Hans Hahn and Intuition

Today is the birthday of Hans Hahn, the Austian mathematician who, along with his brother-in-law-to-be Otto Neurath, started the Vienna Circle of Logical Positivists. He was a philosophically-minded mathematician at a time when the foundations of math seemed up in the air. Take Euclidean geometry. It is a collection of amazingly intricate theorems derived with absolute deductive rigor (mostly, anyway) from a small set of axioms that seemed beyond doubt. Given any two points, you can draw a line between them. Around any point, you can draw a circle of any radius. Equals added to equals yield equals.

But while these seem obvious, what really justifies belief in them. Kant, whose view held sway at the time, appealed to the intutiion. While Kant had a very technical sense of intuition, the notion does derive from our common usage. The human mind is naturally equipped to just know certain basic things. The foundaitons of mathematics are to be included because they are so self-evident to reason itself. They need no justificaiton, they just are true and we just know them.

In his essay, "The Crisis of Intution" and in a prescient passage in the Vienna Circle's founding manifesto, which Hahn co-wrote with Neurath and Rudolf Carnap, he points out the fallibility of the intutuion and the way we pack aculturated beliefs into it. There is no pure intution (in the common sense) and even if there were, it is not perfect. Hence, we must reject intuition as a source of knowledge.

But is this right? Is the intution trustworthy? If so, when? About factual matters? About ethical matters? In terms of self-knowledge? In artisitc matters? In terms of difficult decisions when the reason is stuck between alternatives? Is an appeal to intuition ever sufficient for belief or action?