A quote from Euler

Yesterday I paid tribute here to a great mathematician. Today I offer a quote from him.

"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as there are usually believed to be."

The significance of that observation may not be obvious outside of some consideration of the history of math, the development of calculus in particular. But once we do a little grappling with that history, we see that Euler is making a point here that takes us back to ancient Greece. Back to Zeno, Achilles and tortoise. If Achilles is to catch up with the tortoise here must be a moment at which the difference between them is zero. One way of looking at the problem is to ask what is the next lower number -- one really really close to zero but still a positive number!

Euler here is saying "That is the wrong way of looking at it." Or, "don't create mysteries beyond necessity."

Comments

Searle: The Chinese Room

John Searle has become the object of accusations of improper conduct. These accusations even have some people in the world of academic philosophy saying that instructors in that world should try to avoid teaching Searle's views. That is an odd contention, and has given rise to heated exchanges in certain corners of the blogosphere. At Leiter Reports, I encountered a comment from someone describing himself as "grad student drop out." GSDO said: " This is a side question (and not at all an attempt to answer the question BL posed): How important is John Searle's work? Are people still working on speech act theory or is that just another dead end in the history of 20th century philosophy? My impression is that his reputation is somewhat inflated from all of his speaking engagements and NYRoB reviews. The Chinese room argument is a classic, but is there much more to his work than that?" I took it upon myself to answer that on LR. But here I'll tak...

A Story About Coleridge

This is a quote from a memoir by Dorothy Wordsworth, reflecting on a trip she took with two famous poets, her brother, William Wordsworth, and their similarly gifted companion, Samuel Taylor Coleridge. We sat upon a bench, placed for the sake of one of these views, whence we looked down upon the waterfall, and over the open country ... A lady and gentleman, more expeditious tourists than ourselves, came to the spot; they left us at the seat, and we found them again at another station above the Falls. Coleridge, who is always good-natured enough to enter into conversation with anybody whom he meets in his way, began to talk with the gentleman, who observed that it was a majestic waterfall. Coleridge was delighted with the accuracy of the epithet, particularly as he had been settling in his own mind the precise meaning of the words grand, majestic, sublime, etc., and had discussed the subject with William at some length the day before. “Yes, sir,” says Coleridge, “it is a maj...

A Quote from Parfit

Recently I wrote a little about ethicist Derek Parfit. I've been doing further research on him since, and will now describe his Big Picture as I've come to understand it. Parfit believes that the western world only started taking ethical philosophy seriously (as a domain separate from theology) around the time Nietzsche declared that God was dead. There are only three possibilities, in terms of the God/morality issue: 1) You believe that God exists and that His commands define morality 2) You deny that God exists and, like Nietzsche, infer from this that in the absence of commands there is no right or wrong, or 3) You deny that God exists yet persist in believing and attempting to discern right and wrong. From a certain point of view there could be a fourth category, for people who believe that God exists but that His existence is irrelevant to morality, He doesn't issue commands at all, etc. Still, from DP's perspective that sort of God ...

Jamesian Philosophy Refreshed

Search This Blog