慕容青草的博客
哲學園地
正文
時間的意義在西方哲學裏是個亙古的話題，而諾貝爾文學獎得主現代數理邏輯創始人之一的柏淳羅素對這個話題的討論卻是獨具特色與眾不同。盡管羅素自己承認他的討論並不完美（卻又聲稱是最安全的—--見下麵的【1】），我們仍然可以從中學習領略大師縝密而有創見的思維。下麵我們先來看羅素在《我們關於外部世界的知識[1]》一書中用數學性的哲學思維來構造時間的定義的核心部分內容：
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。。。。。。我們所意識到的事件，不論多麽地短暫，總是要持續一定的時間而不會是隻存在於一個數學意義上的瞬間。即便是在關於運動的數學理論所考慮的物理世界裏，外界印象使我們產生的感覺也不是嚴格的瞬間，因此我們直接意識到的的感官對象都不是瞬間存在的。所以說，瞬間並不存在於我們的經驗數據中，而隻能是（如果是合理的話）推論或構造出的概念。很難看出如何能推論出瞬間這個概念，所以我們隻剩下一個選項，就是構造出瞬間概念實體來。應該怎麽做呢？
我們可以從直接的經驗中了解到不同的事件之間的兩種時間關聯性：它們或是同時的，或是一個早些一個晚些。這兩者都是原始數據中的部分；不可能存在有了兩個事件然後再人為主觀地將時間順序加上去的情況。在一定的極限之內，時間順序同所發生的事件一樣地呈現給觀察者。在任何一個探險故事中，你都可以發現下麵類似這樣的段落：“帶著譏誚的微笑他用左輪手槍指著那位大膽的年輕人的胸膛。‘我數三下然後就開槍，’他說。他冷酷而清晰地數著那一和二。當那個三字從他那正要張開的嘴唇中突出的刹那間，一個耀眼的閃電劃破了天空。”這裏我們看到了同時性---不是如康德要我們相信的那樣地因為那個大膽的年輕人的大腦器官的功能，而是由左輪槍和閃電客觀地構成的。時間的這些關係存在於不是嚴格瞬間的事件之間。因而一個事件可能比另一個開始的更早些，但可以一直延續到第二個事件開始之後，因而與第二個事件之間存在著同時性。如果它一直延續到另一個事件結束之後，那麽它就比那第二事件更晚。早些，同時，以及晚些，對於任何延續一定時間（不論多短）的事件來說，總是相互一致的；隻有當我們處理瞬間發生的事件時才可能出現不一致性。
我們可以發現，我們無法給出所謂的絕對的時間點，而隻能給出由具體事件決定的時間點。我們無法指出某個時間本身，而隻能指出在那個時間所發生的事件。所以在我們無法根據經驗來假定有獨立於事件的時間：隻有依據同時性和承繼性來排序的事件是我們從經驗所能夠得到的。因此，除非我們再引入多餘的形而上的實體概念來，我們隻有借助僅含有事件及其時序關係的構造來定義數學物理能夠認為是瞬間。
我們怎樣才能如我們所希望的那樣僅通過事件來給出一個準確的時間點呢？如果我們任取一個事件，我們無法準確地給出時間點來，這是因為一個事件不是瞬間的，那等於是要它與兩個不同時的事件同時。為了要給出一個準確的時間點，從理論上來說，我們必須能夠確定是否任一個給定的事件在此時間點之前或之後，而且我們必須知道任何一個其它的時間點必須在此時間點之前或之後，但不能與它同時。現在我們假定，有兩個事件A和B而不是僅一個事件A，而且假定A與B有部分的重疊，但是B比A先結束。這樣一來，另一個與A和B都同時的事件就必須存在於A和B的重疊區裏麵；因此我們比僅考慮A或B時更接近於給出一個精確的時間點了。假設C是一個與A和B都同時的事件，但是比A或B都更早地結束。這樣的話，另一個與A和B還有C同時的事件就必須存在於A,B，C三個事件的共同的重疊區裏麵，而且這個重疊區比之前的重疊更短。按照這樣的思路繼續下去，不斷地加入新的事件，每一個新事件都和之前加入的所有的事件同時，我們將得到越來越精確地計時的序列。這就給我們提供了一個可以確定完全準確的時間的方法。
A______________________________________
B_________________________________
C___________
我們來取這樣一組事件，它們之間任意兩個都有重疊，所以就一定存在著這樣一段時間，無論多短，在這段時間裏這組事件中的所有事件都存在著。如果我們還能找到任何其它的與這組事件中的所有事件重疊的事件，那麽我們將新找到的事件也加入到這組事件中來；按照這樣的程序操作（譯者注：顯然這是一種理論性的過程而不是實際的操作），最終在這組事件之外將不會再有任何與這組裏的所有事件都重疊的事件，而這組內的所有事件彼此之間都有同時性存在。我們將這樣一個事件組定義為時間上的瞬間。接下來我們需要來演示這樣一個集合具備我們期待一個瞬間所具有的特點。
對於瞬間我們應該期待著什麽樣的特點呢？首先，他們必須構成這樣一個序列：其中的任意兩個中必須有一個比另一個早；如果某個瞬間在另一個之前，而另一個在第三個之前，那麽第一個也必須在第三個之前。其次，每個事件必須經曆一些量的瞬間；如果兩個事件處於同一個瞬間那麽它們是同時的，而如果一個事件所處的瞬間比另一個事件所處的瞬間早，那麽一個事件就在第二個事件之前（譯者注：這裏原作者似乎還應該強調第二個事件不存在於第一個瞬間）.第三，如果我們假設在任何事件存在的期間某些地方總會出現變化，那麽我們需要的瞬間序列應該是緊致的，也就是說，給出任意兩個瞬間，一定有另外的瞬間存在於它們之間。那麽我們先前所定義的瞬間序列是否具有這些特性呢？
如果一個事件在我們用來如前定義某個瞬間的事件組之內的話，我們將稱這個事件處於那個瞬間；另外，如果定義某個瞬間的集合裏麵有某個事件比定義另一個個瞬間的集合裏麵的某些事件早而且不具有同時性，我們還將稱第一個瞬間早於第二個瞬間。當某個事件比另一個事件發生的早且不具有任何同時性時，我們稱第一個事件“完全先於”第二個事件。這樣我們就知道當兩個事件之間不存在同時性時，其中一個一定是完全先於另一個，另一個一定不會比前麵一個早；我們也知道，如果一個事件完全先於第二個事件，而第二個事件完全先於第三個事件，那麽第一個事件一定完全先於第三個事件。從這些事實來看，我們很容易得出結論說我們之前定義的瞬間構成一個時間序列。
接下來我們需要演示每個事件至少應該處於一個瞬間，也就是說任給一個事件的話，它一定至少是我們定義瞬間時所用的某一個事件組中的成員。為了這個目的，我們來考察與某個事件同時但不在該事件之後發生的的所有事件，即不是完全後於與所給定的事件同時的任何事件。我們將這些事件稱為那個給定事件的“初始同代”事件。可以發現，這樣一組事件便是所給定的事件所存在的第一個瞬間，隻要每一個完全後於那個給定的事件的某個同代的事件都完全後於這個事件的最初的同代。
最後，我們隻要能證明當給出其中一個完全先於另一個的任意兩個事件時，一定存在一些事件它們完全後於第一個事件而與某些完全先於第二個事件的同時，就能說明我們所構成的瞬間的序列是緊致的。至於說現實中的事件在時間上的排序是否真是這樣的，那是一個經驗性的問題；但如果它不成立，就沒有理由認為我們所構造的時間序列是緊致的。[17]（譯者注：大師這裏的論證在邏輯上並不完整）
這樣我們所定義的瞬間序列就滿足（譯者注：由於大師對於緊致性的論證明不完整，這裏的這個“滿足”二字的意思是要打折扣的，是在假如前麵對於緊致性的解釋符合實際情況的前提下的。因此從論證邏輯上來說多少有些半吊子）了所有的數學要求而不需要假設存在任何有爭議的形而上的概念實體。
瞬間也可以用包含關係（譯者注：這裏原文是enclosure-relation，不知中文應如何譯，故權且用包含一詞）來定義，和我們用點來定義完全一樣。當一個對象與另一個具有同時性但又不早於或晚於那個對象時，它在時間上被那第二個對象所包含。任何有包含或被包含的對象在這裏被稱為“事件”。為了使這種時間包含關係能夠成為“造點機”，我們要求(1)它應該是傳遞性的，即如果一個事件包含了另一個，而那個又包含了第三個，那麽第一個就包含了第三個；（2）每個事件包含它自己，但是如果一個事件包含了另一不同的事件，那麽被包含的事件不能再包含前麵那個事件；(3)如果一組事件中至少有一個被所有其它的事件包含，那麽一定有一個事件包含了這組事件所包含的一切，而且它自己也被所有的其它事件所包含；(4) 至少有一個事件是存在的。為了保證時間的無限可分性，我們也要求每個事件應該包含除了自己以外的其它的事件。在假設了這些特征之後，時間的包含就成為一個無限可分的造點機了。現在我們可以這樣來構造一個關於事件的“包含-序列”：選擇一組事件它們中的任意兩個都是一個包含另一個；如果存在另一個包含-序列它的某些成員被我們的之前選的第一個序列的所有的成員所包含，而第二個序列的所有的成員也包含了第一個序列的某些成員的話，那麽這第一個包含-序列就是一個“精準的包含-序列”。這樣一來，一個“瞬間”就是包含了一個精準的包含-序列的成員的所有事件組成的集合。
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[17] 關於上述的時間關係的假設如下：-
I。為了確定瞬間能構成一個時間序列，我們假設：
（a）沒有任何一個事件完全先於它自己。（一個“事件”定義為與某些事同時的任何東西。）
（b）如果某個事件完全先於另一個，而另一個完全先於第三個，那麽第一個就完全先於第三個。
（c）如果某個事件完全先於另一個，它們不會有同時性。
（d）兩個沒有同時性的事件中的一個必須完全先於另一個。
II。為了確定一個給定事件的最初同代能夠是一個瞬間，我們假設：
（e）一個完全後於某給定事件的某些同代的事件將完全後於該給定事件的某個最初同代。
III。為了確定瞬間的序列是緊致的，我們假設：
（f）如果一個事件完全後於另一個事件，那麽存在一個完全後於前麵的事件而與完全先於後麵那個的某些事件同時的事件。
這個假設帶來這樣的結果：如果某個事件覆蓋了直接先於另一個事件的整段時間，那麽它必須和那個事件至少有一個瞬間是重疊的；也就是，不可能有某個事件剛結束另一個事件就開始。我不知道這是否應該被認為是不可接受的。N. Wilner在“對於相對位置的理論的一點貢獻，”中有對於上述問題的數學-邏輯的處理，劍橋哲學學會學報，17刊，5期，441-449頁
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這裏需要對上麵所引的羅素的文章做些簡要的解釋。首先，所引的是羅素的《我們關於外部世界的知識》一書的第四講中的一部分，而這部分是針對所謂的私世界(private world)而言的，這裏的私世界指的是每個人自己所觀察到的世界。羅素在該書的第三講中指出了每個所觀察到的私世界是彼此不同的，且不同於科學所研究的物理世界。該書在本文所引的這段討論的後麵簡單地指出了，每個人的私世界之間是相關聯（所以我們才能有科學所研究的所謂的客觀的世界），而對於私世界如何彼此相關於一個共同的客觀世界的討論的難度很大，但從哲學理解上來看並不具備嚴重的原則性的難度。他並沒有再具體地深入討論。
另外，我們要注意到羅素的那本書是在愛因斯坦發表了賦予時間與空間一個完全不同傳統觀念的革命性的新意義的狹義相對論之後，而在愛因斯坦還沒有發表廣義相對論之前。但是，由於如羅素自己在書中反複強調的，他所做的是對於時間的數學處理（應該說是數學性的哲學思辨），沒有引入額外的形而上學的概念實體，因此，它不會象傳統上一些其他哲學大家們對於時間意義的討論那樣會與狹義或廣義相對論的知識發生衝突。
最後，從本文對於緊致性的討論可以看出，羅素在開始進行時間點的構造時是信心滿滿的，但是在結束時卻發現自己的討論可能有悖於人們生活中對於事件與時間序列之間的關係的經驗常識，如他在[17]中所解釋的，“這個假設（譯者注：這裏的假設指的是任意兩個瞬間點之間存在著其它的瞬間點之說）帶來這樣的結果：如果某個事件覆蓋了直接先於另一個事件的整段時間，那麽它必須和那個事件至少有一個瞬間是重疊的；也就是，不可能有某個事件剛結束另一個事件就開始。我不知道這是否應該被認為是不可接受的。”，因此他以“至於說現實中的事件在時間上的排序是否真是這樣的，那是一個經驗性的問題；但如果它不成立，就沒有理由認為我們所構造的時間序列是緊致的。”這樣一句聽上去軟軟的話來結束他對於時間序列的構造的討論。
我不知道為什麽羅素這裏會擔心不存在“有某個事件剛結束另一個事件就開始”的可能性。這從數學的無限可分上似乎沒有什麽問題。或許他這裏所擔心的是他自己的討論與前麵他提到的拿左輪槍的人所說的數到三之後就開槍這種人們所熟悉的常識性的狀況相違背。因為，一般人們說數到三要幹什麽顯然應該是先數到三，然後再幹什麽。如果他真的在擔心這樣的問題，那麽他應該加一句，他的時間序列構造至少是在大於普朗克常數量級之上的意義上是緊致的，因為從一個人數到三或是一個電腦指令運行完畢到另一個指令的運行開始之間在這個世界的某處總會有些量子量級上的脈動存在的。
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附錄 文中所引用的羅素的文章的英語原文：
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......... Events of which we are conscious do not last merely for a
mathematical instant, but always for some finite time, however short. Even if
there be a physical world such as the mathematical theory of motion supposes,
impressions on our sense-organs produce sensations which are not merely and
strictly instantaneous, and therefore the objects of sense of which we are
immediately conscious are not strictly instantaneous. Instants, therefore, are
not among the data of experience, and, if legitimate, must be either inferred
or constructed. It is difficult to see how they can be validly inferred; thus
we are left with the alternative that they must be constructed. How is this to
be done?
mathematical instant, but always for some finite time, however short. Even if
there be a physical world such as the mathematical theory of motion supposes,
impressions on our sense-organs produce sensations which are not merely and
strictly instantaneous, and therefore the objects of sense of which we are
immediately conscious are not strictly instantaneous. Instants, therefore, are
not among the data of experience, and, if legitimate, must be either inferred
or constructed. It is difficult to see how they can be validly inferred; thus
we are left with the alternative that they must be constructed. How is this to
be done?
Immediate experience provides us with two time-relations
among events: they may be simultaneous, or one may be earlier and the other
later. These two are both part of the crude data; it is not the case that only
the events are given, and their time-order is added by our subjective activity.
The time-order, within certain limits, is as much given as the events. In any
story of adventure you will find such passages as the following: “With a
cynical smile he pointed the revolver at the breast of the dauntless youth. ‘At
the word three I shall fire,’ he said. The words one and two had already been
spoken with a cool and deliberate distinctness. The word three was forming on
his lips. At this moment a blinding flash of lightning rent the air.” Here we
have simultaneity—not due, as Kant would have us believe, to the subjective
mental apparatus of the dauntless youth, but given as objectively as the
revolver and the lightning. And it is equally given in immediate experience
that the words one and two come earlier than the flash. These time-relations
hold between events which are not strictly instantaneous. Thus one event may
begin sooner than another, and therefore be before it, but may continue after
the other has begun, and therefore be also simultaneous with it. If it persists
after the other is over, it will also be later than the other. Earlier,
simultaneous, and later, are not inconsistent with each other when we are
concerned with events which last for a finite time, however short; they only
become inconsistent when we are dealing with something instantaneous.
among events: they may be simultaneous, or one may be earlier and the other
later. These two are both part of the crude data; it is not the case that only
the events are given, and their time-order is added by our subjective activity.
The time-order, within certain limits, is as much given as the events. In any
story of adventure you will find such passages as the following: “With a
cynical smile he pointed the revolver at the breast of the dauntless youth. ‘At
the word three I shall fire,’ he said. The words one and two had already been
spoken with a cool and deliberate distinctness. The word three was forming on
his lips. At this moment a blinding flash of lightning rent the air.” Here we
have simultaneity—not due, as Kant would have us believe, to the subjective
mental apparatus of the dauntless youth, but given as objectively as the
revolver and the lightning. And it is equally given in immediate experience
that the words one and two come earlier than the flash. These time-relations
hold between events which are not strictly instantaneous. Thus one event may
begin sooner than another, and therefore be before it, but may continue after
the other has begun, and therefore be also simultaneous with it. If it persists
after the other is over, it will also be later than the other. Earlier,
simultaneous, and later, are not inconsistent with each other when we are
concerned with events which last for a finite time, however short; they only
become inconsistent when we are dealing with something instantaneous.
It is to be observed that we cannot give what may be called
absolute dates, but only dates determined by events. We cannot point to a time
itself, but only to some event occurring at that time. There is therefore no
reason in experience to suppose that there are times as opposed to events: the
events, ordered by the relations of simultaneity and succession, are all that
experience provides. Hence, unless we are to introduce superfluous metaphysical
entities, we must, in defining what mathematical physics can regard as an
instant, proceed by means of some construction which assumes nothing beyond
events and their temporal relations.
absolute dates, but only dates determined by events. We cannot point to a time
itself, but only to some event occurring at that time. There is therefore no
reason in experience to suppose that there are times as opposed to events: the
events, ordered by the relations of simultaneity and succession, are all that
experience provides. Hence, unless we are to introduce superfluous metaphysical
entities, we must, in defining what mathematical physics can regard as an
instant, proceed by means of some construction which assumes nothing beyond
events and their temporal relations.
If we wish to assign a date exactly by means of events, how
shall we proceed? If we take any one event, we cannot assign our date exactly,
because the event is not instantaneous, that is to say, it may be simultaneous
with two events which are not simultaneous with each other. In order to assign
a date exactly, we must be able, theoretically, to determine whether any given
event is before, at, or after this date, and we must know that any other date
is either before or after this date, but not simultaneous with it. Suppose,
now, instead of taking one event A, we take two events A and B, and suppose A
and B partly overlap, but B ends before A ends. Then an event which is
simultaneous with both A and B must exist during the time when A and B overlap;
thus we have come rather nearer to a precise date than when we considered A and
B alone. Let C be an event which is simultaneous with both A and B, but which
ends before either A or B has ended. Then an event which is simultaneous with A
and B and C must exist during the time when all three overlap, which is a still
shorter time. Proceeding in this way, by taking more and more events, a new
event which is dated as simultaneous with all of them becomes gradually more
and more accurately dated. This suggests a way by which a completely accurate
date can be defined.
shall we proceed? If we take any one event, we cannot assign our date exactly,
because the event is not instantaneous, that is to say, it may be simultaneous
with two events which are not simultaneous with each other. In order to assign
a date exactly, we must be able, theoretically, to determine whether any given
event is before, at, or after this date, and we must know that any other date
is either before or after this date, but not simultaneous with it. Suppose,
now, instead of taking one event A, we take two events A and B, and suppose A
and B partly overlap, but B ends before A ends. Then an event which is
simultaneous with both A and B must exist during the time when A and B overlap;
thus we have come rather nearer to a precise date than when we considered A and
B alone. Let C be an event which is simultaneous with both A and B, but which
ends before either A or B has ended. Then an event which is simultaneous with A
and B and C must exist during the time when all three overlap, which is a still
shorter time. Proceeding in this way, by taking more and more events, a new
event which is dated as simultaneous with all of them becomes gradually more
and more accurately dated. This suggests a way by which a completely accurate
date can be defined.
Let us take a group of events of which any two overlap, so
that there is some time, however short, when they all exist. If there is any
other event which is simultaneous with all of these, let us add it to the group;
let us go on until we have constructed a group such that no event outside the
group is simultaneous with all of them, but all the events inside the group are
simultaneous with each other. Let us define this whole group as an instant of
time. It remains to show that it has the properties we expect of an instant.
that there is some time, however short, when they all exist. If there is any
other event which is simultaneous with all of these, let us add it to the group;
let us go on until we have constructed a group such that no event outside the
group is simultaneous with all of them, but all the events inside the group are
simultaneous with each other. Let us define this whole group as an instant of
time. It remains to show that it has the properties we expect of an instant.
What are the properties we expect of instants? First, they
must form a series: of any two, one must be before the other, and the other
must be not before the one; if one is before another, and the other before a
third, the first must be before the third. Secondly, every event must be at a
certain number of instants; two events are simultaneous if they are at the same
instant, and one is before the other if there is an instant, at which the one
is, which is earlier than some instant at which the other is. Thirdly, if we
assume that there is always some change going on somewhere during the time when
any given event persists, the series of instants ought to be compact, i.e.
given any two instants, there ought to be other instants between them. Do
instants, as we have defined them, have these properties?
must form a series: of any two, one must be before the other, and the other
must be not before the one; if one is before another, and the other before a
third, the first must be before the third. Secondly, every event must be at a
certain number of instants; two events are simultaneous if they are at the same
instant, and one is before the other if there is an instant, at which the one
is, which is earlier than some instant at which the other is. Thirdly, if we
assume that there is always some change going on somewhere during the time when
any given event persists, the series of instants ought to be compact, i.e.
given any two instants, there ought to be other instants between them. Do
instants, as we have defined them, have these properties?
We shall say that an event is “at” an instant when it is a
member of the group by which the instant is constituted; and we shall say that
one instant is before another if the group which is the one instant contains an
event which is earlier than, but not simultaneous with, some event in the group
which is the other instant. When one event is earlier than, but not
simultaneous with another, we shall say that it “wholly precedes” the other.
Now we know that of two events which are not simultaneous, there must be one
which wholly precedes the other, and in that case the other cannot also wholly
precede the one; we also know that, if one event wholly precedes another, and
the other wholly precedes a third, then the first wholly precedes the third.
From these facts it is easy to deduce that the instants as we have defined them
form a series.
member of the group by which the instant is constituted; and we shall say that
one instant is before another if the group which is the one instant contains an
event which is earlier than, but not simultaneous with, some event in the group
which is the other instant. When one event is earlier than, but not
simultaneous with another, we shall say that it “wholly precedes” the other.
Now we know that of two events which are not simultaneous, there must be one
which wholly precedes the other, and in that case the other cannot also wholly
precede the one; we also know that, if one event wholly precedes another, and
the other wholly precedes a third, then the first wholly precedes the third.
From these facts it is easy to deduce that the instants as we have defined them
form a series.
We have next to show that every event is “at” at least one
instant, i.e. that, given any event, there is at least one class, such as we
used in defining instants, of which it is a member. For this purpose, consider
all the events which are simultaneous with a given event, and do not begin
later, i.e. are not wholly after anything simultaneous with it. We will call
these the “initial contemporaries” of the given event. It will be found that
this class of events is the first instant at which the given event exists,
provided every event wholly after some contemporary of the given event is
wholly after some initial contemporary of it.
instant, i.e. that, given any event, there is at least one class, such as we
used in defining instants, of which it is a member. For this purpose, consider
all the events which are simultaneous with a given event, and do not begin
later, i.e. are not wholly after anything simultaneous with it. We will call
these the “initial contemporaries” of the given event. It will be found that
this class of events is the first instant at which the given event exists,
provided every event wholly after some contemporary of the given event is
wholly after some initial contemporary of it.
Finally, the series of instants will be compact if, given
any two events of which one wholly precedes the other, there are events wholly
after the one and simultaneous with something wholly before the other. Whether
this is the case or not, is an empirical question; but if it is not, there is
no reason to expect the time-series to be compact. [17]
any two events of which one wholly precedes the other, there are events wholly
after the one and simultaneous with something wholly before the other. Whether
this is the case or not, is an empirical question; but if it is not, there is
no reason to expect the time-series to be compact. [17]
Thus our definition of instants secures all that mathematics
requires, without having to assume the existence of any disputable metaphysical
entities.
requires, without having to assume the existence of any disputable metaphysical
entities.
Instants may also be defined by means of the
enclosure-relation, exactly as was done in the case of points. One object will
be temporally enclosed by another when it is simultaneous with the other, but
not before or after it. Whatever encloses temporally or is enclosed temporally
we shall call an “event.” In order that the relation of temporal enclosure may
be a “point-producer,” we require (1) that it should be transitive, i.e. that
if one event encloses another, and the other a third, then the first encloses
the third; (2) that every event encloses itself, but if one event encloses
another different event, then the other does not enclose the one; (3) that
given any set of events such that there is at least one event enclosed by all
of them, then there is an event enclosing all that they all enclose, and itself
enclosed by all of them; (4) that there is at least one event. To ensure infinite
divisibility, we require also that every event should enclose events other than
itself. Assuming these characteristics, temporal enclosure is an infinitely
divisible point-producer. We can now form an “enclosure-series” of events, by
choosing a group of events such that of any two there is one which encloses the
other; this will be a “punctual enclosure-series” if, given any other
enclosure-series such that every member of our first series encloses some
member of our second, then every member of our second series encloses some
member of our first. Then an “instant” is the class of all events which enclose
members of a given punctual enclosure-series.
enclosure-relation, exactly as was done in the case of points. One object will
be temporally enclosed by another when it is simultaneous with the other, but
not before or after it. Whatever encloses temporally or is enclosed temporally
we shall call an “event.” In order that the relation of temporal enclosure may
be a “point-producer,” we require (1) that it should be transitive, i.e. that
if one event encloses another, and the other a third, then the first encloses
the third; (2) that every event encloses itself, but if one event encloses
another different event, then the other does not enclose the one; (3) that
given any set of events such that there is at least one event enclosed by all
of them, then there is an event enclosing all that they all enclose, and itself
enclosed by all of them; (4) that there is at least one event. To ensure infinite
divisibility, we require also that every event should enclose events other than
itself. Assuming these characteristics, temporal enclosure is an infinitely
divisible point-producer. We can now form an “enclosure-series” of events, by
choosing a group of events such that of any two there is one which encloses the
other; this will be a “punctual enclosure-series” if, given any other
enclosure-series such that every member of our first series encloses some
member of our second, then every member of our second series encloses some
member of our first. Then an “instant” is the class of all events which enclose
members of a given punctual enclosure-series.
...........
[17] The assumptions made concerning time-relations in
the above are as follows:—
the above are as follows:—
I. In order to secure that instants form a series, we
assume:
assume:
(a) No event wholly precedes itself. (An “event” is
defined as whatever is simultaneous with something or other.)
defined as whatever is simultaneous with something or other.)
(b) If one event wholly precedes another, and the other
wholly precedes a third, then the first wholly precedes the third.
wholly precedes a third, then the first wholly precedes the third.
(c) If one event wholly precedes another, it is not
simultaneous with it.
simultaneous with it.
(d) Of two events which are not simultaneous, one must
wholly precede the other.
wholly precede the other.
II. In order to secure that the initial contemporaries of
a given event should form an instant, we assume:
a given event should form an instant, we assume:
(e) An event wholly after some contemporary of a given
event is wholly after some initial contemporary of the given event.
event is wholly after some initial contemporary of the given event.
III. In order to secure that the series of instants shall
be compact, we assume:
(f) If one event wholly precedes another, there is an
event wholly after the one and simultaneous with something wholly before the
other.
This assumption entails the consequence that if one event
covers the whole of a stretch of time immediately preceding another event, then
it must have at least one instant in common with the other event; i.e. it is
impossible for one event to cease just before another begins. I do not know
whether this should be regarded as inadmissible. For a mathematico-logical
treatment of the above topics, cf. N. Wilner, “A Contribution to the Theory of
Relative Position,” Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449.
be compact, we assume:
(f) If one event wholly precedes another, there is an
event wholly after the one and simultaneous with something wholly before the
other.
This assumption entails the consequence that if one event
covers the whole of a stretch of time immediately preceding another event, then
it must have at least one instant in common with the other event; i.e. it is
impossible for one event to cease just before another begins. I do not know
whether this should be regarded as inadmissible. For a mathematico-logical
treatment of the above topics, cf. N. Wilner, “A Contribution to the Theory of
Relative Position,” Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449.
[1]OUR KNOWLEDGE OF THE EXTERNAL WORLD，Bertrand
Russel，URL：http://www.gutenberg.org/files/37090/37090-h/37090-h.htm
Russel，URL：http://www.gutenberg.org/files/37090/37090-h/37090-h.htm
1）與閱讀哲評或哲普讀物相比，學習柏拉圖，亞裏士多德，笛卡爾，休謨，康德，黑格爾，伯格森，羅素等等這些哲學大師的原著不但可以幫助讀者澄清一些哲評和哲普中常有的對那些大師原著的曲解或誤解，更重要的是可以幫助學習領會大師們的精細，全麵，嚴格地考察和論述問題的思維。可以提高讀者對於充斥於世麵上的邏輯混亂，故弄玄虛，鼓吹哲學隻重理論不重應用的虛幻的偽哲學的鑒別能力。
不象有些專炒哲評哲普的人試圖讓讀者以為的曆史上哲學大家們的主要價值在於他們的理論的結論，恰恰相反，如果你真的去讀那些大家的原著，不但會發現他們有些結論在今天來說是明顯地過時了或錯誤的，而且就是在他們當時論述過程中就可能表現出一些對於自己的論述漏洞的意識以及所進行的權宜的處理。本文所翻譯介紹的羅素對於他所構造的時間序列的緊致性的討論就是一個典型的例子。
很顯然，他在進行討論的開始對於他自己的構造所應具有的數學意義上的緊致性是信心滿滿的。但是，討論到最後，卻發現不是那麽簡單。我們可以想象一下在一個世紀稍微多一點的時候，這位大師在寫那部十多萬字的著作到一半的時候發現自己邏輯上有不完美之處（作為現代數理邏輯的創始人，他是以邏輯嚴格而著稱的）而進行左支右絀煞費苦心（甚至可能寢食難安）的情景，但是他最後還是相當漂亮（graceful）地，雖然顯得有些疲軟地，替自己圓了場----最重要的是他並沒有因此而象今天世界上的很多所謂主流專家那樣采取文過飾非的手法掩飾或跳過自己所麵臨的難題。。。。。。
具體地說，如他在文中的【17】裏所指出的，他給時間序列所加的緊致性要求將導致這樣一個結果：不存在一個事件剛結束另一個事件馬上開始這種情況。
對於這一點，用今天的電腦程序運算更容易理解：在電腦運算中如果一條指令剛結束另一條指令就開始的話，按照羅素所說的緊致性條件，在前麵一個指令結束之後和後麵那個指令開始之前的那個短暫的時間中，仍然會有某些事件存在於整個宇宙的某個地方。。。。當然，如果電腦運算速度極高以致於兩個指令之間的間隙已經遠小於普朗克常數量級，那麽就進入微觀量子脈動層次之後，宏觀的緊致性結論就未必完全成立了。
按照羅素的緊致性假設，由於（至少在宏觀領域中）兩個事件之間（不論多短）總有其它事件存在，因此為了要是緊致性條件與人們日常的一個事件結束之後另一個事件馬上開始的經驗常識相吻合，就需要假設它們之間必須至少有一個重合點（至少是普朗克常數量級之上的宏觀領域中是這樣的）。羅素顯然隱隱地覺到這種對於重合點的要求又有悖於人們的生活常識因而讓他感到不安，但是他又不願放棄作為數學上的嚴格性要求的緊致性條件，所以就在聲明了“我不知道這是否應該被認為是不可接受的。”的前提下，留有餘地地說，“我們隻要能證明當給出其中一個完全先於另一個的任意兩個事件時，一定存在一些事件它們完全後於第一個事件而與某些完全先於第二個事件的同時，就能說明我們所構成的瞬間的序列是緊致的。至於說現實中的事件在時間上的排序是否真是這樣的，那是一個經驗性的問題；但如果它不成立，就沒有理由認為我們所構造的時間序列是緊致的。”
其實，就日常的生活經驗來說，沒有人會在乎兩個相鄰事件之間是否還在宇宙的其它地方存在著什麽事件，或兩個相鄰事件之間是否有重合點（別忘了，他的《我們關於外部世界的知識》不是一本物理書，而是一本哲學書），但是他仍然不願在邏輯細節上含糊（這當然與他所討論的對象----時間所具有的普世性有關，但同時我們也看到他的嚴謹的態度與今天有些鼓吹哲學不在乎應用，怎麽說都行的偽哲學家形成了鮮明的對比）。
另一方麵，在普朗克量級之上的宏觀世界裏，他的緊致性條件是成立的，其實並沒有必要非讓這個條件來削足適履地適應日常的生活經驗。但是，盡管我們不知他在這個問題上對於當時剛興起不太久的量子力學有多熟悉，我們可以肯定他是不願在這個問題上扯進量子力學的，因為那樣一來，他所聲稱的他對於時間的構造是完全數學性的而不需要牽扯多餘的形而上的概念實體的宣言就破功了。
但是，我認為不論是大師們的結論被日後的科學或哲學的發展所淘汰還是大師們本人在論述過程中表現出的權宜或無奈都不會降低大師們在人們心目中的地位，因為他們對於世界哲學乃至一般文明的影響並不僅僅局限於某些具體的結論，更重要的是他們為世人所起到的如何認真有效的誠懇的充滿智慧地進行思維的模範作用。
2）今天的哲評與哲普（包括大師們所做的哲評與哲普）中常出現用人為的標簽來將曆史上的哲學家們的理論進行割裂的情況。這種割裂對於介紹不同時期不同人的哲學在一定程度上是有幫助的，但是客觀上卻不但對於人們理解具體哲學家的理論起到誤導的作用，而且更嚴重的是使得讀者看待哲學發展的時候很容易用隻看樹木不見森林的方式而忽視了不同時期的哲學理論之間的相互承繼和影響。最典型的就是對於唯心論的批判，康德批別人是唯心主義，黑格爾批康德是唯心主義，然後別人又批黑格爾是唯心主義。似乎誰都覺得前人唯心，這在哲學家那裏其實並不打緊，因為他們知道他們所說的唯心指的是什麽。但是，他們沒有考慮到的是他們這種對於唯心主義的批判到了根本不懂哲學卻把哲學當作政治工具的東西方的老百姓那裏，這種對於所謂唯心主義的批判本身就成了一個唯心的標簽式的群眾性鬥爭武器，並因此不但對哲學的發展造成阻礙，而且還常直接對一些相關人士的人生造成傷害。
羅素在《我們關於外部世界的知識》的第四講中提到龐加萊對於時間的觀點過於康德化。其實，他的所謂的私世界本身就是康德的現象界與本體界（糯米饢）劃分的一個邏輯上的延續。根據羅素的私世界理論，對於每個人來說的世界是不同於對於其他人來說的世界的，而物理學所研究的一個單一的世界，是對於每個人來說的私世界進行相關統一而成的，而這種統一並不是天然的，是值得人們去研究的。
這種思想不是人類自古就有的，柏拉圖研究理想國亞裏士多德研究形而上的抽象概念時雖然對於人們認識世界的條件進行過探討，卻沒有明確劃分出個人所麵對的世界與其他人所麵對的世界之間的差異來。到了笛卡爾他從理論上探討了個人的認識與客觀世界之間的不那麽天然的一致性；休謨更是因此指出人們的認識本身不那麽天然，而是與每個人的經驗有關；康德則在休謨的基礎上試圖對於什麽是屬於經驗的什麽屬於非經驗進行探究，但是他的一個結論是人們的認識不可能超出經驗範圍，因而存在現象界與本體界的劃分。
另一方麵，笛卡爾“我思故我在”這句話其實具有兩麵性：一麵是指出個人經驗與外界並非天然的一致，另一麵卻也指出人對於自己的意識是了解的。而黑格爾恰恰是從人對自己的意識是了解的這一麵出發來批康德的現象界與本體界的劃分（盡管他也承認我們根本無法知道外部世界到底是怎麽回事），而同時他的現象學卻在進一步地強調了個人從自己的立場出發來觀察世界的同時試圖找出一個普世統一的所謂辯證規律來。到了羅素這裏，他一方麵批康德的本體界是不可知論，一方麵對黑格爾的絕對理性不以為然，但是他本人對於外部世界的認識在原則上基本上就是康德與黑格爾的理論的延伸：每個人觀察到的世界都是個體特異的，而我們可以用邏輯思辨出一個統一的世界的規律。之所以說他是康德他們的理論的延伸，因為這種觀點本身並非人類自古天然地就有的。羅素的觀點聽起來似乎比康德的現象界與本體界的劃分積極很多，可是康德並沒有否認我們可以用我們的思維來認識世界，隻不過他一方麵強調我們無法知道客觀本體到底是什麽（黑格爾，羅素都沒有否認這一點），另一方麵他把我們對於世界的認識表達為我們用自己的智力來組織出對於世界的描述，這一點與黑格爾和羅素的觀點也並沒有本質的區別。羅素所考慮的用邏輯對於物理世界的分析思考（歸納）本身還不就是人類用自己的語言來組織出對於客觀世界的理論框架嗎？。。。。。。