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CONTENTS
| Ch. | ||
| there must be one principle which acts always alike, and one whose action varies. | ||
| 7. | The eternal mover originates motion by being the primary object of desire (as it is of thought); being thoroughly actual, it cannot change or move; it is a living being, perfect, separate from sensible things, and without parts. | |
| 8 | Besides the first mover there must be as many unmoved movers as there are simple motions involved in the motions of the planets. The number is probably either 49 or 55, As there is but one prime mover, there must be but one heaven. | |
| 9. | The divine thought must be concerned with the most divine object, which is itself. Thought and the object of thought are never different when the object is immaterial. | |
| 10. | ||
| Μ. | ||
| 1. | We pass to immaterial substance. Two kinds of immaterial substances have been believed in, mathematical objects and Ideas, We shall discuss first the former, then the latter, then the view that numbers and Ideas are the substance of sensible things. | |
| 2. | (i) Mathematical objects cannot exist as distinct substances either in or apart from sensible things. | |
| 3. | They can be separated only in thought. Mathematics is not entirely divorced from consideration of the beautiful, as is sometimes
alleged. |
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| 4. | (ii) Arguments which led to the belief in Ideas. Some prove too little, others too much. | |
| 5. | Even if there were Ideas, they would not explain the changes in the sensible world. | |
| 6. | (iii) Various ways in which numbers may be conceived as the substance of things. | |
| 7. | (a) If all units are addible, this gives only mathematical, not ideal number. (b) If all units are inaddible, this gives neither matheatical nor ideal number, (c) If only the units in the same number are addible, this leads to equal difficulties; units must have no difference of kind. | |
| 8. | The views of Platonists who disagree with Plato, and those of the Pythagoreans, lead to equal difficulties. Further objections to ideal numbers: (a) How are the units derived from the indefinite dyad? (b) Is the series of numbers infinite or finite; and if finite, what is its limit? (c) What sort of principle is the one? | |
| 9. | Discussion of the principles of geometrical objects. Criticism of the generation of numbers from unity and plurality, and of spatial | |
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