What is Geometry? Is it True? Why is it Important?
It is oddly hard to think of true statements once you allow doubt to play a role. What could another person say to you that you would absolutely have to believe? Statements people make about themselves are surely not acceptable (any follower of detective fiction will know that that is hopeless). The weather? The date? Are you sure you haven’t been hoodwinked, kidnapped, drugged? If we decide to cut these speculations short of paranoia and allow a reasonable degree of interaction with the world in good faith, we enter an old and vexed distinction between certain and merely probable knowledge. Merely probable knowledge was once known as scientia, the word from which science derives, and it had an aspect of unreliability about it. Today, statements of science are among the most highly regarded (and may well figure in any answer to the opening question).
KeywordsEuclidean Geometry Projective Geometry Axiom System Relative Consistency Pure Logic
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