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3 ideas
| 16647 | Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle] |
| Full Idea: In demonstration a definition of the essence is required as starting point, so that definitions which do not enable us to discover the derived properties, or which fail to facilitate even a conjecture about them, must obviously be dialectical and futile. | |
| From: Aristotle (De Anima [c.329 BCE], 402b25) | |
| A reaction: Interesting to see 'dialectical' used as a term of abuse! Illuminating. For scientific essentialism, then, demonstration is filling out the whole story once the essence has been inferred. It is circular, because essence is inferred from accidents. |
| 24048 | Demonstrations move from starting-points to deduced conclusions [Aristotle] |
| Full Idea: Demonstrations are both from a starting-point and have a sort of end, namely the deduction or the conclusion. | |
| From: Aristotle (De Anima [c.329 BCE], 407a25) | |
| A reaction: A starting point has to be a first principle [arché]. It has been observed that Aristotle explains demonstration very carefully, but rarely does it in his writings. |
| 16646 | To understand a triangle summing to two right angles, we need to know the essence of a line [Aristotle] |
| Full Idea: In mathematics it is useful for the understanding of the property of the equality of the interior angles of a triangle to two right angles to know the essential nature of the straight and the curved or of the line and the plane. | |
| From: Aristotle (De Anima [c.329 BCE], 402b18) | |
| A reaction: Although Aristotle was cautious about this, he clearly endorses here the idea that essences play an explanatory role in geometry. The caution is in the word 'useful', rather than 'vital'. How else can we arrive at this result, though? |