Against Euclidianism

In a live talk, Michael Huemer describes a regrettable detour in the history of philosophy:

Something unfortunate happened early in the history of philosophy, which is: Philosophers discovered Euclid’s Elements which is this wonderful mathematics book, wonderful book of geometry. People used to have to study it in school in their geometry classes.

It starts with these geometrical axioms and then proves all these geometrical theorems. And it’s very convincing. There are all these things are very convincingly proved, and interesting claims as well that are not obvious before they’re proved.

And philosophers looked at it and said okay so that’s how all human knowledge should be. And then they start thinking that philosophy should be that way and so we’re going to lay down the philosophical axioms and so here are the axioms of ethics, okay?

Well, to burst the philosophers’ bubble, most of human knowledge does not work like Euclid’s Elements. Even geometry doesn’t work like Euclid’s Elements. What actually happened was Euclid’s Elements came thousands of the years after the beginning of geometry.

Geometry started with a series out much more concrete formulas for calculating areas and volumes and perimeters which were mostly empirically derived, or they were guesses are, or things that sort of seemed intuitively right to people.

It started in ancient Egypt. It was mostly for surveying reasons that people needed geometry, they needed to know how much land somebody had.

It was thousands of years after the beginning of geometry that Euclid came along and, having seen all of these little formulas and these little geometrical discoveries, then he tried to systematize it.

Geometry did not start by somebody saying “Well, let’s see , you know, a point is something that has no parts, is indivisible and any two points have a straight line between them…” It started out with all these little formulas and then somebody tried to systematize it.

So now in moral philosophy we are not yet at the stage of somebody being able to write down the axioms, we’re still at the stage of collecting the little formulas. And if somebody tries to set down the axioms before you’ve done sufficient work, before thinking enough about more concrete propositions they are almost certainly going to get it wrong.

– transcribed from Huemer’s talk on his common sense defense of libertarianism.

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