Kant and Non-Euclidean Geometry short

# Kant and Non-Euclidean Geometry short - Kant and...

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Kant and Non-Euclidean Geometry

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The mathematical ideal Accept the axioms because they are self- evident. Accept the theorems because they follow from the axioms; they can be deduced by means of logically valid arguments.
Euclid’s five postulates 1. There is exactly one straight line connecting any two points. 2. Every straight line can be continued endlessly. 3. A circle exists with any given center and any given radius. 4. All right angles are equal. 5. The parallel postulate

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The parallel postulate Euclid’s formulation: If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. Playfair’s formulation: Given a line L and a point P not on L, there is exactly one line that passes through P and is parallel to L.
The rise of non-Euclidean geometry The fifth postulate seemed less self-evident to

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## This note was uploaded on 04/23/2008 for the course ARLT 101g taught by Professor Gustafson during the Fall '07 term at USC.

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Kant and Non-Euclidean Geometry short - Kant and...

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