"If the axioms are true, and the subsequent reasoning is sound, then the conclusion is irrefutable. What we now have is a proof: something we can know for sure."
... if the axioms are true. We still don't know for sure absolutely.
"The idea of self-evident truths goes all the way back to Euclid’s “Elements” (ca. 300 B.C.), which depends on a handful of axioms—things that must be granted true at the outset, such as that one can draw a straight line between any two points on a plane."
Strictly speaking, Euclid does not state axioms. He starts with 23 Definitions, 5 Postulates and 5 Common Notions. Drawing a straight line from any point to any point is stated as Postulate 1.
... if the axioms are true. We still don't know for sure absolutely.
"The idea of self-evident truths goes all the way back to Euclid’s “Elements” (ca. 300 B.C.), which depends on a handful of axioms—things that must be granted true at the outset, such as that one can draw a straight line between any two points on a plane."
Strictly speaking, Euclid does not state axioms. He starts with 23 Definitions, 5 Postulates and 5 Common Notions. Drawing a straight line from any point to any point is stated as Postulate 1.
I realize this is a newspaper article.