数学家传记
汉斯·赖兴巴赫是德国科学哲学家,逻辑经验主义的支持者。
汉斯·赖兴巴赫的父母是Bruno Reichenbach和Selma Menzel。Bruno是一位富裕的批发商,赖兴巴赫是他父母的五个孩子之一。Bruno和Selma 赖兴巴赫都是归正会成员,但Bruno的父母是犹太人。尽管这种犹太联系似乎是一个微不足道的细节,然而对于生活在20世纪上半叶德国的人来说,它却极为重要。当然,赖兴巴赫出生在一个[1]的家庭:-
……有教养,对音乐、国际象棋、书籍和戏剧有浓厚兴趣。
赖兴巴赫在汉堡上小学和中学。1910年他离开学校,打算成为一名工程师,并进入斯图加特大学学习工程课程。然而,他的兴趣转向了科学中更理论的方面,1911年在学习一年后离开斯图加特,在柏林、慕尼黑和哥廷根学习数学、物理和哲学课程。在四年间就读三所不同的大学当然并不罕见,因为当时大多数德国学生在几所不同的大学听课。理论物理学家马克斯·普朗克、马克斯·玻恩、阿尔伯特·爱因斯坦和阿诺·索末菲,数学家大卫·希尔伯特,以及新康德主义哲学家Cassirer都是他的老师。赖兴巴赫在大学里除了直接的学术研究之外也很活跃。他对社会有强烈的看法,并在社会话题上直言不讳,利用学生政治来表达自己的观点。1915年,他因关于theory of probabilityDer Begriff der Wahrscheinlichkeit für die mathematische Darstellung der WirklichkeitⓉ的哲学方面的学位论文(概率概念与现实的数学表示)从埃尔朗根大学获得博士学位。他的博士学位由埃尔朗根授予的原因有些奇怪。这篇学位论文有数学部分和哲学部分,赖兴巴赫去了几所大学试图找人接受这篇学位论文。他在埃尔朗根没有找到任何人,而是有两个人接受了他的学位论文,一个接受数学部分,另一个接受哲学部分。1916年,他的学位论文出版。
完成博士学位后,他在德国陆军信号兵团服役30个月,此时该兵团在第一次世界大战期间正激烈地参与几条不同战线的战斗。他被派往俄国前线,在那里患了重病。他被送回柏林,到1917年,他是仅有的五名参加阿尔伯特·爱因斯坦关于相对论的第一门课程的人之一。这个主题引起了赖兴巴赫的兴趣,他投身于对其哲学方面的研究。然而,此时研究对赖兴巴赫来说只是兼职工作,因为他全职受雇于无线电工业。他留在柏林直到1920年,被任命为斯图加特理工学院的教授。在那里他教授各种各样的主题,显示出他兴趣的广度和他的背景:相对论、科学哲学、哲学史、测量学和无线电技术。在他担任这一职位的当年,他出版了他的第一部关于相对论的主要著作Relativitatstheorie und Erkenntnis apriori Ⓣ(《相对论与先天知识》),该书攻击了康德关于空间和时间以及物理学的综合先天理论。随后是诸如Bericht über eine Axiomatik der Einsteinschen Raum-Zeit-Lehre Ⓣ(《关于阿尔伯特·爱因斯坦时空定律公理化的报告》)(1921年)和Der gegenwartige Stand der Relativitatsdiskussion Ⓣ(《相对论讨论的现状》)(1922年)等论文,之后他的第二部主要著作Axiomatik der relativistischen Raum-Zeit-Lehre Ⓣ(《相对论的公理化》)于1924年出版。这部著作再次考察了相对论的哲学意义。随后又有两篇重要论文:Die Bewegungslehre bei Newton, Leibniz und Huyghens Ⓣ(《根据艾萨克·牛顿、哥特弗里德·威廉·莱布尼茨和克里斯蒂安·惠更斯的运动理论》)(1924年)和Die Kausal-strukture der Welt und der Unterschied von Vergangenheit und Zukunft Ⓣ(《世界的因果结构与过去和未来之间的区别》)(1927年)
他成为柏林物理哲学教授职位的候选人,但对他的任命有强烈的反对。他在学生时代政治活跃时,他的观点就已为人所知,而持有这些观点、又像赖兴巴赫那样直言不讳的人,在当时肯定不为德国的许多人所接受。然而,他有一位重要人物大力支持对他的任命,那就是阿尔伯特·爱因斯坦。即便如此,推动这项任命仍是一场斗争,但阿尔伯特·爱因斯坦赢得了争论。1926年,赖兴巴赫被任命为柏林大学物理哲学讲席教授,他采用的教学方法与当时整个德国体系所用的方法非常不同。他鼓励讨论,并让自己随时可供学生与他辩论课程中的话题。他于1928年在柏林创立了Gesellschaft für empirische Philosophie(经验哲学学会),即所谓的柏林学派。Carl Gustav Hempel、理查德·冯·米泽斯、大卫·希尔伯特和Kurt Grelling都成为柏林学派的成员,而赖兴巴赫在1930年承担了另一项重要角色,当时他与Carnap一起担任期刊Erkenntnis(知识)的编辑。在柏林的这些年间,赖兴巴赫发表了更多关于与新物理学相关的空间和时间问题的重要著作。Philosophie der Raum-Zeit-Lehre Ⓣ(空间和时间的哲学)是1928年出版的一部重要文本,两年后是另一部重要著作Atom und kosmos. Das physikalische Weltbild der Gegenwart Ⓣ(原子与宇宙;现代物理学的世界)。事实上,赖兴巴赫此时已为广泛的德国人所熟知,因为他在德国国家广播电台上播讲了构成Atom und kosmos Ⓣ(原子与宇宙;现代物理学的世界)的讲座。1931年,他发表了另一篇论文Ziele und Wege der heutigen Naturphilosophie Ⓣ(现代自然哲学的目标和方法)。
1933年希特勒上台时,赖兴巴赫立即意识到自己会陷入麻烦。他不仅有犹太祖父母,而且通过他的无线电广播而备受瞩目,他的观点与National Socialism的观点完全相悖。来自他在柏林大学的教授职位和国家广播电台职位的解职信来得太晚,没有产生任何效果,因为他预见到了这些信,并在它们到达之前就去了土耳其。他成为伊斯坦布尔大学哲学系主任,并于1933年至1938年担任该职务。在许多方面,赖兴巴赫在新职位上是孤立的,与柏林相比,那里他曾是一个繁荣学派的中心,这种对比一定非常鲜明。然而,他非常积极地赋予伊斯坦布尔大学哲学系更广阔的视野,引入跨学科研讨会和关于科学主题的讲座课程。他在此任职期间还出版了一部重要著作,即Wahrscheinlichkeitslehre; eine Untersuchung über die logischen und mathematischen Grundlagen der WahrscheinlichkeitsrechnungⓉ(概率论;概率论逻辑与数学基础研究)(1935年)。B O Koopman在评论1949年出版的英译本时,开头如下:-
基本上,任何对概率基础的处理都面临两项任务:(I)建立概率陈述的一致性法则(允许从给定概率推导出新概率的法则);以及(II)在没有给出概率的情况下,首先制定分配概率的明确规则。(I)和(II)都涉及概率的意义问题及其应用问题。正如作者所表明的,后一问题在概率中具有独特的形式:其他科学中的应用问题利用概率。整个主题不仅涉及思维法则,还涉及归纳,从而涉及科学知识的基础。本书正是在这一层面上写成的。
赖兴巴赫试图将概率定义为频率的极限,但许多人批评这种方法。他论证说,如果已经进行了次试验,那么可以用来预测下一次试验的唯一证据就是在次试验中观察到的频率。他写道,这是:-
……一个理论所能期望的最大限度。
在签订了一份为期五年的土耳其职位合同后,他于1938年合同期满时移居美国。在那里,他担任了加州大学洛杉矶分校的教授。在他抵达美国的那一年,他与芝加哥大学出版社出版了他的书Experience and prediction: an analysis of the foundations and the structure of knowledge。当然,这本书是他在伊斯坦布尔期间写的。
乔治·萨蒙在[7]中写道:-
赖兴巴赫不仅是一位科学哲学家,也是一位科学性的哲学家。他坚持认为,哲学应当遵循与自然科学相同的精确性和严谨性标准。他无条件地拒绝思辨形而上学和神学,因为它们的主张既不能先验地、基于逻辑和数学得到证实,也不能后验地、基于感官经验得到证实。在这一点上,他同意维也纳学派的逻辑实证主义者,但由于其他深刻的分歧,他实际上从未是一个实证主义者。相反,他是以柏林为中心的逻辑经验主义者团体的主要成员。
我们已经看到,赖兴巴赫撰写了关于归纳、概率和科学哲学的著作。然而,在美国,他还撰写了关于量子力学的哲学基础和时间的重要著作。在第一个主题上,他出版了Philosophic foundations of quantum mechanics(1944年)一书,以及两篇论文Über die erkenntnistheoretische Problemlage und den Gebrauch einer dreiwertigen Logik in der QuantenmechanikⓉ(论认识论问题情境及三值逻辑在量子力学中的使用)(1951年)和Les fondements logiques de la théorie des quanta. Utilisation d'une logique à trois valeursⓉ(量子理论的逻辑基础。三值逻辑的使用)(1954年)。他声称:-
……不存在任何没有因果异常的量子力学的详尽解释。
一种因果异常,即超距作用和接触作用被违反的地方。在两篇论文中,他考察了在量子力学中使用扬·武卡谢维奇的三值逻辑。这包含真值“未定”,以及“真”和“假”。
在他移居后出版的著作中,有Elements of Symbolic Logic(1947年)和The Rise of Scientific Philosophy(1951年)。两者都是通俗读物,其中第二本是他所写书中销量最成功的。阿兰德·海廷在评论第一本时写道:-
这本教科书主要不是为数学家而写,它更强调形式逻辑的解释和应用,而不是形式系统本身的构造。逻辑表达式自始至终被认为是有意义的;特别是,存在被解释为意味着物理存在。作者在哲学上极端的物理主义立场随处可见。
赖兴巴赫去世时正在写两本书:Nomological statements and admissible operations(1954年)和The direction of time(1956年)。由于他的妻子Maria Reichenbach博士的努力,这些书在死后出版。在这部引人入胜的时间研究中,赖兴巴赫区分了时间的次序和时间的方向。他通过以下方式定义次序:-
……如果事件A能对事件B产生物理效应,则事件A发生在事件B之前。
至于时间的方向,他写道:-
……时间的方向只能通过不可逆过程来定义……
换句话说,通过增加熵。
匹兹堡大学的“赖兴巴赫收藏”中有大量信件、讲义和手稿材料。
Hans Reichenbach's parents were Bruno Reichenbach and Selma Menzel. Bruno was a prosperous wholesale merchant, and Hans was one of his parents' five children. Both Bruno and Selma Reichenbach were members of the Reformed Church but Bruno's parents were Jewish. Although this Jewish connection would seem a small point to bring out, nevertheless for someone living in Germany through the first half of the 20th century it would be highly significant. Certainly Hans was born into a family which [1]:-
... was cultured, with a lively interest in music, chess, books and the theatre.
Hans attended primary and secondary schools in Hamburg. He left school in 1910 with the intention of becoming an engineer and he entered the University of Stuttgart taking engineering courses. However his interests moved towards more theoretical aspects of science and he left Stuttgart in 1911 after one year of study and took mathematics, physics and philosophy courses at Berlin, Munich and Göttingen. Being at three different universities over the course of four years was certainly not unusual, for at this time most German students took courses at several different universities. The theoretical physicists Planck, Born, Einstein and Sommerfeld, the mathematician Hilbert, and the neo-Kantian philosopher Cassirer were among his teachers. Reichenbach was also active in the universities outside his immediate academic studies. He had strong views on society and was outspoken on social topics, taking advantage of student politics to air his views. In 1915 he received his doctorate from the University of Erlangen for his thesis on philosophical aspects of the theory of probability Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit Ⓣ. The reason that his doctorate was awarded by Erlangen was slightly strange. The thesis had a mathematical part and a philosophy part, and Reichenbach went to several universities trying to find someone to accept the thesis. He did not find anyone at Erlangen but rather he had his thesis accepted by two people, one who accepted the mathematical part, the other the philosophical part. In 1916 his thesis was published.
After completing his doctorate he served for 30 months in the Signal Corps of the German army, which by this time was heavily engaged in fighting on several different fronts during World War I. He was sent to the Russian front where he contracted a severe illness. He was sent back to Berlin where by 1917 he was one of only five people who attended Einstein's first course on relativity. The topic intrigued Reichenbach and he launched himself into undertaking research on its philosophical aspects. Research, however, was only a part-time job for Reichenbach at this time for he was employed full-time in the radio industry. He remained in Berlin until 1920 when he was appointed professor at the Polytechnic at Stuttgart. There he taught a wide variety of topics showing both the breadth of his interests and his background: relativity, philosophy of science, history of philosophy, surveying, and radio techniques. In the year he took up this position he published his first major text on relativity Relativitatstheorie und Erkenntnis apriori Ⓣ which attacked Kant's synthetic a priori theory of space and time, and of physics. This was followed by papers such as Bericht über eine Axiomatik der Einsteinschen Raum-Zeit-Lehre Ⓣ (1921) and Der gegenwartige Stand der Relativitatsdiskussion Ⓣ (1922) before his second major book Axiomatik der relativistischen Raum-Zeit-Lehre Ⓣ was published in 1924. This work again examined the philosophical meaning of the theory of relativity. Two further important papers followed: Die Bewegungslehre bei Newton, Leibniz und Huyghens Ⓣ (1924) and Die Kausal-strukture der Welt und der Unterschied von Vergangenheit und Zukunft Ⓣ (1927)
He became a candidate for a professorship in the philosophy of physics in Berlin but there was strong opposition to his appointment. His views had become known when he was politically active in his student days, and someone with these views, who was as outspoken as Reichenbach, was certainly not acceptable to many in Germany at this time. However he had a major figure who supported his appointment with great vigour, namely Einstein. Even then it proved a struggle to push the appointment through, but Einstein won the argument. Appointed to the chair in the philosophy of physics at the University of Berlin in 1926 Reichenbach took a very different approach to teaching than that used throughout the German system at that time. He encouraged discussion and made himself available to students who could debate topics in the courses with him. He founded the Gesellschaft für empirische Philosophie (Society for empirical philosophy) in Berlin in 1928, known as the Berlin Circle. Carl Gustav Hempel, Richard von Mises, David Hilbert and Kurt Grelling all became members of the Berlin Circle and Reichenbach took on another major role in 1930 when, together with Carnap, he took on the editorship of the journal Erkenntnis (Knowledge). During these years in Berlin, Reichenbach published further important works on the problems of space and time associated with the new physics. Philosophie der Raum-Zeit-Lehre Ⓣ was an important text published in 1928, followed two years later by another major book Atom und kosmos. Das physikalische Weltbild der Gegenwart Ⓣ. In fact Reichenbach became well-known to a wide range of German people at this time for he broadcast the lectures which made up Atom und kosmos Ⓣ on German state radio. In 1931 he published a further paper Ziele und Wege der heutigen Naturphilosophie Ⓣ.
When Hitler came to power in 1933 Reichenbach realised immediately that he would be in trouble. Not only did he have Jewish grandparents, but he had a high profile through his radio broadcasts and his views were completely at odds with those of National Socialism. Letters of dismissal, both from his professorship at the University of Berlin and from his position with the state radio, arrived too late to have any effect for, anticipating them, and had left for Turkey before they arrived. He became head of the Department of Philosophy at the University at Istanbul and served in that role from 1933 to 1938. In many ways Reichenbach was isolated in his new position, certainly the contrast with Berlin where he had been the centre of a flourishing school must have been striking. However he was very active in giving the Department of Philosophy in Istanbul a much broader outlook, introducing interdisciplinary seminars and lecture courses on scientific topics. He also published a major text while in this post, namely Wahrscheinlichkeitslehre; eine Untersuchung über die logischen und mathematischen Grundlagen der Wahrscheinlichkeitsrechnung Ⓣ (1935). B O Koopman, reviewing the English translation which appeared in 1949, begins at follows:-
Basically, two tasks face any treatment of the foundations of probability: (I) the establishment of laws of consistency of probability statements (laws permitting the derivation of new probabilities from given probabilities); and (II) the formulation of explicit rules for assigning probabilities in the first place, in situations where no probability is given. Both (I) and (II) entail the question of the meaning of probability and the problem of its application. As the author shows, the latter problem has a unique form in probability: the application problem in other sciences makes use of probability. The whole subject bears not only on the laws of thought, but on induction and thus on the bases of scientific knowledge. It is on this level that the book is written.
Reichenbach attempted to define probability as the limit of a frequency but many criticised this approach. He argues that if trials have been carried out, the only evidence one might use to predict the next trial is the frequency observed in the trials. This, he writes is:-
... the most that can be expected of a theory.
Having signed a five year contract for his Turkish position, he emigrated to the United States at its termination in 1938. There he worked as a professor at the University of California at Los Angeles. In the year he arrived in the United States he published with the University of Chicago Press his book Experience and prediction: an analysis of the foundations and the structure of knowledge. Of course this book had been written during his years in Istanbul.
Salmon writes in [7]:-
Reichenbach was not only a philosopher of science but also a scientific philosopher. He insisted that philosophy should adhere to the same standard of precision and rigour as the natural sciences. He unconditionally rejected speculative metaphysics and theology because their claims could not be substantiated either a priori, on the basis of logic and mathematics, or a posteriori, on the basis of sense-experience. In this respect he agreed with the logical positivists of the Vienna Circle, but because of other profound disagreements he was never actually a positivist. He was, instead, the leading member of the group of logical empiricists centred in Berlin.
We have seen that Reichenbach wrote on induction, probability and the philosophy of science. However, in the United States he also wrote major works on the philosophical foundations of quantum mechanics and on time. On the first of these topics he published the book Philosophic foundations of quantum mechanics (1944), and the two papers Über die erkenntnistheoretische Problemlage und den Gebrauch einer dreiwertigen Logik in der Quantenmechanik Ⓣ (1951) and Les fondements logiques de la théorie des quanta. Utilisation d'une logique à trois valeurs Ⓣ (1954). He claimed that:-
... there is not any exhaustive interpretation of quantum mechanics which is free from causal anomalies.
A casual anomaly of where action at a distance takes place and action by contact is violated. In the two papers be examines using Łukasiewicz's three-valued logic in quantum mechanics. This contains the truth value "undecided", as well as that of "true" and "false".
Among other works, published after he emigrated, are Elements of Symbolic Logic (1947) and The Rise of Scientific Philosophy (1951). Both are popular texts, the second being the most successful book he wrote in terms of sales. Heyting, writing about the first, states:-
This textbook, not primarily intended for mathematicians, emphasizes more the interpretation and application of formal logic than the construction of the formal system itself. Logical expressions are considered throughout as having a meaning; in particular, existence is interpreted as meaning physical existence. Everywhere the author's extreme physicalist position in philosophy is explicit.
Reichenbach was working on two books at the time of his death: Nomological statements and admissible operations (1954), and The direction of time (1956). These were published posthumously thanks to the efforts of his wife, Dr Maria Reichenbach. In this fascinating study of time, Reichenbach distinguishes between the order of time and the direction of time. He defines order by:-
... event A occurs before event B if event A can produce a physical effect on event B.
As to the direction of time, he writes that the:-
... direction of time is definable only by means of irreversible processes ...
in other word by means of increasing entropy.
There is a large collection of letters, lecture notes, and manuscript material in "The Hans Reichenbach Collection" at the University of Pittsburgh.
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