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edward
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Posted -
2004/11/21 下午 06:20:49
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根據先前的討論，帶出在標記意義上，實領比神領聖體更為圓滿。
其實雖然恩寵未必可以量化，但人的有限性卻是十分明顯。
在聖事上與主共融：既為「聖事」，則須要有外在標記去盛載無形的恩寵，方為有聖事的效果。
小弟嘗試指出：神領聖體是一個類比的觀念，它祗適用於未能實領聖體的情況。基於它是一項心靈上的預備和對聖體聖事的信德，它亦可帶來恩寵。至於恩寵的「量」，則要顧及不同的情況。
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edward
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Posted -
2004/11/21 下午 06:27:04
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神領聖體與實領聖體不同，是基於它在「聖事外」的特質，預設了不同的可能性。小弟想像出幾個情況。例如：
一、繁忙上班者，不能每天望彌撒。每天在巴士裡「神領聖體」。
二、犯重婚罪的教友，知道自己未能改變生活中的現實困難，在彌撒的舉行中「神領聖體」。
三、在某堂區主保瞻禮彌撒中，因參禮人數眾多，不夠「聖體」。有送聖體員赫然發現聖堂的聖體龕空空如也，於是到祭衣室處，將未祝聖的麵餅放進聖體盒中......因此有不少參加該台彌撒的教友「神領聖體」。
頭兩個情況是「自願」，而第三項則是非自願的。我們的討論，相信是針對「自願」的情況。然而，有哪些是該份意願的元素呢？
例如：「want to have sex」和「actually have sex」是屬於兩個不同的範疇。「神領聖體」帶來的恩寵，比起「實領」聖體來說，總該有它的限度。否則把兩者混為一談，有可能變成精神上的「自慰」。
「千里共嬋娟」雖然浪漫，但卻不能遮掩「分離」的真實和孤寂的感覺。
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Augustine
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Posted -
2004/12/2 上午 09:43:52
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(I'm too busy recently, let's make it short)
1) I agree: "更圓滿"(if 圓滿 is just our commonly understood "infinity") is logically impossible.
2)
Major: "圓滿"(concerning supernatural realities e.g. uncreated grace) is commonly and analogically decribed as the concept of "infinity".
And this infinity is built on our everyday experience of finite beings (like we see 1000 apples and can imagine infinitely many apples).
But of course, no one actually sees the "Infinite". Definitely not the "infinity" built on 1000 apples.
On the other hand,
Minor we know that supernatural graces could become more and more abundant, from sources of Scriptures and Tradition.
Therefore,
Conclusion:there are inadequacies in the attempt by analogy of (countably) infinite to model after supernatural 圓滿. Though it is a good way to explain it.
Corollary 1:
What is contradictory for our common usage of "infinite", (e.g. Infinity + 1 > Infinity) may not be so for supernatural graces. It is still possible to speak of "More" or "Less" graces, though of course, being supernatural, are BOTH of infinite value.
Corollary 2:
Unless in the Beatific Vision when God ( the Infinite---not some phony pantheistic notion of Cosmos or Universe) is directly perceived, we would see for ourselves how he could be the Pure Act while at the same time absolutely immutatable.
3) In theological discussions, mysteries are common. By analogy we could try to explain some of them, but we never claim to understand fully. Failure to recognize this could lead to rationalism, and eventually immanentism.
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edward
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Posted -
2004/12/2 下午 07:33:28
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小弟以為：圓滿在概念上，與無限不必相關。
按照這辭的概念，「圓」或「滿」。「圓」在幾何學是指「曲線在一平面上對於一定點有等距離所環成之面」。
而「滿」則是在「某容器所容之物量達到其極限」。
恩寵與人之間的關係，並非純粹是幾何學或容體的考慮。所以用圓或滿來描述恩寵的狀態，是類比的。
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edward
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Posted -
2004/12/2 下午 07:39:10
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即使在日常生活中，我們說一張唱片很「圓」，或說一個碗盛「滿」飯，都不是嚴格的數學意義。
世界日常生活所可以接觸到的，大概沒有一件事物，可以達到幾何學「圓」的標準；而一個碗盛滿「水」和盛滿「飯」所達致的實質體積，亦非相等的。
在現世的有限事物當中，為何不可以設想有「更圓滿」情況的存在呢？
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Augustine
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Posted -
2004/12/3 上午 10:04:12
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To me, mathematical infinity is not a good analogy of supernatural fullness.
Edward says further that even fullness in nature is not strictly mathematical, and could not be equated to numbers. I also concede.
I would like to add, the reason why we tends to think of fullness in terms of numbers or concepts of infinity derived from finite numbers
(sayings like this cup has capacity 100ml, now it is 99.999999ml so it is "not" full; or, a 100000-sided regular polygon is not a real circle since it is not an infinite-sided circle) is a result of Positivism.
This is sometimes called scientism, the superstitious belief that once you can't quantify something, you can't compare or talk about different modes of being "precisely". This produced far reaching effects in the society.
If you look at the way people nowadays talk about Business Management, human dignity is reduced to the level of numbers. The value a person has is determined by the score he got in innumerable assessments, and the number of qualifications he has.
In education, we see the value of a child "measured" by his exam score, the value of a teacher "measured" by "value-addedness", the value of an adult in the society "measured" by the number of cash in his purse!
THis is a discouraging age indeed.
Modern Science:Quo Venit? Quo Vadis? Are we just screw and nuts as Marx would like to describe us as, in the big machine of society?
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simon
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Posted -
2004/12/3 下午 01:54:04
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Edward,
你問：「在現世的有限事物當中，為何不可以設想有「更圓滿」情況的存在呢？ 」
如果你說「圓滿」和「很好」是同義詞，那麼你的確可以用「更圓滿」來代表「更好」。
問題是「圓滿」是否等於「很好」？
你又說：「圓滿在概念上，與無限不必相關。」
「圓」和「無限」是有關連的。一條直線，其實是一個圓形的Arc，那個圓形的半徑是無限長。
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edward
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Posted -
2004/12/12 上午 12:35:14
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「『圓』和『無限』是有關連的。一條直線，其實是一個圓形的Arc，那個圓形的半徑是無限長。」
若圓形的半徑是無限長，那麼，直徑是否可能存在？無限長的「半徑」，是否可能存在形成arc的「軸心」（axis）？
把一隻蟑螂放在兩個合上的碗中奔跑，不是可更簡單地說明「有限而無邊」嗎？
小弟理解「圓滿」，包含兩個相對的觀念：載體和所載物。若載體有限，則「圓滿」的境界不可能無限。但不排除載體本身的容量，可日益增長。
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simon
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Posted -
2004/12/12 下午 05:40:53
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Edward，
你問：「若圓形的半徑是無限長，那麼，直徑是否可能存在？」
以前我已說了，無限大是不可作加減乘除的，否則你可以證明一等於零。半徑是無限長，若再問直徑是多少，這是一條虛假的問題；等於問無限大乘二是多少一樣，同是虛假的問題。
若你對「圓滿」是這樣解釋，在你的概念中，的確可以存在「大圓滿」、「中圓滿」、「小圓滿」、「我的圓滿比你的圓滿大三倍」之類之類........我只能說，我對圓滿的理解，和你的概念很不同，夏蟲不可語冰也。
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simon
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Posted -
2004/12/12 下午 05:43:34
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補充：我是夏蟲，你不能對我說冰。
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edward
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Posted -
2004/12/12 下午 05:49:00
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西滿兄：
所以我就覺得你關於圓形的概念很有問題。
若按你所言，該個圓形的「邊」和它的「tangent」是否同義？
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simon
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Posted -
2004/12/12 下午 06:12:39
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Edward，
當人家的想法和自己不同時，不要那麼快便「覺得別人的概念有問題」。
「直線是圓形的arc，而這個圓形的半徑是無限長。」這個聰明的想法，當然不是出自我的腦袋。那是一位在大學做研究的數學博士告訴我的。
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edward
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Posted -
2004/12/12 下午 06:41:06
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西滿兄：
梢安勿燥。有問題就是有問題，是有待解決的。
Problem is for solving and not for blaming。
若情況許可，當然要向那位朋友請教一下，才知是否聰明的想法。
以上創見，在哪學報上發表過呢？你能將他的論文email給我嗎？
edvardvs@sinaman.com
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simon
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Posted -
2004/12/12 下午 09:00:20
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Edward，
我很「安」，請放心。
「直線是圓形的arc，而這個圓形的半徑是無限長。」並不是他的論文。他說這句話時，是讓我了解/感受「無限大」的意思。
「2 x 3 = 6」也要論文嗎？
Augustine 似乎是唸數學的，可請他發表一下意見。
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edward
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Posted -
2004/12/12 下午 10:19:50
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西滿兄：
小弟認為，無限者袛有天主。否則「無限」則袛能在數學上存在。
因此，即使用數學來比喻施於人身上的恩寵時，把它規限在「有限」的範圍，你會否認為更為合理？
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simon
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Posted -
2004/12/13 下午 12:15:39
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Edward,
注意說話的用詞。
你先說：「所以我就覺得你關於圓形的概念『很有問題』。」
然後說：「有問題就是有問題，是有待解決的。Problem is for solving and not for blaming。」
如果我對你說：
你的腦袋「很有問題」。
你的德行「很有問題」。
你的感受，會否只是「Problem is for solving。」，而不是「blaming」呢？
「很有問題」一詞，對一般人來說，是帶了頗重的負面意思。
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Augustine
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Posted -
2004/12/13 下午 03:40:03
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I guess “straight line is the arc of a circle of infinite radius” originates from a consideration of the Riemann sphere: in the extended (ie. With “infinity” as a point added) complex plane, the straight line (for instance) Arg(z)=1, which passes through the point of infinity, is the “circumference” of a circle dividing the Riemann sphere into two halves. (I donno if this’s the PhD’s meaning)
If my guess is correct, we should be careful, the Riemann sphere as a sphere is only one of the many shapes it may take, in mathematical/topological terms we say the Riemann Sphere is Homeomorphic to a sphere but not necessarily, in topology a sphere is same as a cube. [In this sense a straight line is the circumference of a circle topologically]
What is really said in the PhD’s assertion? I guess is that a straight on the plane is actually a closed ring (or any simple closed path), the two ends of the straight line being joined up at the point we call “infinity” in the extended complex plane.
I have done my best using the simplest terms. I know most readers are not trained in Complex Analysis or Differential Geometry. I hope these are helpful.
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Augustine
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Posted -
2004/12/13 下午 03:47:04
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"即使用數學來比喻施於人身上的恩寵時，actually把它規限在「有限」的範圍" Indeed, I have said the same earlier.
Mathematical infinity is only an analogy derived from practical experience of numbers 1,2,3,.....100000, it illustrates but cannot represent wholy the meaning of supernatural fullness.
Just as an ant walking on the 2-Dimensional plane cannot conceive of a 3-Dimensional Space. Note: in the ant's understanding, "infinity" exists, (such as a straight with no endpoints), but is it the same "infinity" in 3D space? I don't think so.
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