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On Plato, the Early Church, and Modern Science: An Eclectic Meditation
November 30, 2004 | Jean F. Drew

Posted on 11/30/2004 6:21:11 PM PST by betty boop

On Plato, the Early Church, and Modern Science: An Eclectic Meditation
By Jean F. Drew

God, purposing to make the universe most nearly like the every way perfect and fairest of intelligible beings, created one visible living being, containing within itself all living beings of the same natural order.

Thus does Plato (d. 347 B.C.) succinctly describe how all that exists is ultimately a single, living organism. At Timaeus20, he goes on to say:

“There exists: first, the unchanging form, uncreated and indestructible, admitting no modification and entering no combination … second, that which bears the same name as the form and resembles it … and third, space which is eternal and indestructible, which provides a position for everything that comes to be.”

And thus we find a description of the universe in which Being and Existence (Becoming) — the one God and the multiplicity of things — are bound together as a single living reality whose extension is mediated by Space (which for us moderns implies Time).

Our aim in this essay is to define these ideas and their relationships, and trace their historical development from the ancient world to the present. Taking a page from the late Eric Voegelin (1901–1985, philosopher of history specializing in the evolution of symbolization), we will follow a history-of-ideas approach to these issues. Along the way we will find that not only philosophy and cosmology, but also theology and even modern science can illuminate these seminal conceptions of Platonic thought. We must begin at the beginning, that is, with God — who is absolute Being in Plato’s speculation, of whom the cosmos itself is but the image (eikon) or reflection.

When Plato speaks of God (or when Aristotle does for that matter, as in e.g., Nicomachean Ethics), he is not referring to the Olympian gods, to Zeus, Hera, Athena, Poseidon, and the rest of the gang of “immortals.” For the Olympians are like man in that they are creatures of a creating God. Not only that, but they are a second generation of gods, the first having reigned in the antediluvian Age of Chronos; which is to say that the Olympians’ rule or law is not everlasting, but contingent. Thus they are not self-subsistent, but dependent (contingent) on a principle outside of themselves. We might say that the central difference between Plato’s God and the Olympians consists in the fact that the latter are “intracosmic” gods, and the former is “extracosmic,” that is, transcending all categories and conditions of space-time reality. In contrast, the intracosmic gods are subject to change, to contingency; and so, though they may truly be said to exist in some fashion, cannot be said to possess true Being. (More on these distinctions in a minute.)

It is clear that for Plato, God is the “Beyond” of the universe, or in other words, utterly transcendent, perfectly self-subsistent Being, the “uncaused cause” of all the multiplicity of existents in the universe. In yet other words we can say that, for Plato, the cosmos is a theophany, a manifestation or “presence” of the divine Idea — in Christian parlance, the Logos if I might draw that association — in the natural world.

As Wolfgang Smith notes, “Christian teaching is based upon the doctrine of the Logos, the Word of God, a term which in itself clearly suggests the idea of theophany. Moreover, what is implicit in the famous Prologue of St. John [“In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not.” (John 1:1–5)] is openly affirmed by St. Paul when he declares that “the invisible things of Him from the creation of the world have been clearly seen, being understood by the things that are made, even His power and Godhead” (Rom. 1:20) … The indisputable fact is that at its deepest level Christianity perceives the cosmos as a self-revelation of God.” [Wolfgang Smith, Cosmos and Transcendence, 1984]

Being and Existence (Becoming)
Being is a concept so difficult that it comes close to eluding our grasp altogether. It is utterly beyond space and time; imperishable; entirely self-subsistent, needing nothing from outside itself in order to be complete; essential; immutable; and eternally perduring. Contrast this with the concept of existence, regarding which Plato asks “how can that which is never in the same state be anything?” And this is the clue to the profound difference between being and existence: The existing things of this world are mutable and transient.

We must in my opinion begin by distinguishing between that which always is and never becomes from that which is always becoming but never is. The one is apprehensible by intelligence with the aid of reasoning, being eternally the same, the other is the object of opinion and irrational sensation, coming to be and ceasing to be, but never fully real. In addition, everything that becomes or changes must do so owing to some cause; for nothing can come to be without a cause. [Timaeus, 3:28]

Smith writes of the existing or “becoming” things that

“… they come upon the scene, we know not from whence; they grow, change, and decay; and at last they disappear, to be seen no more. The physical cosmos itself, we are told, is a case in point: it, too, has made its appearance, perhaps some twenty billion years ago, and will eventually cease to exist [i.e., finally succumbing, we are told, to thermodynamic entropy or “heat death”]. What is more, even now, at this very moment, all things are passing away. ‘Dead is the man of yesterday,’ wrote Plutarch, ‘for he dies into the man of today: and the man of today is dying into the man of tomorrow.’ Indeed, ‘to be in time’ is a sure symptom of mortality. It is indicative, not of being, but of becoming, of ceaseless flux.”

All the multiplicity of existents in the universe are in a state of becoming and passing away. But Plato’s great insight is that all things in the state of becoming — that is, all existing things — are whatever they are because they are participations in Being. That is to say, “we perceive the trace of being in all that exists,” writes Smith, “and that is why we say, with reference to any particular thing, that it is.” Existence, in other words, is contingent on Being.

But we wonder: In what way is this possible? And if existents participate in being, what is that Being in which they participate?

In Exodus 3:14 Moses has experienced a theophany: While tending his flock on Mount Horeb, suddenly he hears the voice of God issuing from a burning bush: God is speaking to him! Reverentially, Moses inquires of God what is His name (meaning: what is His nature or character).

And God said unto Moses, I AM WHO AM: and He said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you.

God has told Moses: that He is Being (“I AM”). And the strong implication is that there is no “other” being: “I alone AM.” For “I” is plainly singular in form.

Smith draws the crucial point, “God alone IS. But how are we to understand this? ‘It seems to me,’ writes St. Gregory of Nyssa, ‘that at the time the great Moses was instructed in the theophany he came to know that none of those things which are apprehended by sense perception and contemplated by the understanding really subsist, but that the transcendent essence and cause of the universe, on which everything depends, alone subsists.’ But why? Does not the world exist? Are there not myriads of stars and galaxies and particles of dust, each existing in its own right? And yet we are told that the transcendent essence alone subsists. ‘For even if the understanding looks upon any other existing things,’ the great theologian goes on to say, ‘reason observes in absolutely none of them the self-sufficiency by which they could exist without participating in true Being. On the other hand, that which is always the same, neither increasing nor diminishing, immutable to all change whether to better or to worse (for it is far removed from the inferior and has no superior), standing in need of nothing else, alone desirable, participated in by all but not lessened by their participation — this is truly real Being.’”

Smith continues: “In the words of St. Gregory, ‘that which is always the same, neither increasing nor diminishing, immutable to all change … is truly real being.’ As concerns ‘existing things,’ on the other hand, the teaching implies that these entities are always changing, always in a state of flux, so that their very existence is in a way a process of becoming, in which however nothing is actually produced. This has been said time and again, beginning with Heraclitus and the Buddhist philosophers. And there can be little doubt that it is true: even modern physics, as we can see, points to the same conclusion. Only there is another side to the coin which is not always recognized. Existent things — the very flux itself — presuppose what Gregory and the Platonists have termed ‘a participation in Being.’ The point is that relative or contingent existences cannot stand alone. They have not an independent existence, a being of their own. ‘In Him we live, and move, and have our being,’ says St. Paul….”

St. Augustine confirms the Platonic insight this way:

I beheld these others beneath Thee, and saw that they neither altogether are, nor altogether are not. An existence they have, because they are from Thee; and yet no existence, because they are not what Thou art. For only that really is, that remains unchangeably.

Space
Space is the third essential term of the Platonic cosmology: It is the matrix in which living things and all other existents participate in Being. Plato’s creation myth — the Myth of the Demiurge in Timaeus — elucidates the Platonic conception of Space.

For Plato, the God of the Beyond is so “beyond” that, when it came time for creating the Cosmos, he didn’t even do it himself. He sent an agent: the Demiurge, a mythical being endued by God to be in divine likeness of God’s own perfect love, truth, beauty, justice, and goodness. The embodiment of divine perfections, the Demiurge wishes to create creatures just as good and beautiful as himself, according to the standard of the divine Idea — a direct analog, it seems to me, of the Logos theory of the ancient Church. Indeed, Eric Voegelin sees in the Demiurge the symbol of Incarnation [Order and History Vol. 3: Plato and Aristotle, 1957]:

“The Demiurge is the symbol of Incarnation, understood not as the result of the process but as the process itself, as the permanent tension in reality between the taxis of form or idea and the ataxia of formlessness.”

Similarly to the Christian account, the Demiurge in a certain way creates ex nihilo — that is, out of Nothing. At first glance, Plato is seen specifying, not a pre-existing “material” but a universal field of pure possibility called Chora, “Space.” Perhaps we may find in this concept a strong analogy to Isaac Newton’s concept of Absolute Space (see below).

Chora seems to indicate the idea of an eternal, universal field of pure stochastic potentiality that needs to become “activated” in order to bring actual beings into existence. In itself, it is No-thing, i.e., “nothing.” This “activation” the Demiurge may not effect by fiat: He does not, for instance, “command” to “Let there be Light!” The main tool at his disposal is Peitho, “persuasion.”

And if Chora is not so persuaded, it will remain in a state of “nothingness.” It will remain unformed, in the condition of ataxia. Of itself it is “Nothing”; by itself, it can do nothing. It cannot generate anything out of itself, not even matter in primaeval form.

And thus Plato introduces the figure of the Demiurge into his creation myth, symbolizing form or idea — the principle of (formative) taxia that draws (formless) ataxia into existence. We moderns might be tempted to describe the Demiurge as constituting an “information set” together with an “energy source,” who “persuades” the pure stochastic potentiality of formless, absolute, empty space into actualized form, and thus existence. From the cosmic standpoint, he makes unity out of multiplicity, in harmony and geometrical proportion:

“The best bond is the one that effects the closest unity between itself and the terms it is combining; and this is best done by a continued geometrical proportion.” [Timaeus, 4]

Thus the Demiurge is a kind of “divine geometer,” producing the forms (or mathematical ideas) that Chora can be persuaded to conform to, and thus come into existence.

But the Demiurge does more than just get things started: As bearer of the divine Idea — as pure love and beauty and goodness and truth — he continues always persuading Chora to generate creatures as like himself as possible (i.e., reflecting his own divine qualities at whatever generic stage), throughout all eternity. Thus creation is a continuous process in space-time. Moreover, it is the source and driver of evolution as a universal natural process.

Through the ongoing activity of the Demiurge, men and the world are constantly being informed and renewed by the divine Idea; and thus a unified cosmic whole, a “One Cosmos,” a universal order comes into being at the intersection of time and timelessness, of immanent and transcendent reality, in the medium of Space (and Time).

Compare the Platonic creation myth with the philosophy of Dionysius the [Pseudo-]Areopagite, said to be the Greek converted by St. Paul in Acts, 17:34. For Dionyius, the “names of God” — the divine qualities — are goodness, being, life, wisdom, power, and justice. Joseph Stiglmayr writes [Cath. Encycl. at the entry for Dionysius the Pseudo-Areopagite], that for Dionysius, God is

“… the One Being (to hen), transcending all quality and predication, all affirmation and negation, and all intellectual conception, [Who] by the very force of His love and goodness gives to beings outside Himself their countless gradations, unites them in the closest bonds (proodos), keeps each by His care and direction in its appointed sphere, and draws them again in an ascending order to Himself (epistrophe) … all created things [proceed] from God by the exuberance of being in the Godhead (to hyperpleres), its outpouring and overflowing … and as a flashing forth from the sun of the Deity. Exactly according to their physical nature created things absorb more or less the radiated light, which, however, grows weaker the farther it descends. As the mighty root sends forth a multitude of plants which it sustains and controls, so created things owe their origin and conservation to the All-Ruling Deity…. Patterned upon the original of Divine love, righteousness, and peace, is the harmony that pervades the universe…. All things tend to God, and in Him are merged and completed, just as the circle returns into itself, as the radii are joined at the centre, or as the numbers are contained in unity.”

The Platonic resonances seem unmistakeable in these lines. It appears that both Platonic speculation and the Logos doctrine of the ancient Church as articulated by Dionysius are in agreement that Creator must be “beyond” Creation in order to resonate with it — which resonance is what makes the universe to be alive — i.e., a living universe.

C. A. Dubrey points out [Cath. Encycl. at the entry “Teleology”], that the theology of St. Thomas Aquinas makes it clear that, “Intrinsic finality [we are to think of this as a blend or merger of efficient and final causes in the Aristotelian sense] consists in the fact that every being has within itself a natural tendency whereby its activity is directed towards the perfection of its own nature…. St. Thomas does not hesitate to speak of ‘natural appetite,’ ‘natural inclination,’ and even ‘intention of nature,’ [we moderns might be tempted to add ‘instinct’ to this list] to mean that every being has within itself a directive principle of activity. Accordingly, God does not direct creatures to their ends from outside, but through their own nature…. The Divine plan of creation is carried out by the various beings themselves acting in conformity with their nature.

When, however, this finality is called immanent, this expression must not be understood in a pantheistic sense, as if the intelligence which the world manifests were to be identified with the world itself, but in the sense that the immediate principle of finality is immanent in every being…. Thus the unconscious finality in the world leads to the conclusion that there must be an intelligent cause of the world.” [Emphasis added.]

Aquinas’ insight, and also Plato’s, evokes a reconsideration of Isaac Newton’s concept of Absolute Space. Possibly this may be understood in the following terms. First, Absolute Space is “empty” space. Second, it is not a property of God, but an effect of His Presence; i.e., we advert to theophany again. The question then arises, in what “where” or “when” does this theophany take place? Perhaps Newton’s answer would be: In the beginning, and continuously thereafter. Second, it has been suggested that Newton intends us to understand Absolute Space as the sensorium Dei: “God constitutes space and time through his eternity and omnipresence” [ existendo semper et ubique, durationem et spatium consitutit: Philosophiae Naturalis Principia Mathematica, 3d ed., 1726]. Wolfhart Pannenberg writes,

“Now there are a number of good reasons — suggested by both philosophical and scientific thought — to consider time and space as inseparable. Einstein’s field concept comprises space, time, and energy. It takes the form of a geometrical description, and this seems to amount to a spatialization of time. The totality of space, time, and energy or force are all properties of a cosmic field.

“Long before our own age a theological interpretation of this subject matter had been proposed, and it was Isaac Newton who offered this proposal. It too referred everything to space or, more precisely, to the correlation of force as in the case of a force like gravitation acting at a distance. Newton’s well-known conception of space as sensory of God (sensorium Dei) did not intend to ascribe to God an organ of sense perception, the like of which God does not need, according to Newton, because of divine omnipresence. Rather, Newton took space as the medium of God’s creative presence at the finite place of his creatures in creating them.” [Wolfhart Pannenberg, Toward a Theology of Nature, 1993]

Thus the infinite takes priority over every finite experience, including intellectual experience — a position decisively argued by Descartes, as Pannenberg avers, “in his thesis that the idea of God is a prior condition in the human mind for the possibility of any other idea, even that of the ego itself.”

* * * * * *

The Influence of Platonic Speculation on the Early History of the Church
D. Edmund Joaquin, an insightful and gracious Christian friend, writes, “We understand that the universe is created and sustained by the Word [the Logos], and not only that, but by the Word sounding. God sustains the universe consciously and actively. He has not gone away and left us. In fact, He reveals Himself to us, and His final revelation is in the person of Christ [the Logos]. Christ is not an abstract aspect of God, like wisdom. He is God. He is God incarnating in the world that He himself has made.”

Joaquin further observes that “[the Gospel of] John is written to the Greeks and put into words that they could understand.” It seems there’s a mystery buried in here somewhere. Consider: Socrates was the teacher of Plato, who was the teacher of Aristotle, who was the teacher of Alexander — and Alexander spread Greek culture throughout Eurasia, the Middle East, and the Indian subcontinent. Add to this the fact that the great evangelist, St. Paul, had some difficulty converting the Jews to the Christian faith; but he converted the Greeks in droves. Not only St. John, but also St. Paul speaks in terms the Greek mind could readily grasp, as when he says God is He “in Whom we live and move and have our being.” These historical connections do not appear to be accidental, coincidental, nor incidental to the spread of the early Christian Church.

According to The Catholic Encyclopedia, the Greeks strongly responded to Christianity for its moral beauty as well as its truth. A case in point is St. Justin Martyr. He was a man of Greek culture, born in Palestinian Syria about the year 100 A.D, who converted to the faith around 130 A.D. Justin became one of Christianity’s earliest and most powerful apologists, and ended up condemned by the Roman authority for refusing to sacrifice to the pagan gods, for which offense he was summarily executed by the Imperium, along with several other of his “refusnik” co-religionists. The official record of their martyrdom is extant:

“The Prefect Rusticus says: Approach and sacrifice, all of you, to the gods. Justin says: No one in his right mind gives up piety for impiety. The Prefect Rusticus says: If you do not obey, you will be tortured without mercy. Justin replies: That is our desire, to be tortured for Our Lord Jesus, and so to be saved, for that will give us salvation and firm confidence at the more terrible universal tribunal of Our Lord and Saviour. And all the martyrs said: Do as you wish; for we are Christians, and we do not sacrifice to idols. The Prefect Rusticus read the sentence: Those who do not wish to sacrifice to the gods and to obey the emperor will be scourged and beheaded according to the laws. The holy martyrs glorifying God betook themselves to the customary place, where they were beheaded and consummated their martyrdom confessing their Saviour.”

Jules Lebreton writes (at the entry for St. Justin Martyr in Cath. Encycl.) “Justin tries to trace a real bond between philosophy and Christianity: according to him, both one and the other have a part in the Logos, partially disseminated among men and wholly manifest in Jesus Christ.”

Yet for all their apparent similarities and resemblances in many respects, there is a profound difference between Platonic insight and the Christian one: and this pertains to the relations between God and man.

Both Plato and Justin proclaim the transcendent God. Yet for Plato, God is so “beyond” as to be almost impossible of human grasp. Yet Plato felt the “divine pulls” in his own nature. These Plato thought could be accounted for and articulated by an act of pure unaided intellect, that is by nous, in a state of intense contemplation.

Contrast this position with Justin Martyr’s, who insisted that human wisdom was impossible without the testimony of the Prophets (whom God himself had informed and instructed) and the action of the Holy Spirit. For Plato, man’s relations with God consist of operations of the mind. For Justin, they are operations of the heart, of the Spirit. For Justin, God is not a mental abstraction: He is real Personality with whom one can have direct personal relations, in the Spirit.

A later writer, John Scotus Eriugina (ninth century) elaborates the Justinian position, in the process noting that there is a “downward tendency” of the soul towards the conditions of animal existence, and that this has only one remedy: Divine grace, the free gift of the Holy Spirit. “By means of this heavenly gift,” writes William Turner [at the entry for Scotus in the Catholic Encyclopedia], “man is enabled to rise superior to the needs of the sensuous body, to place the demands of reason above those of bodily appetite, and from reason to ascend through contemplation to ideas, and thence by intuition to God Himself.”

The pull of animal nature is an idea we also find in Plato, and also the countervailing pull from the divine Beyond. Man lives in the metaxy, in the “in-between reality” constituted by the two. Man’s task is to resolve this tension, and establish the proper balance that expresses the highest and best development of his human nature. But man must do this entirely by himself by means of nous or reason. There is no spiritual help “extra” to the human psyche available to facilitate this process.

In contrast, as Lebreton points out, Justin Martyr

“…admits that the soul can naturally comprehend what God is, just as it understands that virtue is beautiful … but he denies that the soul without the assistance of the Holy Ghost [Spirit] can see God or contemplate him directly through ecstasy, as the Platonic philosophers contended. And yet this knowledge of God is necessary for us: ‘We cannot know God as we know music, arithmetic, or astronomy’; it is necessary for us to know God not with an abstract knowledge but as we know any person with whom we have relations. The problem which it seems impossible to solve is settled by revelation; God has spoken directly to the Prophets, who in their turn have made Him known to us…. It is the first time in Christian theology that we find so concise an explanation of the difference that separates Christian revelation from human speculation.” [Emphasis added]

* * * * * *

Natural Law, Contingency, and the Scientific Method
The Platonic model encourages us to recognize that the universe is zoon empsychon ennoun, a living creature endowed with soul and intelligence. The myth of the Demiurge describes the world process as a type of incarnation, a dynamic relation of absolute being and contingent becoming evolving in space and time in a manner expressing a perduring taxia–ataxia relation. The Cosmos itself — the totality of all existing things — like its constituents, for example man and even the stars, is an eikon of being-in-becoming, a reflection or image of the divine Idea. Time itself is but a “moving image of eternity.” The life of the cosmos is wholly dependent, contingent on the Idea from which it manifests.

It is a lawful, orderly universe, yet one in which new occurrences are always arising. These new events are coming from, as it were, a “sea of contingency” analogous to Plato’s conception of Space, that is Chora — the infinite field of unformed, pure potentiality.

The immediately foregoing ideas, of course, are not scientific ones strictly speaking. Still, there are elements here that perhaps science would do well to consider, in order to maintain the integrity of its own method. For one thing, it seems science itself, in its disclosure of the regularities of nature, seems to have an in-built tendency to overlook contingency. We may define an event as contingent if a description of it is neither self-evident nor necessary, “if it could have happened differently,” as Ted Peters puts it in his Preface to Pannenberg’s Towards a Theology of Nature.

C. A. Dubray writes [“Teleology,” Cath. Encycl.], “The fact that the world is governed by laws, far from giving any support to the mechanistic conception, is rather opposed to it. A law is not a cause, but the expression of the constant manner in which causes produce their effects.” In other words, natural laws are expressions of observable regularities that occur in the world of existent phenomena in ordinary space-time reality. Thus, the laws themselves have no force as “causes”: they are descriptions.

Yet the focus on regularity inevitably masks the particularity and contingency of unique events. As Ted Peters notes, it is here that “we run into a problem of focus in the scientific community, because virtually all the theoretical attention is given to the regularity of nature’s laws, while the contingency of natural events slips into the nearly invisible background.” Peters continues:

“What researchers concentrate on are the uniformities that can be expressed in timeless equations. A dictionary of equations describing these uniformities allegedly constitutes scientific knowledge…. A closer examination, however, reveals that the applicability of these equations to concrete cases of natural processes requires certain initial and marginal conditions, conditions that in every case are contingent. Only when contingent conditions permit can we expect a natural law to operate as expected.”

To the extent that the scientific method of inquiry is premised on an “If/Then” logical construction — which seems ever to be the case — the method itself is an exercise in contingency, yet nonetheless one in which “Determinacy gets thematized, whereas contingency gets ignored.” Arguably this is a serious bias having epistemological implications; for e.g., “if the laws of classical dynamics are in principle temporally reversible, the actual course of natural events from which those laws have been abstracted is not. The reality of nature is first and foremost a historical reality.”

Pannenberg suggests a corrective for this “bias,” acknowledging: “That modern science so easily lends itself to abuse cannot be prevented in principle. It is one of the risks involved in the abstract study of regularities that either are inherent in nature itself or can be imposed on natural processes [e.g., as in ideological, technical, or engineering solutions]. This risk cannot be met on the level of scientific description itself but must be met first on the level of philosophical reflection on the work of science. It is on this level that the abstract form of scientific description must be considered with special attention to what it is “abstracted from” and what is methodically disregarded in the abstract formulas of science.”

And so contingent conditions — i.e, initial and boundary conditions — must be restored to their proper place in our deliberations, for they “are required for any formula of natural law to be applied. They are contingent at least in that they cannot be derived from the particular formula of law under consideration.… The mathematical formula of a natural law may be valid without regard to time. The physical regularity that is described by such a formula is not independent of time and temporal sequence. But it is only that physical regularity which makes the mathematical formula a law of nature. This suggests that the laws of nature are not eternal or atemporal because the fields of their application, the regularities of natural processes, originate in the course of time. Thus it also becomes understandable that new patterns of regularity emerging in the sequence of time constitute a field of application for a new set of natural laws….”

We may recognize that the total process of natural events presents itself to observation as a mesh of contingency and regularities. It is the task of science to pursue thematically the aspect of regularity. But, asks Pannenberg, can science “ever succeed in bringing into view the entirety of nature as determined in all details by a number of laws that are in any case not infinitely complex? This would mean at the same time that a stage of research is conceivable from which nothing more could be discovered. Many natural scientists have had this nightmare because of the successes of their own research. Fortunately it probably is not a truthful dream.”

For, says Pannenberg, “laws always uncover what is necessary superimposed on what is contingent. Given the undeniable contingency of occurrences in natural events, can we recognize in their special character as occurrences … [that] regularity as their own element in such a way that the presence of regularity can be thought together with the contingency of occurrences, not only under abstraction from the contingency of occurrences?” [Emphasis added]

Which is why Pannenberg advocates an opening up of new viewpoints in scientific research, “not because physical hypotheses or insights can be derived from them but because they open up and enlarge the intellectual space on which the formation of physical hypotheses depends…. In physics also, horizons of questioning have to be opened up first of all in order that hypotheses that arise in them can be examined by experiment and classified theoretically.”

Perhaps we need a greater appreciation of the “fitness” of the scientific method to engage the truly great questions of life, which ever seem to involve the relations of law and contingency. Leibniz propounds two great questions of perennial interest to the human mind: (1) Why are things the way they are and not some other way? (2) Why does anything exist at all?

Such questions, scientists will readily tell you, are beyond the purview of the scientific method. But does that mean such questions have no force or meaning such that they should not be asked at all?

Perhaps the incapability of the scientific method to answer such questions owes to the fact that all the great physical laws are acknowledged to be time-reversible; but we know that existence in space and time is not a time-reversible process. As Pannenberg states, it is a historical process. We might even say it is an evolutionary process.

Which suggests an analogy that might enlighten these questions, sharpen their meanings, and suggest additional questions: an analogy to direct human experience. Pannenberg writes of human beings, who do seem to live in a “time-irreversible,” that is “historical” process:

“Human beings never live only in the now. Rather, they experience their present as heirs of the past and as its active change. They anticipate the future in fear, hope, and planning; and in the light of such anticipation of the future they return to their present and the heritage of their past. The fact that we know of historical continuity is at least also conditioned by this peculiarity of human experience with time. If there is a new event, then it modifies the context of our consciousness of time which is already found present. It throws light back on earlier occurrences which have become a part of our experience already. In the same way, ideas that occur to us throw light on our previous expectations and plans in justifying, fulfilling, modifying, or disappointing and thwarting them. Thus the contingent event always enters already into a context of experience or tradition…. The future, beginning in the present happenings, is thus the origin of the perspective in which the past occurrences are put by every new experience.”

Worldviews and Paradigm Shifts
It is perhaps a truism that we tend to find what we’re looking for by screening out any and all potential elements which do not fit the pattern of our expectation. Arguably, the scientific method may be said inherently to suffer exposure to potential danger from this side, as suggested in the above remarks. Indeed, Schröedinger’s theory of wavefunction seems to predict this. Consider these remarks from Stephen M. Barr [Modern Physics and Ancient Faith, 2003]:

“In quantum theory, as traditionally formulated, there are ‘systems’ and ‘observers.’ Or rather, in any particular case, there is the system and the observer. The observer makes measurements of the system. As long as the system is undisturbed by external influences (that is, as long as it is ‘isolated’), its wavefunction — which is to say its probability amplitudes — will evolve in time by the Schröedinger equation…. However, when a measurement is made of the system the observer must obtain a definite outcome. Suddenly, the probability for the outcome that is actually obtained is no longer what the mathematics said it was just before the measurement, but jumps to 100 percent. And the probabilities for all the alternative outcomes, the ones that did not occur, fall to 0 percent.”

Thus we might say that the “reality” we humans experience ever involves “a moving goal-post.” And as the mover of this goal-post, the human agent is most indispensably involved in this process.

Faced with such “indeterminacy” regarding the foundations of experience, it is not surprising that people usually have recourse to mediating worldviews, or organized frames of ideational reality that constitute the conceptual space in which active experience is engaged and accordingly analyzed and interpreted. Certainly Plato has offered such a model. And so has Nobel laureate Jacques Monod [in Chance and Necessity, 1971]:

“Chance alone is the source of every innovation, of all creation in the biosphere. Pure chance, absolutely free but blind, is at the very root of the stupendous edifice of evolution. The central concept of biology … is today the sole conceivable hypothesis, the only one compatible with observed and tested fact. All forms of life are the product of chance….”

Needless to say, these two models are polar opposite conceptualizations. Yet having received each on “good authority,” which do we choose?

Such are not idle considerations; for as James Hannam points out [“The Development of Scientific and Religious Ideas,” 2003], “grand theories … often suffer death by detail where it is found that up close the situation is too complicated for the theory to handle…. [Yet] in the end, after it has changed the course of the river of enquiry, the theory can end up as a mortlake cut off from the general flow….”

Hannam cites historian Thomas Kuhn, who documents an historical process he terms “paradigm shift,” describing a situation in which the findings of authoritative science move “out of science and into practically every other field of human endeavor.” Once a given, albeit partial or even defective theory becomes “dominant,” writes Hannam, “far from being thrown out, a falsified theory is enhanced to deal with new information until such time as it finally collapses under the weight of anomalous results. Then, after a chaotic period, a new theory emerges that can deal with the anomalies and normal service resumes…. A paradigm refers to but one field, say classical mechanics or health policy whereas the ideology/worldview is the general background that underpins all the paradigms.”

The worldview (or ideology, if you prefer), for better or worse, implicitly shapes the background knowledge of thinking agents to which new experiences constantly are being conformed. Hannam says that worldview “is often so deeply embedded in the psyche that it is very rarely considered explicitly except by specialists,” but that nonetheless, “the worldview is seen as [a] self-confirming fact of life and hence it is not strictly rational…. The existence of a dominant worldview does not mean that a particular individual is unable to think outside the box but rather that his ideas are unlikely to fall on fertile ground. Unless new ideas can be stated in a language that makes them comprehensible to his peers, his intention in writing will not be met.”

Which is the not-too-subtle way to put the fact that every man has a worldview, without exception, whether articulate or inarticulate; and that somehow, for the “intention of writing to be met” — that is, for accurate and meaningful (i.e., successful) communication of ideas to take place — some deeper, common ground of shared truth must first be accessed, for the purpose of providing a more capacious intellectual space in which the human pursuit of knowledge and wisdom might unfold or evolve from its present point of attainment.

But where today in our modern world is such a common ground or field to be found? Hannam proposes the examination of the history of ideas as a possibly useful method in the search for common ground. He writes,

“To examine the history of ideas the only fair way to proceed would seem to place before ourselves the evidence and authority that the historical agents had before them and assume they acted rationally on that basis. Otherwise, there is no hope of ever tracing intellectual development because ‘cause and effect’ assumes some sort of logical causality that is impossible with non-rational agents. The best that could be hoped for would be a catalog of mental positions, with no way to say how one led to another except by being pushed by blind exterior forces. This might be precisely what determinists are advocating but they would have to give up any hope of finding causes and restrict themselves to explanations.”

Perhaps we moderns would do well to reconsider the common assumption that people living before our own time were somehow inferior in knowledge, experience, and observational powers as compared with our own status as enlightened individuals. Arguably, the ancient world produced some of the most powerful thinkers in the history of mankind, formulating ideas that were, in the words of Hannam, “the fruits of unfettered metaphysical speculation that inevitably hits on the right answer occasionally.”

Democritus, for example, proposed a theory predicting the atom as the ultimate constituent of matter, more than two-thousand years before the technical means existed to isolate atoms experimentally or, as Hannam notes, any “useful applications for them” could be found. Then it was discovered that the atom itself is an ordered constellation of even finer parts. There seems to be an historical progression of ideas here, the new building up on a framework originally laid up in the past, modifying it, improving on it in light of new insights and technical capabilities.

Hannam gives another example of more recent vintage: “Copernicus needed Nicole Oresme’s solution as to why we do not feel the movement of the Earth even though in Oresme’s time it was just a curiosity as no one thought the Earth actually was moving … each new idea, once accepted, shifts the boundaries of the worldview and makes it possible for further new ideas to be accepted into the pale.”

We can extend the examples even further. Reimann constructed a geometry, apparently because his mind could grasp the logic and beauty it revealed for its own sake. But at the time, it had no apparent “external referent” in the field of nature. It was a beautiful and glorious abstraction — until Einstein came along, and picked it up “off the shelf” as it were, to become the very language of relativity theory.

Thus it might be said that the evolution or “progress” of science depends on successive enlargements of the conceptual space it requires to do its work. In other words, science inherently is a participation in the historicity of the world.

Whatever our personal worldview, perhaps it would be well to recall that science is an historical process. Perhaps this understanding could open up additional, needed conceptual space that science itself requires in order to advance.


TOPICS: Philosophy
KEYWORDS: aquinas; augustine; christianity; churchhistory; contingency; cosmology; epistemology; justinmartyr; metaphysics; newton; ontology; plato; quantumfieldtheory; relativitytheory; schroedinger; spacetime; theology
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1 posted on 11/30/2004 6:21:13 PM PST by betty boop
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To: Alamo-Girl; D Edmund Joaquin; marron; Phaedrus; logos; beckett; cornelis; Diamond; Dumb_Ox; ...

Thought you might have an interest in these subjects -- if you have the time, please feel free to comment. Your thoughts would be most welcome!


2 posted on 11/30/2004 6:23:37 PM PST by betty boop
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To: PatrickHenry; Doctor Stochastic; js1138; tortoise; RadioAstronomer; VadeRetro; Dimensio; ...
Don't know whether this is exactly your cup of tea....

But if you dislike cosmology/metaphystics/theology, you can always skip down to the bold head, "Natural Law, Contingency, and the Scientific Method." Which is followed by another bold head, "Worlviews and Paradigm Shifts." The first starts near the bottom, the next follows closely.

Still, I hope you have the time and interest to get with "the culture" first.

In any case, it is always a great pleasure to hear from you.

So, if you have the time and interest, please do stop by and share your critique with me.

3 posted on 11/30/2004 6:30:17 PM PST by betty boop
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To: betty boop

There was probably no such person as Plato. There was a school. Before you say he had a history, a wealthy Athenian family, all that, remember they had the same kind of history for Theseus. At least they had a ship, or they say they did, for Theseus.


4 posted on 11/30/2004 6:47:00 PM PST by RightWhale (Destroy the dark; restore the light)
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To: betty boop

If you believe something because it makes you feel good to believe it, doesn't that make you a hedonist?


5 posted on 11/30/2004 6:48:30 PM PST by BCrago66
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To: betty boop

Ping so I can read this later when I am suppose to be doing work.


6 posted on 11/30/2004 6:50:46 PM PST by escapefromboston (manny ortez: mvp)
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To: betty boop

plato ping


7 posted on 11/30/2004 6:53:09 PM PST by silverleaf (Fasten your seat belts- it's going to be a BUMPY ride.)
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To: betty boop

Thanks for the ping, BB. This looks like it may be your most ambitious work yet. An impressive effort. I'll try to digest it ... but you know my limitations.


8 posted on 11/30/2004 6:57:43 PM PST by PatrickHenry (The List-O-Links for evolution threads is at my freeper homepage.)
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To: betty boop
The indisputable fact is that at its deepest level Christianity perceives the cosmos as a self-revelation of God.” [Wolfgang Smith, Cosmos and Transcendence, 1984]

Slow down Wolfgang. This is precisely what the early Church did not say. The Church Fathers made a clear distinction between the created world and the uncreated and stated that there is no similarity between the two whatsoever. This was the doctrine of the Church that drove the Neoplatonism of Clement and Origen and the eternal ideas or forms of Plato from the church forever, at least in the East. In this theology of the Church, creation is not self-revelation of God.

Furthermore, the Fathers make a distinction bewteen the uncreated essence of God and the uncreated energies or divine attributes of God. God's essense is unknowable, ineffable, inconceivable, incomprehensible. Revelation of God is only possible by means of the uncreated energy or divine grace which is His outward face to his creation.

The situation in the West was different and with St. Augustine and later the scholastics, the philosophy of Plato and Aristotle enter the theological thinking of the Church. This is most likely what Wolfgang is referring to. This Platonic perspective many be true for some theologians, but it is not an indisputable fact for Christianity as a whole and certainly not at its deepest level.

9 posted on 11/30/2004 7:00:52 PM PST by stripes1776
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To: betty boop

WOW - please add me to your ping list. This is the stuff I have been digging into this past year through a return to college and much - much reading on the side. So much to learn, so little time!
I look forward to future discussions!


10 posted on 11/30/2004 7:07:46 PM PST by freeagle
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To: stripes1776

You have a point. I suggest that even in Clement has a horse in your race. But allowing that Clement can be faulted for his apologetic, the word "Fathers" could be used less broadly than you propose. :)


11 posted on 11/30/2004 7:14:20 PM PST by cornelis
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To: betty boop

I'm not sure I like Plato's idea. I don't think I am just part of a giant sponge. ;^)


12 posted on 11/30/2004 7:22:35 PM PST by AndrewC (New Senate rule -- Must vote on all Presidential appointments period certain.)
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To: betty boop

betty boop

add me to your ping list


13 posted on 11/30/2004 7:40:04 PM PST by ckilmer
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To: cornelis
But allowing that Clement can be faulted for his apologetic, the word "Fathers" could be used less broadly than you propose.

Okay, how about St Theophilus of Antioch, St Irenaeus, St Athansius, St Basil, St Gregory of Nazianzus, St Gregory of Nyssa, St Epiphanius of Cyprus, St John Chrysostom, St Cyril of Alexandria, St Macarius, St Dionysius the Areopagite, St Maximus the Confessor, St John Damascene. That would take us up to about the 7th or 8th Century. Is that defined narrowly enough?

14 posted on 11/30/2004 7:42:48 PM PST by stripes1776
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To: betty boop
Kudos, betty boop! Excellent! Thank you so much for this wonderful essay!
15 posted on 11/30/2004 7:44:23 PM PST by Alamo-Girl
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To: stripes1776

Now you're talking!


16 posted on 11/30/2004 7:46:34 PM PST by cornelis
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To: betty boop

read later


17 posted on 11/30/2004 7:57:49 PM PST by LiteKeeper (Secularization of America is happening)
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To: RightWhale
There was probably no such person as Plato.

Dream on, kiddo.

18 posted on 11/30/2004 8:02:06 PM PST by betty boop
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To: BCrago66
If you believe something because it makes you feel good to believe it, doesn't that make you a hedonist?

"Feel good" has nothing to do with it. This isn't about "body"; this isn't about "the creature"; this is about the human mind, thinking -- as it has, from time immemorial.

Do you have a problem with that?

19 posted on 11/30/2004 8:04:29 PM PST by betty boop
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To: betty boop
As Pannenberg states, it is a historical process. We might even say it is an evolutionary process.

That should give both sides the heegie beegies--if it should sink in.

20 posted on 11/30/2004 8:07:52 PM PST by cornelis
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To: betty boop

betty boop

add me to your ping list


21 posted on 11/30/2004 8:08:12 PM PST by ckilmer
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To: AndrewC
I don't think I am just part of a giant sponge. ;^)

Well never fear, my friend: I don't think Plato ever thought that his theory would in any way consign you, a human being, to the status of "a giant sponge."

Plato is not a Buddhist. I don't even think the Buddhists would consign you to such a status in nature. But then, I am only a very general reader in Buddhist philosophy, being fully engaged by the Christian one -- and more than that, in its eschatology.

Whatever the case, I strongly doubt that Plato was a pantheist.

22 posted on 11/30/2004 8:14:56 PM PST by betty boop
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To: escapefromboston
This is really off topic, but I applaud your choice of Manny Ortiz for MVP! (I read that in your tag line.) I am, after all, a life-long Red Sox fan.... :^) And I am dancing on air, ever since the semi-finals against the Yankees. :^) Everything after that was anticlimactic.

We won the 2004 World Series!!!!! And deserved to!!!!!!!!!!!

There is a God in heaven!!!!!!!!!!!!!!

23 posted on 11/30/2004 8:19:43 PM PST by betty boop
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To: PatrickHenry
...you know my limitations....

No, I really don't, PH. I find you a pretty amazing person. If you have any "limitations" at all, I suspect they may be self-imposed. FWIW = 0.

24 posted on 11/30/2004 8:21:33 PM PST by betty boop
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To: stripes1776
The Church Fathers made a clear distinction between the created world and the uncreated and stated that there is no similarity between the two whatsoever.

Can I get any specific cites in support of this allegation? Such would be welcome, in the interest of the pursuit of God's everlasting truth....

25 posted on 11/30/2004 8:25:53 PM PST by betty boop
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To: cornelis
That should give both sides the heegie beegies--if it should sink in.

LOL cornelis!!! I do believe you may be right about that! :^)

26 posted on 11/30/2004 8:27:58 PM PST by betty boop
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To: betty boop
"A later writer, John Scotus Eriugina (ninth century) elaborates the Justinian position, in the process noting that there is a “downward tendency” of the soul towards the conditions of animal existence, and that this has only one remedy: Divine grace, the free gift of the Holy Spirit. “By means of this heavenly gift,” writes William Turner [at the entry for Scotus in the Catholic Encyclopedia], “man is enabled to rise superior to the needs of the sensuous body, to place the demands of reason above those of bodily appetite, and from reason to ascend through contemplation to ideas, and thence by intuition to God Himself.” "

Yes, the 'downward tendency' is the necessary thrustblock against which we push to exercise the muscles of our desire for God. To yield to the downward tendency as a rule, is to waste the Grace (time) of God. A weightlifter would make little progress pumping feathers.

Eriugina and Turner define the process of growth and eventual illumination in proper form. Thoroughly enjoyed the read. Thanks for posting this.

27 posted on 11/30/2004 8:29:09 PM PST by Eastbound ("Neither a Scrooge nor a Patsy be")
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To: betty boop
Can I get any specific cites in support of this allegation? Such would be welcome, in the interest of the pursuit of God's everlasting truth....

I would recommend "The Vision of God" by Vladimir Lossky. It is less than 200 pages and will serve as a good introduction to the development of theology in the early church in the eastern part of the Roman Empire. I must admit I couldn't make much sense of it the first time I read it, mainly because it didn't coincide with the previous Neoplatonic interpretations of Christianity that I had read. I read it again 6 months later and discovered that I had a very different understanding of Christianity because of this book.

28 posted on 11/30/2004 9:09:03 PM PST by stripes1776
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To: betty boop

Heavy stuff! What you assembled is an effort
of love. I really enjoy reading it, even though
some of is way past me. But it is good exercise
for these brain neurons.

Two questions:
Q1: At death do we revert to that state
we were in prior to conception?

Q2: If we exist in a universe without
beginning or end, then have we
enjoyed infinite existences without
recollections?

A note about infinity. Infinities have
different orders. e.g. The cardinality
of the real numbers is higher than that
of the integers. The set of integers is
said to be a "countable" set. But the RN
are not, since they can't be put in a one
to one correspondence with the integers.

Since time is continuous like the real
numbers, it has the same cardinality as
the RN. The point here is that "infinity"
and "nothing" are concepts that we just
can't comprhend, but we are here and
that is a "miracle", isn't it?


29 posted on 11/30/2004 10:17:03 PM PST by cliff630 (cliff630 (Didn't Christ ask Pilate, "What is the Truth." Even while looking in the face of TRUTH))
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To: cliff630

29 posted on 11/30/2004 10:17:03 PM PST by cliff630 (cliff630 (Didn't Christ ask Pilate, "What is the Truth." Even while looking in the face of TRUTH))
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Uh, you may want to correct your tagline. Pilate asked Christ, not the other way around.


30 posted on 12/01/2004 12:14:57 AM PST by The Grammarian ("Preaching is in the shadows. The world does not believe in it." --W.E. Sangster)
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To: The Grammarian
Unbelievable! That is sacrilegious of me.
That shows how we don't believe our
lying eyes. Thanks so much for being
the first to catch this egregious error.
31 posted on 12/01/2004 2:40:18 AM PST by cliff630 (cliff630 (Didn't Pilate ask Christ, "What is the Truth." Even while looking in the face of TRUTH))
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To: betty boop

What mother would name her child 'The Flat One'?


32 posted on 12/01/2004 9:38:19 AM PST by RightWhale (Destroy the dark; restore the light)
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To: cliff630; Alamo-Girl; D Edmund Joaquin; marron; freeagle; ckilmer; Phaedrus; logos; beckett; ...
A note about infinity. Infinities have different orders. e.g. The cardinality of the real numbers is higher than that of the integers. The set of integers is said to be a "countable" set. But the RN are not, since they can't be put in a one to one correspondence with the integers.

I'm so glad you liked it, cliff! Plus you ask great questions!

Regarding your first question, I really have no idea. Plus I don't know of any way I could possibly find out for sure, sitting here on my own little perch in 3+1D spacetime. Not only have I no recollection of any personal preexistence; but I can't even recollect the birth experience itself. Possibly if there was a preexistence it's buried deep in the unconscious mind. But I wouldn't take that statement to the bank!

As for the second question, it seems clear that the universe had a beginning in time (or at the very least that time began "in the beginning," along with space and matter), which implies it may have an end in time....

But your own observation about infinities having different orders is so interesting, and may actually shed some light on this problem. (I may be in over my head here; if I am, please do let me know.) Both the integers and the real numbers are said to represent infinite sets, yet the latter set is ever so much "richer" than the former, containing an infinitely greater number of elements such that there is no direct correspondence, or cardinality between the two sets. The set of real numbers contains all the elements of the set of integers as elements of itself, plus all the rational and irrational numbers (but not numbers having any imaginary parts). We do seem to have qualitatively different types of infinities here. The integers, or countable numbers, seem analogous to the natural human understanding of the idea of infinity, however imperfect, where the real numbers seem analogous to the nature of infinity as it is in itself. (So to speak.) In other words, the set of integers may be said to be analogous to immanent experience (i.e., its members are "countable'), where the set of real numbers transcends all experience and quite possibly the universe altogether.

Perhaps we then may say that the integers are analogous to time, and the real numbers analogous to eternity. I'll need to think on that some more. I've been working on a little essay on time and the "eternal now." Maybe if I can get it cleaned up, I can post it here. I'll ping it to you if I do, cliff.

Thank you so very much for your thought provoking post!

33 posted on 12/01/2004 11:02:14 AM PST by betty boop
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To: betty boop
In other words, the set of integers may be said to be analogous to immanent experience (i.e., its members are "countable'), where the set of real numbers transcends all experience and quite possibly the universe altogether.

Essentially true in many ways. Everything in our universe is countable, a property that gives us the laws of physics we observe. We can indirectly describe non-countable spaces, but only in terms compatible with countable and algorithmically finite spaces. If you look at our universe as a system (rather than the definition of "universe" which nothing is outside), it is possible that the universe exists within a non-countable space. Countable computers (like humans) are generally incapable of operating on non-countable spaces, to the extent that normal concepts of "computation" are not even applicable.

Countability is a very deep mathematical assumption for mathematics applicable to our universe. And in fact, our universe is by all mathematical measures a classic example of an algorithmically finite system (a type of countable space). The type of space you are in determines what properties and capabilities will exist within that space -- subjectively you would find countable spaces to be "richer" than non-countable spaces. That might change if you were an aleph-n (n>0) computer though.

34 posted on 12/01/2004 11:36:41 AM PST by tortoise (All these moments lost in time, like tears in the rain.)
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To: betty boop
I am, after all, a life-long Red Sox fan.... :^) And I am dancing on air, ever since the semi-finals against the Yankees. :^) Everything after that was anticlimactic.

All those years of exile and suffering! We Cardinal fans cannot relate to it, even after being swept in 4.

Cordially,

35 posted on 12/01/2004 12:02:38 PM PST by Diamond
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To: tortoise; cliff630; Alamo-Girl; marron; freeagle; ckilmer; Phaedrus; logos; beckett; ...
If you look at our universe as a system (rather than the definition of "universe" which nothing is outside), it is possible that the universe exists within a non-countable space. Countable computers (like humans) are generally incapable of operating on non-countable spaces, to the extent that normal concepts of "computation" are not even applicable.

Fascinating, tortoise -- but might these remarks apply equally regardless of whether the universe is a "system" or an "organism?" I know you prefer the former model; and I the latter. Either type of universe might be said to be an entity of which nothing is "outside." For in a certain way, whichever you choose, can we not say that it exists in a non-countable space, and that this space is itself a "part of the system (organism)" -- because whichever model we choose, the universe would be directly contingent (i.e., utterly dependent) on it for its own existence?

It seems possible to me that humans do in fact ultimately live in an "uncountable space" and for the very reason you give: that "normal concepts of 'computation' are not even applicable to such spaces."

This seems to hold equally true, whether we opt for your idea of a system arising in a non-countable space, or an organism arising from Newton's concept of absolute space, which he terms the sensorium Dei.

I really like this: "Countability is a very deep mathematical assumption for mathematics applicable to our universe. And in fact, our universe is by all mathematical measures a classic example of an algorithmically finite system (a type of countable space). The type of space you are in determines what properties and capabilities will exist within that space -- subjectively you would find countable spaces to be "richer" than non-countable spaces. That might change if you were an aleph-n (n>0) computer though."

Please elaborate your point regarding the significance of the aleph-n (n>0) computer as it pertains to the present issues?

Thank you so much for your thought-provoking observations, tortoise!

36 posted on 12/01/2004 12:52:36 PM PST by betty boop
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To: betty boop

Don't forget that the real numbers are catagorical. There is essentially only one model for the real numbers. The integers are more problematical. There is no unique model for the integers. There is no set of axioms that uniquely selects the integers from the reals. (There is a set that selects the integers from the rationals, however.)


37 posted on 12/01/2004 1:02:44 PM PST by Doctor Stochastic (Vegetabilisch = chaotisch is der Charakter der Modernen. - Friedrich Schlegel)
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To: Diamond
All those years of exile and suffering!

Tell me about it, Diamond! I didn't know you were a Cardinals fan. So I'm sorry about that "anticlimactic" remark.... :^) But you know the Yankees and BoSox are always at each other hammer-and-tong. So it was great finally to beat them in the World Championship.

True story: a very elderly gentleman -- age 114 -- was a life-long Red Sox fan, too. Within one month of the World Series, he passed away. Perhaps he was just determined to hang on long enough to see the Sox win the Series; and then he promptly died, his great wish having been granted.

It's so good to see you!

38 posted on 12/01/2004 1:07:48 PM PST by betty boop
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To: RightWhale
What mother would name her child 'The Flat One'?

Did any mother ever really do that?

39 posted on 12/01/2004 1:12:52 PM PST by betty boop
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To: stripes1776
The Church Fathers made a clear distinction between the created world and the uncreated and stated that there is no similarity between the two whatsoever.

"No similarity whatsoever" is a formal absurdity and is not possible.

40 posted on 12/01/2004 1:34:11 PM PST by Taliesan (The power of the State to do good is the power of the State to do evil.)
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To: stripes1776

"The Mystical Theology of the Eastern Church" is one of the best books ever written.


41 posted on 12/01/2004 1:36:14 PM PST by Taliesan (The power of the State to do good is the power of the State to do evil.)
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To: Eastbound
Yes, the 'downward tendency' is the necessary thrustblock against which we push to exercise the muscles of our desire for God. To yield to the downward tendency as a rule, is to waste the Grace (time) of God. A weightlifter would make little progress pumping feathers.

The downward tendency should not be resisted directly. To attempt it is to experience the despair of Romans 7.

The spiritual life is lived by cooperating with grace -- and voila! -- in some secret way the carnal man melts away. Sort of like walking on water. Sort of like leaven in a lump. Sort of like the wind blows.

42 posted on 12/01/2004 1:40:41 PM PST by Taliesan (The power of the State to do good is the power of the State to do evil.)
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To: Taliesan
"The downward tendency should not be resisted directly. To attempt it is to experience the despair of Romans 7."

Yes. To resist consciously is like trying to not think of an elephant. And yes, Grace coupled with desire for the higher goal, completion in God, is like floating away.

43 posted on 12/01/2004 2:44:54 PM PST by Eastbound ("Neither a Scrooge nor a Patsy be")
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To: betty boop
Perhaps we then may say that the integers are analogous to time, and the real numbers analogous to eternity

Interesting, however there is no number for infinity in the real number system. The symbol for infinity (which corresponds to the idea of eternity) represents a process that goes on forever, e.g. adding real numbers together forever. But it isn't a number. It is a direction.

However Liebnitz developed the calculus by assuming the existence of infinitesimals--infinitely small numbers larger than zero but smaller than the smallest non-zero real number. In the first semester of calculus, when you learn the Liebniz notation for differentiation, dy/dx, the instructor will tell you that is not a ratio--it's just a symbol for taking the derivative of y with respect to x. But that isn't the way Liebniz thought of it. To him it was indeed a ratio, i.e. the slope, of two infinitely small numbers.

Integration is of course the inverse of differentiation. And here again Liebniz thought of it as the summation of an infinite number of infinitely small areas. This rather amazing feat results in a finite, real number. This is the way that mathematicians thought of the calculus for 200 hundred years until Weierstrauss came along with his rigorous concept of limits. So for the past 100 years calculus has been defined only within the real number system. Infinitesimals and infinitely large numbers have been banished from the classroom.

Well, almost. Abraham Robinson discovered the hyperreal number system in the 1960s which includes the real numbers along with infinitesimals and infinitely large numbers. With this development, he defined an infinitesimal calculus in a rigorous way. But, unfortunately, it has never caught on with the teaching profession. Others have done this with the superreal and surreal numbers, but they haven't caught on either.

44 posted on 12/01/2004 3:10:20 PM PST by stripes1776
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To: betty boop

Looking forward to pondering this - thanks for sharing.


45 posted on 12/01/2004 3:43:48 PM PST by bluejean (Support the USA - Convict Democrats of Treason)
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To: RightWhale; Alamo-Girl; cornelis; marron; tortoise; Doctor Stochastic; D Edmund Joaquin; ...
Sorry for my bad manners, RightWhale. You are entitled to a better reply than the one I gave earlier.

The existence of a real person by the name of Plato, living at the time alleged for him, is amply attested to by an enormous body of work produced over a very long and very productive lifetime, in which certain themes ever recur, seeking ever better theoretical solutions, which the writer had the modesty to propose as "myths."

Myth gets a bad rap these days. Yet I think Eric Voegelin was entirely correct to say that "the myth remains the legitimate expression of the fundamental movements of the soul" (Order and History, Vol III, 1956.)

I think this is what Plato actually had in mind, in his work; which is why he did not leave us with a "systematic philosophy"; but only with the openness of mythical language.

Plus the other thing one notices about this magnificent corpus is that it is the creation of a world-class literary artist.

All in all, I think it is indisputable that this lifetime's work was effectuated by a single unified personality, who went by the name of Plato. And he had enough friends around in his day to attest to the actuality of his personal existence.

But then, you alreay know all that, don't you, RW? I think you're just "funning me!"

46 posted on 12/01/2004 5:45:57 PM PST by betty boop
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To: betty boop

His academy far outlived him, and that early Christian said something like I am the Truth, the Way, and the Life, which is similar to saying I am Plato. Plato means Road, or the Way. There is a lot of Plato in Christianity.


47 posted on 12/01/2004 6:21:52 PM PST by RightWhale (Destroy the dark; restore the light)
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To: stripes1776
I think it was Cauchy who introduced limits. Weierstrass was more into the arithmetization of analysis.

Note that projective geometry treats infinity as an ordinary number (or at least the point at infinity is an ordinary point.)
48 posted on 12/01/2004 9:05:13 PM PST by Doctor Stochastic (Vegetabilisch = chaotisch is der Charakter der Modernen. - Friedrich Schlegel)
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To: Doctor Stochastic; stripes1776; Alamo-Girl; marron
Note that projective geometry treats infinity as an ordinary number (or at least the point at infinity is an ordinary point.)

Doc, tell me truly: Do you think this is a reasonable assumption?

49 posted on 12/01/2004 9:31:20 PM PST by betty boop
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To: stripes1776

Excellent post, stripes. I hope to reply tomorrow; for it's late now, and I need to get some sleep. (Another workday tomorrow, ya know.)

Till then, pleasant dreams and sleep tight.


50 posted on 12/01/2004 9:34:12 PM PST by betty boop
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