Single Idea 16646

[catalogued under 14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence]

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.

Gist of Idea

To understand a triangle summing to two right angles, we need to know the essence of a line

Source

Aristotle (De Anima [c.329 BCE], 402b18)

Book Reference

Aristotle: 'The Basic Works of Aristotle', ed/tr. McKeon,Richard [Modern Library Classics 2001], p.536


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?