The worth of Knowledge

[Anymouse]

But the points in-between the measurements on the graph are not empirical, they have been invented and may be completely fallacious.

I hold that if somebody claimed that 'In Euclidean geometry, the internal angles of a triangle add up to 180 degrees', then their claim is 100% true. I have verified it and I know it to be true. There is no element of faith whatsoever.

Your friend Diffidus might argue, however: You have not measured "all" triangles, therefore you cannot know "all" triangles have only 180 degrees of angles, in the manner that to disprove all crows are black, one must only turn up a single white crow.

However, every time you measure another 180 degree triangle, it makes the chance of finding one that is not a little bit smaller. At some point, one can reasonably expect the next one will have 180 degrees, and say with confidence there are none that won't.