On Plato, the Early Church, and Modern Science: An Eclectic Meditation

November 30, 2004 | Jean F. Drew

[betty boop]

The soul ...is like a drunkard, when she touches change...But when returning into herself she reflects, then she passes into the other world, the region of purity, and eternity, and immortality, and unchangeableness, which are her kindred....

Lovely, beckett! I gather Plato wishes us to understand that the human being lives both in time and timelessness, in physical existence and also in eternity.

Thank you so much for posting these beautiful passages, and also for your very kind words.

[betty boop]

You might think that the Christian East has more affinity with Plato, seeing the eventual friendship the West struck up with Aristotle, but they (the East) would not think so.... I say this as a lifelong protestant who loves both traditions (though perhaps both would sniff at me!) and thus has no dog in the fight, since we don't do Theology at all in the protestant tradition. :-)

I am definitely going to have to get a hold of Vladimir Lossky, Taliesan! Thank you so much for this most informative post.

[betty boop]

Get with the (Erlanger) program, Betty.

I'd be glad to check it out, Doc. Got a source for me?

Thanks so much for writing!

[StJacques]

Regarding the brief back and forth on the early Church Fathers and the "clear distinction between the created world and the uncreated" who stated that "there is no similarity between the two whatsoever" I would like to suggest that the viewpoint stripes has expressed denoting a distinction between eastern and western Christianity and the role of Augustine is, in my opinion, right on the mark and is well supplemented by the additional names he brings to the table after introducing the idea. I also do not believe this dispute originates with anything that is included in this inspiring essay -- good work betty -- but may in fact originate in something that is outside of it, which is directly related to the concepts of "the created world and the uncreated," namely, the distinct ways in which western and eastern Christianity viewed the separation of the sacred and the secular, which is much more important in the west due to Augustine's influence.

I've only just finished the essay and I would like to ponder a thing or two it introduces, but I want to return later to put up an additional post on something I think can help to inform its content, namely; the intellectual ferment within the Hellenistic and Roman world during the period of the rise of Christianity and specifically its integration of Greek philosophical ideas between the time of St. Paul and up to Augustine. The manner in which that ferment was resolved had tremendous implications for the development of scientific thought and the vestiges of this resolution remain with us today.

I don't have the time to put this up now, but I'll be back later to expand on what I have just stated.

This was a thought-provoking essay betty.

[betty boop]

I want to return later to put up an additional post on something I think can help to inform its content, namely; the intellectual ferment within the Hellenistic and Roman world during the period of the rise of Christianity and specifically its integration of Greek philosophical ideas between the time of St. Paul and up to Augustine. The manner in which that ferment was resolved had tremendous implications for the development of scientific thought and the vestiges of this resolution remain with us today.

Oh, you are most welcome here, StJacques! Take all the time you need to do it; but I for one am waiting with "baited breath" for your exposition on these points.

Looking forward to hearing from you, I'm so glad for your post!

[Doctor Stochastic]

Google is Our Friend

It was mostly meant as a joke. The Erlanger program is a method of studying geometry invented by Felix Klein.

[ckilmer]

To him it was indeed a ratio, i.e. the slope, of two infinitely small numbers.
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does the slope toward zero have the same curve as the slope toward infinity. or is "slope" in this instance merely an attempt to map a two dimensional figure (slope) onto, in turn, a one dimensional (zero) and four dimensions (infinity/eternity)

If they did have the same "slope" would that suggest that, say, a black hole is the inverse in "relationship" to whatever is "outside" the universe. What would inverse mean in this case.

I am no mathematician/physicist but as far as I can tell there is a very slushy boundary between what is countable--using the definitions for "countable" as set down in this thread--on the very large scale and what is countable on the very small scale. Things don't just cut off. Now your countable and now you're not.

Rather, things become less and less countable until gradually...infinity--or zero as the case may be.

But I'm not so sure that they become less countable in the same way. (But if they became less countable in the same way they might have the same slope:-)

[Alamo-Girl]

I’d like to offer some background information and links for the discussion.

Alexander the Great

betty boop noted that Alexander the Great was taught by Aristotle who was taught by Plato who was taught by Socrates. I'd like to add two comments:

(1) Alexander “normalized” the Greek language to a common Greek which greatly facilitated the spread of the Gospel and general knowledge throughout the Greek speaking world and

(2) Daniel prophesied about Alexander the Great. Josephus recorded this concerning the (alleged) confrontation with Alexander at Jerusalem:

Flavius Josephus in his Jewish antiquities 11.317-345

And when Jaddus understood that Alexander was not far from the city, he went out in procession, with the priests and the multitude of the citizens. The procession was venerable, and the manner of it different from that of other nations. It reached to a place called Sapha, which name, translated into Greek, signifies a prospect, for you have thence a prospect both of Jerusalem and of the temple. And when the Phoenicians and the Samarians that followed him thought they should have liberty to plunder the city, and torment the high-priest to death, which the king's displeasure fairly promised them, the very reverse of it happened; for Alexander, when he saw the multitude at a distance, in white garments, while the priests stood clothed with fine linen, and the high-priest in purple and scarlet clothing, with his mitre on his head, having the golden plate whereon the name of God was engraved, he approached by himself, and adored that name, and first saluted the high-priest.

The Jews also did all together, with one voice, salute Alexander, and encompass him about; whereupon the kings of Syria and the rest were surprised at what Alexander had done, and supposed him disordered in his mind. However, Parmenion alone went up to him, and asked him how it came to pass that, when all others adored him, he should adore the high-priest of the Jews? To whom he replied, 'I did not adore him, but that God who has honored him with his highpriesthood; for I saw this very person in a dream, in this very habit, when I was at Dion in Macedonia, who, when I was considering with myself how I might obtain the dominion of Asia, exhorted me to make no delay, but boldly to pass over the sea thither, for that he would conduct my army, and would give me the dominion over the Persians; whence it is that, having seen no other in that habit, and now seeing this person in it, and remembering that vision, and the exhortation which I had in my dream, I believe that I bring this army under the Divine conduct, and shall therewith conquer Darius, and destroy the power of the Persians, and that all things will succeed according to what is in my own mind.'

And when he had said this to Parmenion, and had given the high-priest his right hand, the priests ran along by him, and he came into the city. And when he went up into the temple, he offered sacrifice to God, according to the high-priest's direction, and magnificently treated both the high-priest and the priests. And when the Book of Daniel was showed him wherein Daniel declared that one of the Greeks should destroy the empire of the Persians, he supposed that himself was the person intended. [3] And as he was then glad, he dismissed the multitude for the present. But the next day he called them to him, and bid them ask what favors they pleased of him; whereupon the high-priest desired that they might enjoy the laws of their forefathers, and might pay no tribute on the seventh year.[4] He granted all they desired. And when they asked him that he would permit the Jews in Babylon and Media to enjoy their own laws also, he willingly promised to do hereafter what they desired. And when he said to the multitude, that if any of them would enlist themselves in his army, on this condition, that they should continue under the laws of their forefathers, and live according to them, he was willing to take them with him, many were ready to accompany him in his wars. …

Justin Martyr

Justin Martyr is beautifully discussed in the above article. For anyone interested, I'd like to offer a link to his writings: Ante-Nicene Fathers, Vol. I – First Apology of Justin Martyr

In the above, Martyr states that Plato had “borrowed his statement that God, having altered matter which was shapeless, made the world” from the Hebrew prophets (Moses in particular).

Martyr also believed that Plato was (unknowingly) speaking of Christ in Timoeus where he said "He placed him crosswise in the universe".

Philo of Alexandria

Philo hasn't been mentioned yet, but Lurkers may be interested in reading more about him: IEP: Philo of Alexandria

Philo was a Hellenized Jew who lived 20 BC to 50 AD, in Christ’s incarnate time on earth. He is noted for trying to reconcile Jewish thought with Greek philosophy.

Of particular interest to this discussion might be his Model of Creation and his response to Eternal Creation:

Thus Philo postulates a crucial modification to the Platonic doctrine of the Forms, namely that God himself eternally creates the intelligible world of Ideas as his thoughts. The intelligible Forms are thus the principle of existence to the sensible things which are given through them their existence. This simply means in mystical terms that nothing exists or acts except God. On this ideal model God then orders and shapes the formless matter through the agency of his Logos (Her. 134, 140) into the objects of the sensible world:

Now we must form a somewhat similar opinion of God [Philo makes an analogy to a plan of the city in the mind of its builder], who, having determined to found a mighty state, first of all conceived its form in his mind, according to which form he made a world perceptible only by the intellect, and then completed one visible to the external senses, using the first one as a model (Op. 19).

Philo claims a scriptural support for these metaphysics saying that the creation of the world was after the pattern of an intelligible world (Gen. 1:17) which served as its model.

[Alamo-Girl]

LOLOL! I can't believe how sloppily I worded that last post. Must be tired ... off to bed now...

[betty boop]

Hello Stripes! When I wrote earlier to suggest that perhaps integers are analogous to time, and real numbers to eternity, I was thinking in terms of the number line that is composed of both. The reals comprise both rational and irrational numbers, each of which can be imagined as having an infinite number of digits to the right of the decimal point. The digit series of a rational number presents itself as a sequence of elements that eventually will be found to repeat, ad infinitum. This is not the case for the irrational numbers, whose digit series is found to be not a sequence at all (at least sequence or periodicity has not been detected yet), but an infinite series of digits that appear to be distributed at random. The most famous example of an irrational number is pi of course, which does not appear to be a countable number at all, yet is a quantity fundamental to the development of Euclidean geometry. On the number line, pi appears in the “band” between the finite integers 3 and 4. With respect to the rationals and the irrationals, we seem to be looking at two completely different orders of infinity, e.g., one that is “quasi-finite” (the rationals), and the other “infinite” (the irrationals). The number line carries both types of numbers, integers and reals, both rational and irrational, all lined up “cheek to jowl,” so to speak. The “picture” one gets is that of a line smoothly progressing in time, with bursts of infinity interposed all along its extent pointing out of time to timelessness. And the number line itself is infinite, “in both directions” indicated by <0 and >0. Truly it appears that infinities come in different orders, or “sizes.”

I don’t know whether this makes any sense. I admit that when it comes to higher mathematics, I still have my “training wheels on.” So feel free to correct my understanding as needed: I have a lot to learn.

You write that there is “no number for infinity in the real number system,” thus the idea of infinity must be presented symbolically — roughly speaking, the symbol takes the form of a “snake biting its own tail,” with a good “twist” in the middle (so to speak). You point out that infinity is a direction. I don’t dispute this. Yet paradoxically, direction implies a process in time. In what way can we reconcile the idea of process in time with infinity, which you note corresponds to the idea of eternity (or timelessness)?

This problem has preoccupied philosophers since ancient times. Plotinus (204–270 A.D.) argued that time and the sequence of its movements are understandable only under the presupposition of a complete wholeness of time that he termed eternity, aion. As Wolfhart Pannenberg writes (Toward a Theology of Nature),

“The whole of time, according to Plotinus, cannot be conceived as the whole of a sequence of moments, because the sequence of temporal moments can be indefinitely extended by adding further units.… In his conception the total unity of the whole of life is indispensable in the interpretation of the time sequence, because it hovers over that sequence as the future wholeness that is intended in every moment of time, so that the significance of eternity for the interpretation of time in Plotinus results in a primacy of the future concerning the nature of time….”

Thus, “the infinite has priority over any finite part.” And in Kant’s development of Plotinus’ concept of time, this statement applies not only to the case of time, but also to the case of space — which to my mind at least seems to anticipate a crucial insight of modern relativity theory, and also of quantum field theory.

Pannenberg points out that this concept corresponds to “the Israelite understanding of eternity as unlimited duration throughout time,” i.e., the concept of time that runs throughout the Old Testament. (To my mind, this idea seems roughly analogous to the irrationals on the number line.)

It appears Pannenberg’s own model is a development from the Plotinian insight into the nature of time. He writes:

“I have developed this concept of eternity from the human experience of time, from the relativity of the distinction of past, present, and future corresponding to the relativity of the directions in space. In view of the relativity of the modes of time to the aspect of the human being experiencing time, this resulted in the assumption that all time, if it could be, so to speak, surveyed from a ‘place’ outside the course of time, would have to appear as contemporaneous.”

To borrow Alamo-Girl’s perceptive description here, in other words, from this perspective, the 4D block would appear, not as a progression of discrete events moving from past, present, to future, but as a “plane” or “brane.” Pannenberg continues:

“This assumption is confirmed by a unique phenomenonon of the human experience of time through the experience of an ‘expanded present’ in which not only the punctiliar now but everything on which a position may be taken still or already is considered as present…. Understood in the sense of the suggestions above, the concept of eternity [i.e., infinity] comprehends all time and everything temporal in itself….

“The worldview of the theory of relativity also can be understood in the sense of a last contemporaneousness of all events that for us are partitioned into temporal sequence.” [ibid, p. 100f.]

Of course, as Pannenberg himself notes, the perspective from which one could view such things “would not coincide with any position in the world process.”

In Pannenberg’s model, “creation can be conceived, on the ground of the theory of relativity, as an eternal act that comprises the total process of finite reality, while that which is created, whose existence happens in time, originates and passes away temporally.”

Thus, the way I figure it, eternity is not itself “duration;” rather it is the “matrix” in which ‘durations’ — temporal events (seemingly exhibiting the idea of, not only ‘duration,’ but also of ‘passing away’) — take place. Including scientific observations and measurements, which are often based on “abstractions” such as Planck time – the teensiest piece of “punctiliar time” that the human mind can measure or grasp.

Thus, eternity is the “Eternal Now” – which is not a datum of human sensory experience, for sure; rather it is a concept to which the human mind (and heart) can aspire and understand.

* * * * * *

Thank you so much, Stripes, for the discussion of Liebnitz’s understanding of his own work and what the academy has seemingly reduced it to. I was unaware that mathematics or the natural sciences could ever be exposed to the work of the deconstructionists, who ever seek to separate the “author” from his “text,” so as to make of the “text,” in effect, whatever they want. I guess I’ve been mistaken about this. Yet to me, the “author’s intention” is indispensable to the understanding of any “text.”

Just goes to show you how irredeemably “old-fashioned” I am.

Thank you so much for your informative and thought-provoking post.

[betty boop]

Thanks, Doc! Surely, "Google is our friend." I'm sure I'll have better luck in the search for Felix Klein than I did with my search for "Erlanger."

[betty boop]

Excellent, Alamo-Girl! Truly the Daniel prophecy regarding Alexander is amazing. But there it is. Thank you so much for the links to Justin Martyr and to Philo. Philo's insight that "the creation of the world was after the pattern of an intelligible world (Gen. 1:17) which served as its model" indicates a bridge between the Platonic Idea and the Israelite understanding of the creation. And Justin's observation that Plato was (unknowingly) speaking of Christ in Timaeus when Justin says "[Plato] placed him [i.e., the Demiurge] crosswise in the universe" indicates a bridge between the Platonic Idea and the Logos theory of the early Christian Church.

True ideas "evolve," it seems. Thank you so much for your excellent post and invaluable links. I expect to be spending some time with both Justin and Philo very soon!

[safisoft]

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.

He is called Dionysius the Pseudo-Areopagite because he was a fake. The so-called writings of Dionysius have been demonstrated as fakes from no earlier than the 7th Century CE. Dionysius attempted to gain acceptance of his philosphical bent by anacrhonistically projecting them into the First Century and as coming from the Apostle Paul.

Get this, plain and simple: the marriage of Greek philosophy with the Bible was one of the biggest errors ever perpetrated on humanity. The so-called church fathers like Martyr, Origen, Tertullian, Augustine and Clement had nothing in common with the Jewish sages known to us as the Apostles. None.

Greek thinking has NOTHING in common with biblical thinking.

Philosophy attempts to discover truth, and instead arrives at 'your truth'. This is the oldest deception: that men are wise enough to go beyond the plain revelation of God's words.

In the Garden, the Serpent asked, "Has indeed God said..." And attempted to use a rational argument for the Woman. The Woman used rational thought to annul God's instructions (after all, she did not even know what death was).

Justin Martyr considered Plato to be inspired by God and that his words were a type of Scripture. Origen considered Plato's explanation of Logos to be the SAME as John 1.

A philosophical approach to God's Word is merely slavery for the mind. Martyr, Origen, Clement, Augustine, Aquinas et al were WRONG.

Colossians 2:8: Beware lest anyone cheat you through philosophy and empty deceit, according to the tradition of men, according to the basic principles of the world, and not according to Messiah.

[cornelis]

Greek thinking has NOTHING in common with biblical thinking

St. Paul was much less extreme. When he came to Athens, he sought out few points of common ground. Those Greeks actually had more in commone with Christianity than so many -isms of contemporary thought.

If some of the Fathers were overly influenced by Greek thinking, there ought to be some credit at least for engaging the conversation and noting the important differences. That's much harder to do than blanket denials. Stripes1776 provided a list of those who engage the difficult issues and wish to point out the limits of philosophy. (A side note: the absolutist divide between Greek and Biblical thinking seems to be a product of modern forms of hyper rationalism.) In short, the fact that the two so easily meld is ample evidence that they have a lot in common.

[safisoft]

the fact that the two so easily meld is ample evidence that they have a lot in common.

A rationalist statement.

[ckilmer]

The coming of Jesus marks the end of bible and also the end of a specifically Jewish Story. However, the old testament is not a specifically Jewish story until Abraham (though the jewish geneologists can trace their line back to adam.) Furthermore God's original revelation of himself is not unique to the Jews. St Paul mentions this twice in two very different contexts.

Here are two examples. Notice in verse Acts 17:28 that Paul mentions that certain Greek Poets have witnessed the Creator God. In the second example below in Romans 1:20 Paul mentions that even barbarians have witnessed the Creator God (so they too are without excuse when they change from worshiping the Creator to worshipping created things.)

Acts 17 :: King James Version (KJV)

16
Now while Paul waited for them at Athens, his spirit was stirred in him, when he saw the city wholly given to idolatry.
17 Therefore disputed he in the synagogue with the Jews, and with the devout persons, and in the market daily with them that met with him.
18 Then certain philosophers of the Epicureans, and of the Stoicks, encountered him. And some said, What will this babbler say? other some, He seemeth to be a setter forth of strange gods: because he preached unto them Jesus, and the resurrection.
19 And they took him, and brought him unto Areopagus, saying, May we know what this new doctrine, whereof thou speakest, is?
20 For thou bringest certain strange things to our ears: we would know therefore what these things mean.
21 (For all the Athenians and strangers which were there spent their time in nothing else, but either to tell, or to hear some new thing.)
22 Then Paul stood in the midst of Mars' hill, and said, Ye men of Athens, I perceive that in all things ye are too superstitious.
23 For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, him declare I unto you.
24 God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands;
25 Neither is worshipped with men's hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things;
26 And hath made of one blood all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the bounds of their habitation;
27 That they should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us:
28 For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.
29 Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man's device.
30 And the times of this ignorance God winked at; but now commandeth all men every where to repent:
31 Because he hath appointed a day, in the which he will judge the world in righteousness by that man whom he hath ordained; whereof he hath given assurance unto all men, in that he hath raised him from the dead.
32 And when they heard of the resurrection of the dead, some mocked: and others said, We will hear thee again of this matter.
33 So Paul departed from among them.
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Romans 1 :: King James Version (KJV)

14 I am debtor both to the Greeks, and to the Barbarians; both to the wise, and to the unwise.
15 So, as much as in me is, I am ready to preach the gospel to you that are at Rome also.
16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.
17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness;
19 Because that which may be known of God is manifest in them; for God hath shewed it unto them.
20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:

[cornelis]

Are you faulting what is reasonable?

[ckilmer]

Stripes1776 provided a list of those who engage the difficult issues and wish to point out the limits of philosophy.
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philosphy ends in the personality and character of man
theology ends in the personality and character of God.

[stripes1776]

does the slope toward zero have the same curve as the slope toward infinity.

You ask very intersting questions. Let me try to address the mathematical side of your questions as briefly as I can, but certainly not briefly enough.

Much of mathematics today uses the real number system in which all numbers are finite. This includes zero. However, there is a restiction on zero that the other real numbers don't have: division by zero is undefined. The reason is that division by zero is an infinite process.

Mathematicians who confine their considerations to the real number system have a symbol for infinity, but it is NOT a number. It is a process of applying operations like addition or multiplication or substraction or division forever. And since most mathematicians die before they reach forever, they just call this infinity and or say this is undefined and move on to the next equation.

Slope is a ratio of two numbers. Consider a right triangle. The hypotenuse which is the slanted side obviously has a slope. To calculate it divide the length of the vertical side of the triangle by the length of the horizontal side. The result of that division is the slope of the hypotenuse and it is constant for every point on the hypotenuse.

Now keep the vertical and horizontal legs of the triangle the same, but replace the slanted line for the hypotenuse with a piece of cooked speghetti with lots of curves. What is the slope of this piece of curvey spaghetti? It obviously changes for every point on the curved line that represents the spaghetti.

Back 350 years ago when Liebniz helped to invent the calculus, mathematicians were not resticted to the real number system. They also used numbers called infinitesimals which are so small that you can think of them as zero. To find the slope of the spaghetti curve, Leibniz shrank the vertical and horizontal sides left over from our original triangle until those sides became infinitesimals. So you can think of this as dividing zero by zero, i.e. 0/0. The amazing result was an equation that gave him a finite slope that varied for every point on the curved spaghetti. Wow!!!

About 100 years ago mathematicians became very uneasy about infinitesimals and dividing 0 by 0, so they threw out infinitesimals, and redefined calculus in terms of the concept of limits and real numbers only.

Now, when I first took calculus, I was lost. I didn't understand limits at all and found them confusing and cumbersome. I started studying the history of the development of calculus. Since Leibniz used infinitesimals, I began to think of calculus in terms of infinitesimals. A light bulb went on, and I began to solve calculus problems with ease. But I didn't dare to tell my instructor that I was secretly thinking about dividing infinitesimals instead of taking limits of real numbers.

My purpose for bring all this up was that betty was thinking about writing an essay about numbers and eternity. I thought I would offer more food for thought if she cares to chew on any of it. I will let the philosophers on this thread address your philisophical questions.

[cornelis]

philosphy ends in the personality and character of man theology ends in the personality and character of God.

I also think of it in a similar way. Something with the direction that the two take. There is, of course, theology that ends in the personality of man, because that's where it begins. So where things begin is also a difficulty.

In their most famous works, both Augustine and Calvin begin with the difficulty of a beginning. Neither resolve it by getting rid of one for the other. That's smart. Otherwise you'd have 100% God and no man or 100% man and no God.

There's an excellent little book that has helped me in this regard by Etienne Gilson: Reason and Revelation in the Middle Ages. He compares those schools who hold the priamcy with reason (Averroes)and those who hold the primacy with faith (Tertullian).