The term "Jewish Kalam" is used by modern historians, but is not a term by which Jewish thinkers designated themselves. In all likelihood, they were simply known by the Arabic term Mutakallim?n "Kalamists", as they are referred to by Maimonides and other Jewish writers.
The best known practitioner of Jewish Kalam was Saadia Gaon, and Jewish Kalam represented the philosophical battlefield upon which Saadia attacked the proponents of Karaite Judaism. Maimonides in his The Guide for the Perplexed frequently references and disputes positions of Kalam, both Jewish and Muslim, and in general conveys an opinion of Kalam that is highly uncomplimentary. Judah Halevi also makes reference to Jewish followers of the Kalam, but mentions only Karaite Jews.
Some of the basic principles of the Jewish Kalam are as follow . See also Maimonides's characterization of the principles below.
Maimonides refers repeatedly to the Mutakallim?n (Kalam philosophers) in The Guide for the Perplexed . Some examples of his characterization of Kalamic thought can be found at the end of Book I (Chapters 73-76).
As for that scanty bit of argument (kalam) regarding the notion of the unity of God and regarding what depends on this notion, which you will find in the writings of some Gaonim and in those of the Qaraites, the subject matter of this argument was taken over by them from the Mutakallim?n of Islam and that this bit is very scanty indeed if compared to what Islam has compiled on this subject. Also it has so happened that Islam first began to take this road owing to a certain sect, namely, the Mu?tazila, from whom our co-religionists took over certain things walking upon the road the Mu?tazila had taken. After a certain time another sect arose in Islam, namely, the Ash?ariyya, among whom other opinions arose. You will not find any of these latter opinions among our co-religionists. This was not because they preferred the first opinion to the second, but because it so happened that they had taken over and adopted the first opinion and considered it a matter proven by demonstration-- Maimonides, (Pines 1963)
Maimonides continues in that section to provide a history of Kalamic thought, its sources and subsequent development, and then proceeds to condemn a certain laxity of thought to be found in this philosophical school. In particular, Maimonides takes strong issue with the Kalamic proof of God's existence and unity from the Creation of the World in time. While Maimonides himself does regard the world as having been created ex nihilo (rather than being eternally existing, as Aristotle would have it; see GP, Book II Chapter 25, for example), Maimonides also considers this proposition as being far from obvious, and in all likelihood not susceptible to proof. He thus regards the Kalamic approach as starting from a position of convenience rather than from an irrefutable premise, and their methodology as being entirely tainted by their eagerness to produce certain results which support their prior beliefs.
Additionally he considers their premises to "run counter to the nature of existence that is perceived." He writes that "every one of their premises, with few exceptions, is contradicted by what is perceived of the nature of that which exists, so that doubts come up with regard to them." However, it can be noted below, that in many cases the Kalamists were indeed more prescient than Maimonides himself in their beliefs regarding the discrete nature of matter, existence of vacuum, and other physical characteristics of the natural world.
In Book I Chapter 73, Maimonides presents the 12 premises of the Mutakallim?n, and disputes most of them. The premises are, in brief, as follow:
Not all of these principles were elements of the Jewish Kalam as practiced by particular thinkers. For example, atomism was a principle embraced by earlier Karaite Jews but not by the Geonim or later Karaites. Harry Austryn Wolfson, in his study on the Jewish Kalam, considers it doubtful whether any Jewish thinkers ever embraced the denial of causality.
In Book I Chapter 74, Maimonides reproduces the seven methods by which the Mutakallim?n demonstrate that the world is created in time. In Chapter 75, Maimonides reproduces the five methods by which the Mutakallim?n demonstrate the unity of God. In Chapter 76, Maimonides reproduces the three methods by which the Mutakallim?n demonstrate the incorporeality of God. Needless to say, Maimonides finds most of these methods to be philosophically inadequate and naïve.
Among the personalities associated with the Jewish Kalam are the following, many of whom were Karaites:
Because the composition of written works was yet uncommon at the time that the Jewish Kalam flourished, there are few surviving books from this era. Instead, what we have are selected quotes and paraphrases such as found in Maimonides and Saadia, but mostly we have what Wolfson calls "mere names," individuals who are identified as prominent Kalamic thinkers but who left no evidence of their work or lives. Wolfson provides a list of some of these "mere names." He also suggests that all the Jewish thinkers of this period were likely referred to as Mutakallim?n, as suggested by references from Moses ibn Ezra and others.
Jewish Kalamic thought had influences on many later Jewish philosophers, including Judah Halevi, Joseph ibn Tzaddik, Bahya ibn Paquda, and Maimonides, who criticized it vigorously. Many of the works of the Jewish Kalamists were not translated from Arabic into Mishnaic Hebrew, and so their influence greatly diminished as the Golden Age of Arabic-language Jewish scholarship drew to a close.