A fairly well-known xtian
"""""In reading early modern philosophy especially, I have grown profoundly sick of being told that the sum of the three angles in a triangle is equal to two right angles. Apparently that's the absolute best example of a mathematically certain truth. I've read it about eight times in the first hundred pages of Hobbes's Leviathan. I don't understand why this is the go-to example......."""""
As anyone who actually finished the first 20 chapters or so of Leviathan realizes, the Leviathan is not a work in analytical philosophy. Indeed one might question whether Hobbes insisted on logical necessity, even in regards to geometry. The section being referred to (e.g. the sum of the angles of any triangle equals 180 degrees/two right triangles) may be found in Ch. IV, and does not concern Euclid: it concerns language, terminology, "the consequences of appellations," and one might say empirical epistemology:
"""""By this imposition of names, some of larger, some of stricter signification, we turn the reckoning of the consequences of things imagined in the mind into a reckoning of the consequences of appellations. For example, a man that hath no use of speech at all, (such as is born and remains perfectly deaf and dumb), if he set before his eyes a triangle, and by it two right angles (such as are the corners of a square figure), he may by meditation compare and find that the three angles of that triangle are equal to those two right angles that stand by it. But if another triangle be shown him different in shape from the former, he cannot know without a new labour whether the three angles of that also be equal to the same. But he that hath the use of words, when he observes that such equality was consequent, not to the length of the sides, nor to any other particular thing in his triangle; but only to this, that the sides were straight, and the angles three, and that that was all, for which he named it a triangle; will boldly conclude universally that such equality of angles is in all triangles whatsoever, and register his invention in these general terms: Every triangle hath its three angles equal to two right angles. And thus the consequence found in one particular comes to be registered and remembered as a universal rule; and discharges our mental reckoning of time and place, and delivers us from all labour of the mind, saving the first; and makes that which was found true here, and now, to be true in all times and places.""""""
Really, one might read this as sort of early constructivism. Hobbes suggests that geometrical knowledge depends on learning terms, as well as perception of the form: the word "triangle" has a precise definition: Every triangle has three angles equal to two right angles. That needn't mean that triangles float in some platonic realm; that's a rule of human thinking which holds for all triangles. One doesn't update the Pythagorean theorem with additional "facts." While not exactly Carnap, Hobbes does hint at positivism.
More importantly, however, is that the example comes from a rather insignificant paragraph in the opening pages of Leviathan. Hobbes, of course, generally occupies himself with political topics (though that politics rests on fairly sound naturalist assumptions). He was not a Gallileo or a Descartes. Writing during the English Civil War, Hobbes wanted to erect a political structure in hopes of preventing revolution and violence: he fears the possibility of "bellum omnium contra omnes", which would be (and often has been) human life without government, a condition Hobbes terms the state of nature. In the state of nature, life tends to be, in Hobbes' famous words, "solitary, poor, nasty, brutish, and short."
That sort of secular thinking does not impress most in the land of blogs. Why bother with a social contract (or Constitution, really), not to say politics based on rational self-interest?: instead, focus on a trivial illustrative example (marginalia, as the snobs say), and then dismiss the entire work. The silly bitch about examples allows one to avoid taking on the raison d'etre of the Leviathan--Hobbes' contracturalism (and his dislike of aristotelian-catholic tradition). The political theory presents far too many difficulties for K-boy, and the naturalist implications (if not a-theistic implications) are rather unnerving; ergo, focus on one minor point, dismiss, and delete any who dissent. That's how PoMo censors operate.