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Avempace, known as "Ibn al-Sa’igh" by Jewish tradition, is rarely recognized for his philosophical and astronomical works that influenced and were employed by many Medieval Jewish philosophers during and after his short life. The first record of Avempace's influence on Jewish philosophy comes from a well-known Jewish contemporary author and philosopher: Judah Halevi. In Chapter 1 of his greatest philosophical work, The Kuzari, Halevi summarizes three ideas directly influenced by works of Ibn Bajja: one's unification with the Active Intellect is attainable during their lifetime, this unification implies cognitive identity with others who are aware of the truth, and a philosopher's life is a solitary regimen. (Pines, S. (1980) “Shi‘ite Terms and Conceptions in Judah Halevi’s Kuzari,” Jerusalem Studies in Arabic and Islam, 2: 165–251.)

The renowned polymath and Jewish philosopher, Maimonides, was possibly born in the same year of Avempace's death, yet he preserved and studied the works of the deceased Andalusian. Maimonides admired Avempace for his achievements, stating that "[Ibn Bajja] was a great and wise philosopher, and all of his works are right and correct". Maimonides also valued Ibn Bajja's commentary on Aristotle's works on astronomy. (Marx, A. (1934–1935) “Texts By and About Maimonides,” The Jewish Quarterly Review (n.s.), 25: 379.)

In one of his three major works, The Guide for the Perplexed, Maimonides assesses Hebrew Bible theology with Aristotelian philosophy, directly drawing influence from Ibn Bajja philosophical and scientific ideas. Specifically incorporating Avempace's philosophies regarding the existence of a single intellect after death, the union of man with the Active Intellect, the division of man into three classes of increasing consciousness, and the proposal of the prophet as an ideal solitary man. (Moses Maimonides (1963) The Guide of the Perplexed, tr. S. Pines, 2 vols. (Chicago: University of Chicago Press).). (Hayoun, M.-R. (1987) “Moses of Narbonne and Ibn Bajja (I): the edition of the Hebrew translation of the Regimen of the Solitary Man (in Hebrew),” Daat, 18: 27–44.)