The first potential intellect is pure potentiality to know anything; the second potential intellect knows axioms such as "The whole is bigger than the part"; the third has already acquired conclusions through syllogistic reasoning and the intuition of middle terms, but does not consider them at the moment; the "acquired intellect" comes about when the human intellect connects with the active intellect (De anima I.5). This theory exerted a profound influence on scholastic intellect theory, especially in the period from Dominicus Gundisalvi to Albertus Magnus. The scholastics inherited from Avicenna the principal idea that the activity of the human intellect can be differentiated into different phases of gradual development and into different acts of syllogistic reasoning (Hasse 1999 and 2000, 191–200http://plato.stanford.edu/entries/arabic-islamic-influence/#Tra
In the writings of Albertus Magnus, the influence of Avicenna is combined with that of Averroes, who distinguishes two intellects apart from the separate active intellect: the material intellect, which is pure potentiality (and unique, see section 5.4 below) and the speculative intellect, which is the actuality of the grasped intelligible. Averroes and Avicenna both teach that the human and active intellect conjoin in the moment of intellection. Averroes, in particular, claims that a perfect conjunction with the active intellect resulting in God-like knowledge is possible in this life (Comm. magnum De anima III.5 and III.36).
Albertus Magnus, in his early De homine (qu. 56 a. 3), adopts the Avicennian doctrine of three potential intellects in his scholastic reformulation, but in his later works, under the influence of Averroes, transforms it into a theory of intellectual ascension. The highest level of the human intellect is called "acquired intellect" (intellectus adeptus) and results from the conjunction between the potential and the active intellect, both parts of the human soul. In this stage, the intellect is able to grasp all intellectual knowledge, and does not need to have recourse to the senses again. In virtue of this intellect, a human being becomes God-like (De anima 3.3.11). Thomas Aquinas sharply disagrees. The intellect can never dispense with the senses, since it needs the phantasms for conceiving an intellectual form. This is why perfect intellectual knowledge is not possible in this life (Summa theol. Ia q. 84 a. 7).
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