Averroes is the third and final Muslim philosopher on the reading list. Averroes is best contrasted with his predecessor Avicenna rather than Ghazali; both Averroes and Avicenna were Aristoteleans, while Ghazali was highly critical of the Aristoteleans on religious grounds. Where Averroes and Avicenna differed most noticeably was over the philosophical status of Islam -- though I can't recall how this difference went, and it's not going to be on the exam anyways.
For our purposes, we care only about Averroes' revisions to the Aristotelean understanding of the structure of the intellect. As discussed in the capsule on De anima, Aristotle has a model of cognition on which the intellect functions in almost exactly the same way as the sense organs, passively receiving the 'intelligible' (as opposed to material or sensible) forms.
Averroes, in his commentary, clarifies by positing at least two aspects to the intellect, the agent and material. The material intellect corresponds to the passive sense organs, while the agent intellect actualizes the imaginative forms qua intelligibles so that they can be imposed on the material intellect. That last, rather spectacular, bit is almost verbatim. This is supposed to work something like the sun illuminating an object for sight: the sun actualizes the object qua sensible (in particular, coloured), so that its sensible form can be imposed on the eye.
Things get even more fun when Averroes goes on to argue that the material intellect is numerical identical among all rational beings. That is, we all share the same material intellect. Averroes recognizes, at two distinct places, that this immediately leads to the objection that we have different thoughts. As near as I can tell, Averroes' solution is that
the conjunction of the intelligibles with us human beings takes place through the conjunction of the intelligible forms (and they are the imaginative forms) with us, that is, through that part which is in us in respect to them in some way like a form.
Of course, it's the last clause which is absolutely critical, and which someone (whether Averroes or the translator) has completely garbled. Dumont also has no explanatory notes on this aspect of Averroes' thought. Hyman and Walsh give only a single sentence: "Knowledge becomes particular through phantasms which accompany it in the imagination of everyone who knows." This seems to indicate that the only aspect of one's mind that is numerically distinct from anyone else's mind is the imagination, but I'm not really sure.
Maimonides, from Guide of the perplexed
Like the reading from City of God, I do not consider this philosophy, strictly speaking. Maimonides deals with two issues in these selections: predication of God, and the eternality of the world, and the arguments in both section are primarily theological. Thus, concerning predication, Maimonides argues that it is improper to predicate anything of God other than negations and actions. For example, the sentence 'God exists necessarily' is only legitimate if it is understood as a paraphrase for 'God's non-existence is impossible'; or 'God is incorporeal' must mean 'God is not a body'. On the other hand, 'God is just' is acceptable, even as an affirmative, as it describes an action. Maimonides argues for this based on God's radical simplicity: because of this simplicity, God does not have components for a definition that can be broken down into essential predication; nor can God be 'accessorized' with accidents; nor can God, properly speaking, stand in any relation to creatures, as that would be a category error.
I'm sure Maimonides has some philosophical insights to offer -- the Guide was all about bringing Aristoteleanism and Judaism together -- and he obviously inspired Aquinas (he'll answer Maimonides on this point in the first reading), but it's hard to see how intricate arguments based on God's simplicity have compelling philosophical content for non-theists.
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Interesting philosophical link: Carnivores on the run!