It literally means, "pure act." Created beings have potentiality that is not actuality, imperfections as well as perfection. Only God is simultaneously all that He can be, infinitely real and infinitely perfect: `I am who I am`(Exodus 3:14). His attributes or His operations, are really identical with His essence, and His essence includes essentially His existence.' back
Aquinas 13 Summa: I 2 3: Whether God exists? I answer that the existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . The second way is from the nature of the efficient cause. . . . The third way is taken from possibility and necessity . . . The fourth way is taken from the gradation to be found in things. . . . The fifth way is taken from the governance of the world. back
Aquinas 20 Summa I, 3, 7: Whether God is altogether simple? 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back
Aristotle Metaphysics, Book XII 'But since there is something which moves while itself unmoved, existing actually, this can in no way be otherwise than as it is. For motion in space is the first of the kinds of change, and motion in a circle the first kind of spatial motion; and this the first mover produces. The first mover, then, exists of necessity; and in so far as it exists by necessity, its mode of being is good, and it is in this sense a first principle.' back
Bernard Lonergan - Wikipedia Bernard Lonergan - Wikipedia, the free encyclopedia 'Bernard J.F. Lonergan, SJ, CC (17 December 1904 – 26 November 1984) was a Canadian Jesuit priest, philosopher, and theologian regarded by some as one of the most important thinkers of the twentieth century.[1] Lonergan's works include Insight: A Study of Human Understanding (1957) and Method in Theology (1972), as well as two studies of Thomas Aquinas, several theological textbooks, and numerous essays, including two posthumously published essays on macroeconomics. A projected 25-volume Collected Works is underway with the University of Toronto Press. He held appointments at the Pontifical Gregorian University, Regis College, Toronto, as Distinguished Visiting Professor at Boston College, and as Stillman Professor of Divinity at Harvard University. back
Brouwer fixed point theorem - Wikipedia Brouwer fixed point theorem - Wikipedia, the free encyclopedia 'Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself. back
Cantor's diagonal argument - Wikipedia Cantor's diagonal argument - Wikipedia, the free encyclopedia 'Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. Such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which Cantor began. The diagonal argument was not Cantor's first proof of the uncountability of the real numbers; it was actually published much later than his first proof, which appeared in 1874. However, it demonstrates a powerful and general technique that has since been used in a wide range of proofs, also known as diagonal arguments by analogy with the argument used in this proof. The most famous examples are perhaps Russell's paradox, the first of Gödel's incompleteness theorems, and Turing's answer to the Entscheidungsproblem.' back
Charles Dubray - Actus purus Actus Purus - Catholic Encyclopedia 'So that God is not a becoming, as in some pantheistic systems, nor a being whose infinite potentiality is gradually unfolded or evolved. But He possesses at once all perfections. He is simultaneously all that He can be, infinitely real and infinitely perfect. What we conceive as His attributes or His operations, are really identical with His essence, and His essence includes essentially His existence. For all intelligences except His own, God is incomprehensible and indefinable. The nearest approach we can make to a definition is to call Him the Actus Purus. It is the name God gives to Himself: "I am who am", i.e., I am the fullness of being and of perfection.' back
Conservation of energy - Wikipedia Conservation of energy - Wikipedia, the free encyclopedia ' In physics, the conservation of energy' states that the total amount of energy in any isolated system remains constant but cannot be recreated, although it may change forms, e.g. friction turns kinetic energy into thermal energy. In thermodynamics, the first law of thermodynamics is a statement of the conservation of energy for thermodynamic systems, and is the more encompassing version of the conservation of energy. In short, the law of conservation of energy states that energy can not be created or destroyed, it can only be changed from one form to another.' back
Differential equation - Wikipedia Differential equation - Wikipedia,the free encyclopedia 'A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines. Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly. back
Eigenfunction - Wikipedia Eigenfunction - Wikipedia, the free encyclopedia 'In mathematics, an eigenfunction of a linear operator, A, defined on some function space is any non-zero function f in that space that returns from the operator exactly as is, except for a multiplicative scaling factor. More precisely, one has Af = λf for some scalar, λ, the corresponding eigenvalue.' back
God - Catholic Encyclopedia God - Catholic Encyclopedia 'God Etymology of the Word "God" Discusses the root-meaning of the name "God", which is derived from Gothic and Sanskrit roots.
Existence of God Formal dogmatic Atheism is self-refuting, and has never won the reasoned assent of any considerable number of men. Nor can Polytheism ever satisfy the mind of a philosopher. But there are several varieties of what may be described as virtual Atheism which cannot be dismissed so quickly.
Nature and Attributes of God In this article, we proceed by deductive analysis to examine the nature and attributes of God to the extent required by our limited philosophical scope. We will treat accordingly of the infinity, unity, and simplicity of God, adding some remarks on Divine personality.
Relation of God to the Universe The world is essentially dependent on God, and this dependence implies (1) that God is the Creator of the world — the producer of its whole substance; and (2) that its continuance in being at every moment is due to His sustaining power.
The Blessed Trinity The Trinity is the term employed to signify the central doctrine of the Christian religion — the truth that in the unity of the Godhead there are Three truly distinct Persons: the Father, the Son, and the Holy Spirit.
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God - Wikipedia God - Wikipedia, the free encyclopedia 'God is the English name given to a singular being in theistic and deistic religions (and other belief systems) who is either the sole deity in monotheism, or a single deity in polytheism. God is most often conceived of as the supernatural creator and overseer of the universe. Theologians have ascribed a variety of attributes to the many different conceptions of God. The most common among these include omniscience (infinite knowledge), omnipotence (unlimited power), omnipresence (present everywhere), omnibenevolence (perfect goodness), divine simplicity, and eternal and necessary existence.' back
No cloning theorem - Wikipedia No cloning theorem - Wikipedia, the free encyclopedia 'The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.' back
Parmenides - Wikipedia Parmenides - Wikipedia, the free encyclopedia 'Parmenides of Elea (early 5th century BC) was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy, his only known work is a poem which has survived only in fragmentary form. In it, Parmenides describes two views of reality. In the Way of Truth, he explained how reality is one; change is impossible; and existence is timeless, uniform, and unchanging. In the Way of Opinion, he explained the world of appearances, which is false and deceitful. These thoughts strongly influenced Plato, and through him, the whole of western philosophy.' back
Turing machine - Wikipedia Turing machine - Wikipedia, the free encyclopedia 'Turing machines are extremely basic abstract symbol-manipulating devices which, despite their simplicity, can be adapted to simulate the logic of any computer algorithm (as we understand them). They were described in 1936 by Alan Turing. Though they were intended to be technically feasible, Turing machines were not meant to be a practical computing technology, but a thought experiment about the limits of mechanical computation; thus they were not actually constructed. Studying their abstract properties yields many insights into computer science and complexity theory.' back

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