莱维·本·热尔松Gersonides

莱维·本·热尔松以许多不同的名字为人所知。除了热尔松之外，最常见的似乎是热尔松和热尔松本格森。然而，其他人称他为热尔松本格森，较少见的还有格尔索尼、巴尼奥尔的利奥、巴尔内奥利的利奥、利奥·犹大、利奥·希伯来，或缩写拉尔巴格。本文所附的大量参考文献证明了历史学家进行了大量研究。然而，关于他的生平所知甚少，一些历史学家声称确定的事情，有时会被其他人质疑。因此，我们这里给出的‘事实’仅仅是大多数人相信的那些。热尔松确实来自一个杰出学者的家庭。他的父亲是格森·本·所罗门，一位写了Sha'ar ha-Shamayim的学者。热尔松指出他的祖父是热尔松哈科恩，据信他是他母亲的父亲。热尔松还与纳赫曼尼德斯（1194-1270）有密切关系，后者是一位西班牙学者、拉比和犹太宗教领袖，以其在哲学、诗歌和医学方面的工作而闻名。热尔松是犹大·德莱斯菲尔的表亲，其孙子是西蒙·本·泽马赫·杜兰（1361-1444），一位写了多部著名著作的西班牙犹太拉比。

我们知道热尔松住在奥兰治，这个城镇今天在法国，但当他住在那里时并非如此。事实上，这相当重要，因为热尔松出生时的法国国王是腓力四世，被称为美男子腓力。他在1306年将犹太人驱逐出法国，夺取他们的财产并没收所有欠他们的钱，但热尔松没有受到影响。然而，即使在普罗旺斯，犹太人也过得很艰难，热尔松在Milhamot（1329年）的序言中写道，犹太人的苦难：-

……如此强烈，以至于他们使冥想变得不可能。

1309-1377年期间是罗马天主教教廷在阿维尼翁的时期，这些教皇与犹太人关系相当好。热尔松当然与该地区的领导人，无论是犹太人还是基督徒，都关系良好。他将自己的一部作品献给了教皇克莱门特六世，一位阿维尼翁教皇，另一部作品是应莫城主教维特里的菲利普的要求而写的。还有一部作品是应一群犹太和基督教贵族的要求而写的。正如我们刚刚所写已经明显的那样，我们对热尔松所知的少量信息来自他的作品。遗憾的是，这些作品包含关于他生平的很少信息。同样，在他生前其他人的著作中也有提到他，但同样很少能收集到关于他生平的信息。例如，艾萨克·德·拉特斯在他的一部作品的序言中写道：-

伟大的王子，我们的导师热尔松本格森，是许多有价值著作的作者。他写了关于圣经和塔木德的评注；在所有科学分支中，尤其是逻辑学、物理学、形而上学、数学和医学方面，他在地球上无人能及。

这自然引出两个问题。热尔松是如何成为如此多学科的专家的？他又是如何谋生的？这两个问题都无法确切回答，但我们可以说一点。例如，鉴于他出身于学者家庭，几乎可以肯定他接受了家庭成员在宗教事务方面的训练。然而，没有证据表明他可能在哪里接受过科学训练，因此许多专家认为他在这些主题上是自学成才的。至于他的职业，最常见的理论是他靠医学专长谋生，但其他理论认为他通过放贷或占星术赚钱，或者他经济独立，不需要谋生。人们可能会认为，在如此多领域精通的人应该能轻松阅读当时的语言，但情况似乎并非如此。他说普罗旺斯语，但所有作品都用希伯来语写作。这乍看可能不太可能，因为他许多作品只有拉丁语版本存世。然而，这些是译本，希伯来语原文已失传。他确实将拉丁语称为“基督徒的语言”，几乎所有历史学家都认为他不懂拉丁语。每当他引用如亚里士多德等作者的拉丁语作品时，他总是用希伯来语给出引文。同样，据信他不懂阿拉伯语，因此不得不通过希伯来语译本阅读阿拉伯学者的作品。这些推论显然对他的教育有一定影响。关于他生平的唯一其他（几乎确定的）事实是，他娶了上文提到的犹大·德莱斯菲尔的妹妹，因此与妻子有远亲关系；没有记录显示这段婚姻有子女。我们现在来看热尔松的作品。

首先我们考察他对数学的贡献。他在1321年写了Art of Calculation（或Art of the Computer），有时被错误地描述为Book of Number。它涉及算术运算，包括提取平方根和立方根。在这部作品中，他还研究了级数的求和、排列和组合，以及基本的代数恒等式。他给出了自然数的平方和和立方和的公式，并研究了二项式系数。在证明中，他使用归纳法，使其成为最早使用这一重要技术的文本之一。在[57]和[58]中，Shai Simonson发表了热尔松这部非凡作品中的问题。事实上，正是Art of Calculation 让我们能够给出热尔松的出生年份，因为他说他在1321年完成写作时，他三十三岁。

1342年，应莫城主教之请，他撰写了The Harmony of Numbers，其中包含一个证明：(1,2)、(2,3)、(3,4)和(8,9)是仅有的几对连续整数，其因子只有2或3。一年后，他撰写了On Sines, Chords and Arcs，考察了三角学，特别是证明了平面三角形的正弦定理，并给出了5位数字的正弦表。他使用克劳狄乌斯·托勒密的方法计算正弦表，其表非常精确。在这部著作中，他研究了弦、正弦、正矢、余弦，但没有研究正切（当时尚未使用）。Gino Loria建议将正弦定理以热尔松命名，但他并非第一个提出该定理的人，12世纪的贾比尔·伊本·阿弗拉赫已知晓该定理，但他可能重新发现了它。他还出版了两部几何著作，一部是对欧几里得前五卷的评注和导论，但未以公理化方式呈现。另一部是Science of Geometry，仅存残篇。有趣的是，热尔松对欧几里得的平行公设感兴趣，似乎参与了一场关于它能否从其他公理推导出来的热烈辩论。他基于关于直线收敛或发散的假设，证明了平行公设，该假设（当然必然）等价于平行公设；详见[43]。

我们现在来看热尔松对天文学的一些贡献。其中之一与天文仪器有关。他发明了雅各布杖，一种测量天体之间角距离的仪器。我们应该注意，“雅各布杖”这个术语不是热尔松使用的，而是他的基督教同时代人使用的；他使用了一个希伯来语名称，翻译为“深奥之揭示者”。它被描述为由以下部分组成：-

……一根长$4{1\over2}$英尺、宽约一英寸的杖，带有六到七个可沿杖滑动的穿孔板，每块板是杖长的整数分之一以便于计算，用于测量恒星或行星之间的距离，以及太阳、月亮和恒星的高度和直径。

这远非他对天文仪器改进的唯一贡献。在[23]中，伯纳德·戈德斯坦考察了热尔松在仪器设计方面的各种创新。一个显著的例子是为星盘的外刻度圈设计了一种横向刻度，用于读取度的十五分之一。我们注意到，值得注意的是，大约250年后，第谷·布拉赫在他的大型墙象限仪上使用了类似的横向刻度。戈德斯坦还在[23]的附录中考察了热尔松为雅各布杖设计的横向刻度。我们注意到，虽然热尔松构建刻度的方法在理论上是正确的，但它需要进行似乎极其困难的测量，因此也许该理论从未付诸实践。

这些仪器在热尔松的主要著作The Wars of the Lord的天文学部分中有所描述，该著作从1317年开始，历时十二年，于1328年11月24日完成。该著作分为六卷，其中第五卷涉及天文学。天文学部分应教皇克莱门特六世的要求于1340年被翻译成拉丁语，但该译本包含了热尔松后来对著作的修订。我们稍后会看其他几卷，但目前我们对第五卷做一些评论，仅这一卷就包含136节。前20节的希伯来语文本，连同翻译和评论，发表在[8]中。H·W·古根海默在一篇评论中写道：-

这是热尔松任何天文学著作的希伯来文第一版；正如编者所指出的，由于作者对克劳狄乌斯·托勒密持批判态度，他的著作没有找到多少愿意承认读过它的读者（该书在阿维尼翁的教廷被译成拉丁文）。这前20节包含一个总的哲学导论、热尔松的三角学、对他发明的一种用于精确测定角差的仪器（雅各布杆）的构造和使用的描述、关于星盘精确构造的评论以及他发明的改进、随后是确定子午线和恒星位置的实际与理论方法，最后是一个证明：克劳狄乌斯·托勒密的理论不符合事实——既不符合月球的事实（在本轮运动中必须从它的两侧看到它），也不符合行星的事实，以及对替代（偏心圆）理论的初步探索。

因此，热尔松对精确天文仪器的热情源于一种愿望，即确保任何提出的理论模型实际上与观测相符，而观测越精确，理论就越能受到检验。热尔松拒绝克劳狄乌斯·托勒密的体系是一个大胆的举动，而且确实显示了他的性格力量，因为他准备反对这样一个被深深信奉的宇宙标准模型。然而，他意识到克劳狄乌斯·托勒密的模型不符合事实。最重要的是，尽管对本轮和其他校正装置的各种修补总是可以用来校正天体的位置，但它仍然使天体的视大小与观测到的大小相去甚远。例如，根据克劳狄乌斯·托勒密的模型，火星的大小应变化6倍，但热尔松观测到该行星的大小只变化2倍。热尔松在1337年观测了一次日食。在观测到这一事件后，他提出了一个新的太阳理论，并进而通过进一步的观测来检验它。热尔松观测到的另一次食是1335年10月3日的月食。他描述了月球运动的几何模型，并使用暗箱对月球、太阳和行星进行了其他天文观测。José Luis Mancha在评论[25]时写道：-

面对天体现象在物理学与数学描述之间的冲突，[热尔松]拒绝（违背亚里士多德传统）将天文学局限于仅仅是一种预测理论的范围内，并打算（违背大多数托勒密传统）构建一种对天空和天体运动的真实数学表示——而不仅仅是一种可能的表示——同时能够满足观测和自然哲学的要求。

在解释了热尔松拒绝克劳狄乌斯·托勒密的模型之后，我们必须明确，热尔松给出的模型是类似类型的，由48个球层组成。其中一些球层与地球同心，而另一些则不是。热尔松认为这些固体球层被流体层隔开，流体层润滑它们的运动，每个球层由一个非物质的智能推动。他给出了流体层大小的迭代计算，并由此得出对宇宙大小的计算，这与克劳狄乌斯·托勒密的计算有非常显著的差异。例如，对于克劳狄乌斯·托勒密，到恒星天球的距离是20,000个地球半径，而热尔松计算出它是$160 \times 10^{12}$个地球半径。当然，这些信念与真理相去甚远，例如他相信银河位于恒星天球上，并靠反射太阳光而发光。然而，他的月球模型非常有趣，因为他能够消除本轮，并得出一个比克劳狄乌斯·托勒密的模型更符合观测的模型，见[28]和[29]。第五卷的第99章包含为1320年奥兰治子午线制作的天文表。

尽管花了一些时间考虑热尔松的数学和天文学贡献，我们还没有提到他工作的主体，即哲学和宗教研究；他写了许多复杂的圣经注释。重要的是要认识到，热尔松的科学工作常常与犹太教冲突。他在The Wars of the Lord的序言中写道，使我们对他在此类冲突上的观点毫不怀疑：-

律法不能阻止我们认为我们的理性促使我们相信的东西是真实的。

我们承诺过要多谈一点The Wars of the Lord。事实上，这部著作的六卷旨在考察六个哲学问题：灵魂的不朽；预言；上帝的全知；神圣的天意；天球的本质；以及物质的永恒性。这六个问题分别在六卷中各考察一个，首先讨论早期哲学家的观点，特别是亚里士多德。在讨论灵魂不朽时，热尔松考察了物质理智，他认为物质理智与人生俱来但仅具有潜在存在，而获得性理智则通过获得的概念和观念达到有效存在。热尔松论证说，获得性理智不会随身体的死亡而消失，从而实现不朽。关于预言，热尔松考虑它是否可能，并强烈主张它是可能的。对于像热尔松这样相信占星术的人来说，这样的结论是不可避免的。第三卷的主题，上帝的全知，是哲学家们长期争论的话题，热尔松给出了他自己的观点[56]：-

他说，上帝崇高的思想包容一切宇宙法则，这些法则调节着自然的演化、天体对月下世界的一般影响，以及物质被赋予的特定本质；但月下事件，即现象世界的纷繁细节，却隐藏在他的精神之外。然而，不知道这些细节并非不完美，因为在认识事物的普遍条件时，他知道个体中本质的、因而也是善的东西。

关于神圣的天意，热尔松得出结论：有些人受一般天意的保护和引导，而另一些人则处于个体天意之下。我们已经相当详细地考察了第五卷，即热尔松的天文学理论，因此还需评论讨论创世和奇迹的第六卷。关于创世，他反对“从无中生有”的理论，转而主张“无形式的、无属性的惰性未定物质”一直存在。这实际上是潜在的物质，在上帝瞬间的创世行为中被赋予形式和存在。他关于奇迹的论证很有趣，因为他声称奇迹存在，但既不是由于上帝，也不是由于先知。他论证说，它们是主动理智的结果。但奇迹有其自身的局限：它们不能改变自然法则；它们不能产生矛盾；它们不能影响天球的运动。

让我们引用Tamar Rudavsky的结论[53]来结束这篇传记：-

热尔松的哲学思想与犹太传统思想格格不入。热尔松反映了以下特征：首先，他的著作展示了占星术信仰与神学信仰之间根本的相互作用与和谐。显然，占星术的吸引力在于它提供了有用的信息，同时它看起来和运作起来像一门科学。……热尔松相信地球上的生命有意义，地球上的事件有秩序。占星术是确定这种意义的一种手段。热尔松关于预言、天意、自由意志和恶的观点反映了这种哲学决定论的成分。尽管他的评注在犹太神学中占据核心地位，但他的哲学著作却被拒绝。……直到近年来，热尔松才在哲学史上获得了应有的地位。随着学者们重新发现他的思想，并使他的著作集为现代读者所利用，热尔松再次被赞赏为一位富有洞见、始终如一的哲学家。

Levi ben Gerson is known by a large number of different names. Other than Levi ben Gerson, the commonest seem to be Gersonides and Levi ben Gershon. However, others refer to him as Levi ben Gershom, and less commonly as Gersoni, Leo de Bagnols, Leo de Balneolis, Leo Judaeus, Leo Hebraeus , or by the acronym Ralbag. The large number of references attached to this article testify to the large number of studies by historians. Yet little is known of his life and what some historians claim as certain, is sometimes disputed by others. The 'facts' we give here are, therefore, simply those which are believed by the majority. Levi ben Gerson certainly came from a family of outstanding scholars. His father was Gershon ben Solomon, a scholar who wrote Sha'ar ha-Shamayim. Levi states that his grandfather was Levi ha-Kohen, and it is believed that he was his mother's father. Levi was also closely related to Nahmanides (1194-1270) who was a Spanish scholar, a rabbi and Jewish religious leader who is known for his work on philosophy, poetry, and medicine. Levi was a cousin of Judah Delesfils whose grandson was Simon ben Zemah Duran (1361-1444), a Spanish Jewish rabbi who wrote several famous works.

We know that Levi ben Gerson lived in Orange, a town which today is in France but this was not so when he lived there. This is, in fact, quite significant, for the king of France at the time Levi was born was Philip IV, known as Philip the Fair. He expelled the Jews from France in 1306 seizing their property and confiscating all money owed to them, but Levi was not affected. However, even in Provence Jews had a difficult time and Levi wrote in Preface to Milhamot (1329) that the suffering of the Jews:-

... are so intense that they render meditation impossible.

The period 1309-1377 is that of the Roman Catholic papacy in Avignon and these popes had quite good relations with the Jews. Levi certainly had good relations with leading men of the district, both Jewish and Christian. He dedicated one of his works to Pope Clement VI, one of the Avignon popes, and another work was requested by Philip of Vitry, Bishop of Meaux. Yet another of his works was written at the request of a group of Jewish and Christian noblemen. As is already evident from what we have just written, what little information we have about Levi comes from his works. Sadly, these contain very little information about his life. Similarly, there are mentions of him in the writings of others during his lifetime, but again little can be gleaned about his life. For example Isaac de Lattes writes in the Preface to one of his works:-

The great prince, our master Levi ben Gershon, was the author of many valuable works. He wrote a commentary on the Bible and the Talmud; and in all branches of science, especially in logic, physics, metaphysics, mathematics, and medicine, he has no equal on earth.

This leads naturally to two questions. How did Levi ben Gerson become an expert in so many subjects? How did he make a living? Neither question can be answered with any certainty, but we can say a little. For example, given the family of scholars he came from, it is almost certain that he received training in religious matters by family members. There is no evidence where he could have received a scientific training, however, so many experts believe that he was self-taught in these topics. As to his profession, the most common theory is that he made a living from his medical expertise, but other theories suggest that he made money from money lending, or astrology, or that he was of independent means and did not need to earn a living. One might expect that someone expert in so many areas would read the languages of the day with ease but this appears not to be the case. He spoke Provençal but wrote all his works in Hebrew. This may at first look unlikely since only Latin versions of many of his works survive. However, these are translations, the original Hebrew text being lost. He certainly refers to Latin as the "language of Christians," and almost all historians believe that he could not read Latin. Whenever he quotes from Latin works by authors such as Aristotle, he always gives the quotation in Hebrew. Similarly, it is believed that he could not read Arabic, so had to read the works of the Arabic scholars in Hebrew translations. These deductions clearly have some bearing on his education. The only other (almost certain) fact about his life is that he married the sister of Judah Delesfils, whom we mentioned above, so was distantly related to his wife; no record exists of any children from the marriage. We now look at Levi's works.

First we examine his contributions to mathematics. He wrote Art of Calculation (or Art of the Computer) in 1321, which is sometimes incorrectly described as the Book of Number. It deals with arithmetical operations, including extraction of square roots and cube roots. In this work he also looks at the summation of series, permutations and combinations, and basic algebraic identities. He gives formulas for the sum of squares and the sum of cubes of natural numbers as well as studying the binomial coefficients. In proofs, he uses induction making this one of the earliest texts to use this important technique. In [57] and [58], Shai Simonson publishes the problems from this remarkable work by Levi. In fact, it is the Art of Calculation which allows us to give the year of Levi's birth, since he says he finished writing it in 1321, when he was thirty-three years old.

In 1342, at the request of the bishop of Meaux, he wrote The Harmony of Numbers which contains a proof that (1,2), (2,3), (3,4) and (8,9) are the only pairs of consecutive numbers whose only factors are 2 or 3. One year later, he wrote On Sines, Chords and Arcs which examined trigonometry, in particular proving the sine theorem for plane triangles and giving 5 figure sine tables. He calculated his sine tables using Ptolemy's methods and his tables are very accurate. In this work he studied chords, sines, versed sines, cosines but not tangents (which were not in use at this time). Gino Loria suggested that the sine theorem be named after Levi but he was not the first to present the theorem, which was known to Jabir ibn Aflah in the 12th century, but he may have rediscovered it. He also published two geometry books, one being a commentary and introduction to the first five books of Euclid, but not presented axiomatically. The other is the Science of Geometry of which only a fragment has survived. It is interesting to note that Levi was interested in Euclid's parallel postulate and appears to have been part of a lively debate about whether it could be deduced from the other axioms. He proved the parallel postulate with an argument based on an assumption on the convergence or divergence of straight lines that is (as of course it must be) equivalent to the parallel postulate; see [43] for further details.

We now look at some of Levi's contributions to astronomy. One of these is associated with astronomical instruments. He invented Jacob's staff, an instrument to measure the angular distance between celestial objects. We should note that the term 'Jacob's staff' was not used by Levi but rather by his Christian contemporaries; he used a Hebrew name which translates as 'Revealer of Profundities'. It is described as consisting:-

... of a staff of $4{1\over2}$ feet long and about one inch wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars.

This was far from his only contribution to improvements in astronomical instruments. In [23] Bernard Goldstein looks at Levi's various innovations in instrument design. A striking example is the design of a transversal scale for reading fifteenths of degrees on the graduated outer circle of an astrolabe. We note that, remarkably, it was around 250 years later that Tycho Brahe used a similar transversal scale on his great mural quadrant. Goldstein also, in an appendix to [23], examines Levi's transversal scale for the Jacob staff. We note that while Levi's method for constructing the scale is theoretically correct, it requires making measurements that seem extremely difficult, so perhaps the theory was never put into practice.

These instruments are described in the astronomical part of Levi's major work The Wars of the Lord which took him twelve years to compose beginning in 1317 and finishing on 24 November 1328. The work is divided into six books, with the fifth of these dealing with astronomy. The astronomy part was translated into Latin at the request of Pope Clement VI in 1340 but this translation includes later revisions of the work by Levi. We will look later at some of the other books but for the moment we make some comments on Book V which alone contains 136 sections. The Hebrew text, with translation and commentary, of the first 20 sections is published in [8]. H W Guggenheimer writes in a review:-

This is the first edition of any of Levi's astronomical writings in Hebrew; as the editor points out, because of the author's critical attitude towards Ptolemy his work did not find many readers who were willing to acknowledge that they had read it (which was translated into Latin at the papal court of Avignon). These first 20 sections contain a general philosophical introduction, Levi ben Gerson's trigonometry, a description of the construction and use of an instrument invented by him (the Jacob staff) for exact determination of angular differences, remarks about the exact construction of the astrolabe and improvements invented by him, followed by practical and theoretical methods for the determination of the meridian and the position of stars and, finally, a proof that Ptolemy's theory does not account for the facts - neither for the moon (which in an epicycle motion would have to be seen from both its sides) nor for the planets, and a preliminary exploration of alternative (excentric circle) theories.

So Levi's passion for accurate astronomical instruments came from a desire to make sure that any proposed theoretical model was actually in accord with observation, and the more accurate the observation, the better a theory could be put to the test. It was a bold move by Levi to reject Ptolemy's system and certainly shows his strength of character that he was prepared to argue against such a deeply held standard model of the universe. However, he realised that Ptolemy's model does not match the facts. Most importantly, although various tinkerings with epicycles and other corrective devices could always be used to correct the position of the heavenly objects, it still left the apparent size of the objects far from that which was observed. For example, according to Ptolemy's model the size of Mars should vary by a factor of 6 but Levi observed only a factor of 2 in the size of the planet. Levi observed a solar eclipse in 1337. After he had observed this event he proposed a new theory of the Sun, which he proceeded to test by further observations. Another eclipse observed by Levi was the eclipse of the Moon on 3 October 1335. He described a geometrical model for the motion of the Moon and made other astronomical observations of the Moon, Sun and planets using a camera obscura. José Luis Mancha, reviewing [25] writes:-

Faced with the conflict between physical and mathematical accounts of celestial phenomena, [Levi] rejected (against Aristotelian tradition) the confinement of astronomy within the limits of a merely predictive theory, and intended (against most of the Ptolemaic tradition) to construct a true mathematical representation - not only a possible one - of the heavens and the motions of the heavenly bodies, being able to satisfy at the same time the requirements of observation and natural philosophy.

Having explained that Levi rejected Ptolemy's model, we must make it clear that the model which Levi gives is of a similar type consisting of 48 spheres. Some of these spheres are concentric with the Earth, while others are not. Levi considers that these solid spheres are separated by layers of fluid that lubricate their motions, each sphere being moved by an immaterial intelligence. He gives an iterative calculation for the size of the fluid layer and is led to a calculation of the size of the universe which differs very significantly from Ptolemy's. For example, for Ptolemy the distance to the sphere of fixed stars is 20,000 Earth radii, while Levi calculates it to be $160 \times 10^{12}$ Earth radii. Of course these beliefs were well wide of the truth such as his belief that the Milky Way was on the sphere of the fixed stars and shines by the reflected light of the Sun. His lunar model, however, is very interesting for he was able to eliminate epicycles and come up with a model which agreed with observation much better than that of Ptolemy, see [28] and [29]. The 99th chapter of Book V consists of astronomical tables made for the meridian of Orange in 1320.

Despite spending some time on considering Levi's mathematical and astronomical contributions, we have not yet mentioned the bulk of his work which was on philosophy and religious studies; he wrote many complex Biblical commentaries. It is important to realise that Levi's scientific work was often in conflict with Judaism. He leaves us in no doubt as to his views on such conflicts writing in the Preface to The Wars of the Lord:-

The Law cannot prevent us from considering to be true that which our reason urges us to believe.

We promised to say a little more about The Wars of the Lord. In fact the six books of this work are designed to examine six philosophical questions: the immortality of the soul; prophecy; God's omniscience; divine providence; the nature of the celestial spheres; and the eternity of matter. These six questions are examined, one in each of the six books, beginning with a discussion of the views of earlier philosophers, in particular Aristotle. In his discussion of the immortality of the soul, Levi examines the material intellect, which he believes is born with man but only has potential existence, but acquired intellect reaches an effective existence by acquired ideas and conceptions. The acquired intellect, Levi argues, does not cease to exist with the death of the body, so achieving immortality. On prophecy, Levi considers whether it is possible and argues strongly that it is. For anyone like Levi who believes in astrology, such a conclusion is inevitable. The topic of the third book, God's omniscience, was a subject debated at length by philosophers and Levi gives his own views [56]:-

The sublime thought of God, he says, embraces all the cosmic laws which regulate the evolutions of nature, the general influences exercised by the celestial bodies on the sublunary world, and the specific essences with which matter is invested; but sublunary events, the multifarious details of the phenomenal world, are hidden from His spirit. Not to know these details, however, is not imperfection, because in knowing the universal conditions of things, He knows that which is essential, and consequently good, in the individual.

On divine providence, Levi reaches the conclusion that some are protected and guided by general providence while others are under an individual providence. We have looked in some detail at Book V, Levi's astronomical theories, so it remains to comment on Book VI which discusses creation and miracles. On creation, he argues against the 'ex nihilo' theory, arguing instead that 'inert undetermined matter, devoid of form and attribute' had existed for all time. This was really potential matter brought into form and being in an instant act of creation by God. His argument regarding miracles is interesting, for he claims that they exist but are neither due to God nor to prophets. They are the result, he argues, of the active intellect. But miracles have their own limitations: they cannot alter the laws of nature; they cannot produce a contradiction; and they cannot affect the motion of the celestial spheres.

Let us end this biography by quoting from Tamar Rudavsky's conclusion [53]:-

Gersonides' philosophical ideas went against the grain of traditional Jewish thought. Gersonides reflects the following characteristics: first, his writings demonstrate a fundamental interplay and harmony between astrological and theological beliefs. It is clear that the appeal of astrology lay in the fact that it offered useful information, while it looked and operated like a science. ... Gersonides believed that life on earth had a meaning, and that terrestrial events had an order. Astrology was a means of ascertaining that meaning. Gersonides' views on prophecy, providence, free-will and evil reflected ingredients of this philosophical determinism. Whereas his commentaries occupied a central place in Jewish theology, his philosophical work was rejected. .... Only in recent years has Gersonides received his rightful place in the history of philosophy. As scholars have rediscovered his thought and have made his corpus available to a modern audience, Gersonides is once again appreciated as an insightful, ruthlessly consistent philosopher.