Rabbi Levi Ben Gershom, Gersonides -

רלב"ג

Levi ben Gershon, better known by his Latinised name as Gersonides or the abbreviation of first letters as RaLBaG (1288–1344), philosopher, Talmudist, mathematician, astronomer/astrologer. He was born at Bagnols in Languedoc, France. According to Abraham Zacuto and others, he was the son of Gerson ben Solomon Catalan.

Biography

As in the case of the other medieval Jewish philosophers little is known of his life. His family had been distinguished for piety and exegetical skill in Talmud, but though he was known in the Jewish community by commentaries on certain books of the Bible, he never seems to have accepted any rabbinical post. It has been suggested that the uniqueness of his opinions may have put obstacles in the way of his preferment. He is known to have been at Avignon and Orange during his life, and is believed to have died in 1344, though Zacuto asserts that he died at Perpignan in 1370.

Works

Philosophical and religious works

Part of his writings consist of commentaries on the portions of Aristotle then known, or rather of commentaries on the commentaries of Averroes. Some of these are printed in the early Latin editions of Aristotle’s works. His most important treatise, that by which he has a place in the history of philosophy, is entitled Sefer Milhamot Ha-Shem, ("The Wars of the Lord"), and occupied twelve years in composition (1317–1329). A portion of it, containing an elaborate survey of astronomy as known to the Arabs, was translated into Latin in 1342 at the request of Pope Clement VI.

The Wars of the Lord is modeled after the plan of the great work of Jewish philosophy, the Guide for the Perplexed of Maimonides. It may be regarded as a criticism of some elements of Maimonides' syncretism of Aristotelianism and rabbinic Jewish thought. Ralbag's treatise strictly adhered to Aristotelian thought. The Wars of the Lord review:

• 1. the doctrine of the soul, in which Gersonides defends the theory of impersonal reason as mediating between God and man, and explains the formation of the higher reason (or acquired intellect, as it was called) in humanity—his view being thoroughly realist and resembling that of Avicebron;
• 2. prophecy;
• 3. and 4. God's knowledge of facts and providence, in which is advanced the theory that God does not know individual facts. While there is general providence for all, special providence only extends to those whose reason has been enlightened;
• 5. celestial substances, treating of the strange spiritual hierarchy which the Jewish philosophers of the middle ages accepted from the Neoplatonists and the pseudo-Dionysius, and also giving, along with astronomical details, much of astrological theory; and
• 6. creation and miracles, in respect to which Gersonides deviates widely from the position of Maimonides.

Gersonides was also the author of a commentary on the Pentateuch and other exegetical and scientific works.

Views on God and omniscience

In contrast to the theology held by other Jewish thinkers, Jewish theologian Louis Jacobs argues, Gersonides held that God does not have complete foreknowledge of human acts. "Gersonides, bothered by the old question of how God's foreknowledge is compatible with human freedom, holds that what God knows beforehand is all the choices open to each individual. God does not know, however, which choice the individual, in his freedom, will make."

Another neoclassical Jewish proponent of self-limited omniscience was Abraham ibn Daud. "Whereas the earlier Jewish philosophers extended the omniscience of God to include the free acts of man, and had argued that human freedom of decision was not affected by God's foreknowledge of its results, Ibn Daud, evidently following Alexander of Aphrodisias, excludes human action from divine foreknowledge. God, he holds, limited his omniscience even as He limited His omnipotence in regard to human acts".

"The view that God does not have foreknowledge of moral decisions which was advanced by ibn Daud and Gersonides (Levi ben Gershom) is not quite as isolated as Rabbi Bleich indicates, and it enjoys the support of two highly respected Achronim, Rabbi Yeshayahu Horowitz (Shelah haKadosh) and Rabbi Chaim ibn Attar (Or haHayim haKadosh). The former takes the views that God cannot know which moral choices people will make, but this does not impair His perfection. The latter considers that God could know the future if He wished, but deliberately refrains from using this ability in order to avoid the conflict with free will."

Rabbi Isaiah Horowitz explained the apparent paradox of his position by citing the old question, "Can God create a rock so heavy that He cannot pick it up?" He said that we cannot accept free choice as a creation of God's, and simultaneously question its logical compatibility with omnipotence.

Views of the afterlife

Gersonides posits that people's souls are composed of two parts: a material, or human, intellect; and an acquired, or agent, intellect. The material intellect is inherent in every person, and gives people the capacity to understand and learn. This material intellect is mortal, and dies with the body. However, he also posits that the soul also has an acquired intellect. This survives death, and can contain the accumulated knowledge that the person acquired during their lifetime. For Gersonides, Seymour Feldman points out, "Man is immortal insofar as he attains the intellectual perfection that is open to him. This means that man becomes immortal only if and to the extent that he acquires knowledge of what he can in principle know, e.g. mathematics and the natural sciences. This knowledge survives his bodily death and constitutes his immortality."

Works in mathematics and astronomy/astrology

Gersonides wrote Maaseh Hoshev in 1321 dealing with arithmetical operations including extraction of square and cube roots, various algebraic identities, certain sums including sums of consecutive integers, squares, and cubes, binomial coefficients, and simple combinatorial identities. The work is notable for its early use of proof by mathematical induction, and pioneering work in combinatorics. The title Maaseh Hoshev literally means a Work of Calculation, but it is also a pun on a biblical phrase meaning "clever work". Maaseh Hoshev is sometimes mistakenly referred to as Sefer Hamispar (The Book of Number), which is an earlier and less sophisticated work by Rabbi Abraham ben Meir Ibn Ezra (1090–1167). In 1342, Levi wrote On Sines, Chords and Arcs, which examined trigonometry, in particular proving the sine law for plane triangles and giving five-figure sine tables.

One year later, at the request of the bishop of Meaux, he wrote The Harmony of Numbers in which he considers a problem of Philippe de Vitry involving so-called harmonic numbers, which have the form 2m·3n. The problem was to characterize all pairs of harmonic numbers differing by 1. Gersonides proved that there are only four such pairs: (1,2), (2,3), (3,4) and (8,9).

He is also credited to have invented the Jacob's staff, an instrument to measure the angular distance between celestial objects. It is described as consisting -

   …of a staff of 4.5 feet (1.4 m) long and about one inch (2.5 cm) 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.

Levi observed a solar eclipse on March 3, 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.

Some of his 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. Gersonides was also the earliest known mathematician to have used the technique of mathematical induction in a systematic and self-conscious fashion and anticipated Galileo’s error theory.

The lunar crater Rabbi Levi is named after him.

Gersonides believed that astrology was real, and developed a naturalistic, non-supernatural explanation of how it works. Julius Guttman explained that for Gersonides, astrology was:

   founded on the metaphysical doctrine of the dependence of all earthly occurrences upon the heavenly world. The general connection imparted to the prophet by the active intellect is the general order of the astrological constellation. The constellation under which a man is born determines his nature and fate, and constellations as well determine the life span of nations. …The active intellect knows the astrological order, from the most general form of the constellations to their last specification, which in turn contains all of the conditions of occurrence of a particular event. Thus, when a prophet deals with the destiny of a particular person or human group, he receives from the active intellect a knowledge of the order of the constellations, and with sufficient precision to enable him to predict its fate in full detail. …This astrological determinism has only one limitation. The free will of man could shatter the course of action ordained for him by the stars; prophecy could therefore predict the future on the basis of astrological determination only insofar as the free will of man does not break through the determined course of things.

Gersonides is the only astronomer before modern times to have estimated correctly stellar distances. Whereas all other astronomers put the stars on a rotating sphere just beyond the outer planets, Gersonides estimated the distance to the stars to be ten billion times greater, of the order of 100 light-years (in modern units).

Using data he collected from his own observations Gersonides' refuted Ptolemy's model in what the notable physicist Yuval Ne'eman has considered as "one of the most important insights in the history of science, generally missed in telling the story of the transition from epicyclic corrections to the geocentric model to Copernicus' heliocentric model". Ne'eman argued that after Gersonides reviewed Ptolemy's model with its epicycles he realized that it could be checked, by measuring the changes in the apparent brightnesses of Mars and looking for cyclical changes along the conjectured epicycles. These thus ceased being dogma, they were a theory that had to be experimentally verified, "a la Popper". R. Levi developed tools for these measurements, essentially pinholes and the camera obscura.

The results of his observations did not fit Ptolemy's model at all. Gersonides concluded that the model was no good. He tried (unsuccessfully) to improve on it. That challenge was finally answered, of course, by Copernicus three centuries later, but Gersonides was the first and only one to falsify the Alexandrian dogma - the first known instance of modern falsification philosophy. Levi also showed that Ptolemy's model for the Lunar orbit, though reproducing correctly the evolution of the Moon's position, fails completely in predicting the apparent sizes of the Moon in its motion. Unfortunately, there is no evidence that the findings had an impact on later generations of astronomers, even though Gersonides' writings were translated and available.

You state that Gersonides calculated that the stars were 10 billion times farther away from Earth than what Ptolemy claimed, i.e. in the order of 100 light years. This should be about 100,000 light years (107,055 to be more precise).

As the mean radius is about 6,370 km this works out to 127,323,954 km. Gersonides however took it to be more than 159 x 1012. So Gersonides works out to 1.012830 exp19 km. As a light year is 9.4608exp13 km it works out to 107,550 light years, which is indeed very close to 10 billion times as far as Ptolemy's distance.

Talmudic works

• Shaarei Tsedek (published at Leghorn, 1800): a commentary on the thirteen halachic rules of the Tanna, R'Yishmael;
• Mechokek Safun, an interpretation of the aggadic material in the fifth chapter of Tractate Bava Basra;
• A commentary to tractate Berachos; two responsa. Only the first work is extant.

In modern fiction

Gersonides is an important character in the novel The Dream of Scipio by Iain Pears, where he is depicted as the mentor of the protagonist Olivier de Noyen, a non-Jewish poet and intellectual. A (fictional) encounter between Gersonides and Pope Clement VI at Avignon during the Black Death is a major element in the book's plot.

רבי לוי בן גרשון (בר"ת: רלב"ג) (1288 – 1344) היה פרשן המקרא, איש אשכולות, מדען, רופא, מתמטיקאי, ומחשובי הפילוסופים היהודיים. פעל בחבל פרובאנס שבדרום צרפת

רלב"ג היה בקי במתמטיקה ובאסטרונומיה. הוא פיתח שני מכשירי תצפית אסטרונומיים משוכללים, ובשל כך זכה לשם בין מלומדי דורו. עניינו באסטרונומיה השפיע רבות על הפילוסופיה שלו. היו לו תרומות גם בתחום המתמטיקה. מחקריו באסטרונומיה זכו להערכה רבה ותורגמו ללטינית בפקודת האפיפיור קלמנס השישי, וכן קרוי על שמו מכתש בירח - המכתש Rabbi Levi. בספרו "מעשה חושב" (1321), הוכיח משפטים שונים בקומבינטוריקה, בהם חישוב מספר הצירופים והתמורות, ואף כתב הוכחות באינדוקציה מתמטית.

בשיטתו הפילוסופית הולך רלב"ג אחרי הרמב"ם ואריסטו, אך גם חולק עליהם בחריפות (למשל, הוא מבטל מכל וכל את תורת שלילת התארים המיימונית) ומעלה שורה של רעיונות מקוריים, חלקם יוצאי דופן במחשבה היהודית.