Philosophy
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?
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Philosophy
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?
- Happy Birthday, Kurt Godel
Today would be the 104th birthday of Kurt Godel, one of the great geniuses of the 20th century. Born in Austria (a part that is now in the Czech Republic), he attended the university in Vienna where began his studies in mathematics. While a mathematical...
- Smartest People You've Never Heard Of (poincare Edition)
I'd been considering an occasional series about fascinating characters from intellectual history that are largely absent from the collective mind and with all of the fuss over the confirmation of the solution of Poincare's conjecture (for a nice...
- Ultimate Dr. Seuss Geek Topic
In The Cat In The Hat Comes Back, the Cat comes returns to visit the brother and sister during the winter-time when they are tasked with shovelling a large amount of snow. The Cat goes into the house and takes a bath, leaving a large ring around the bath...
- Immanuel Kant
(1724-1804) ?Two things fill my mind with ever-increasing wonder and awe, the more often and the more intensely the reflection dwells on them: the starry heavens above me and the moral law within me,? is the statement carved on the gravestone of Kant...
- Logical Positivism: Schlick, Carnap, A. J. Ayer
.Strongly influenced by the Tractatus of Wittgenstein, a group of philosophers in Vienna in 1920s initiated a movement which came to be known as Logical Positivism, and the group of philosophers became famous as the Vienna Circle. The Vienna Circle was...