heart of the wise; Re: A Deep Sense of Miserable Ignorance
John Baez has given us the classic Taoist tale of ignorance (monks, brige, fish). A Christian nugget is:
“The heart of the wise inclines to the right, but the heart of the fool to the left.”
[Ecclesiastes 10:2]
See also the special 125th anniversary issue of Nature:
FRONTIERS OF IGNORANCE
Nature 372, November 2002
As a result of that issue, I taught several hundred senior citizens a course entitled “The Frontiers of Ignorance.”
In teaching Astronomy, Biology, Computer Science, Mathematics, and many other subjects I am again and again startled by penetrating questions from students that clarify for me that something which I thought I understood, I didn’t understand well enough.
Cf. Thomas Kuhn’s “Structure of Scientific Revolution” – which, agree or disagee, changed the dialogue on the subject. David Corfield knows this better than I.
For that matter, attention to the most deeply buried footnotes in science journals make it clear that good scientists admit that their work is on the frontiers of ignorance. Much of what was in textbooks when I was a boy is sinply untrue today. And tomorrow…?
De Sousa on “Darwin’s Doubt” and Plantinga; mRe: A Deep Sense of Miserable Ignorance
The question of how ignorant we are is coupled to the question of whether Mathematics is a social contruct. Recent debate on this harks back to Darwin’s comments.
Darwin on My Mind
Literary Review of Canada
Volume 16, Number 2
March 2008
Pages 20-21
Darwin on My Mind
Evolutionary theory best explains how—and why—we reason.
A REVIEW
by Michael Ruse
Why Think? Evolution and the Rational Mind
Ronald de Sousa
Oxford University Press
194 pages, hardcover
ISBN 9780195189858
Everything we believe about evolution could be false. And this is obviously to reduce Darwinian epistemology to a reductio ad absurdum. If our theory of knowledge embraces indifferently the true and the false, so long as it is expedient, we are in deep trouble. Plantinga calls this “Darwin’s Doubt,” because it was even expressed by a worried Darwin himself, in correspondence written toward the end of his life: “With me the horrid doubt always arises whether the convictions of man’s mind, which has been developed from the mind of the lower animals, are of any value or are at all trustworthy. Would anyone trust in the convictions of a monkey’s mind, if there are any convictions in such a mind?” (As a matter of fact, Darwin immediately excused himself as a reliable authority on such philosophical questions, but Plantinga leaves this somewhat awkward point unmentioned.)
De Sousa has a two-part response to this criticism. First, he argues that our mathematical abilities cannot be the result of natural selection. “On the evolutionary scale, mathematics is part of our present rather than of our evolutionary past. It is therefore out of the question for mathematical talent as such to have been a factor in evolution by natural selection.” Then he goes on to say:
“Once mathematics had emerged into the light of day, there was still nothing to guarantee that it could prove useful outside the domains in which our practical skills had already been operating for millennia. And yet, pure mathematics notoriously finds all kinds of startling applications in the solution of technological and scientific problems that our ancestors could not possibly have conceived of, and it does so by generating theories that would have remained wholly unintelligible to them. That strongly supports the idea that mathematics can uncover aspects of the universe of which neither the usefulness nor even the existence could possibly have been manifested in the environment of our evolutionary adaptations (EEA) in which the basic functions of the brain were being shaped by natural selection. As [Eugene] Wigner has argued, this constitutes at least prima facie evidence for the conclusion that the truths of mathematics do not merely reflect projective constructions of our brains, but probably correspond to an objective reality.”
I am not sure about either of these steps. It is true that an ability for calculus was not needed in the jungle or the move out onto the plains—students of human evolution think that the key break from the chimps occurred about five million years ago when our ancestors came down from the trees and out into the open—but this is not to say that the components of reasoning abilities were not produced by selection. There are good biological reasons why humans have innate abilities at counting, working with sets, geometrical understanding, and so forth. It is true that these rather modest talents then need to be put together, but that is what education is all about.
In any case, I agree that the power of mathematics is pretty impressive. Let me correct that—incredibly impressive. And I agree it is hard to see how it works so well if it is not true. But I am not sure that this will meet Plantinga’s criticism. He argues that even if we discount the known ways that selection misleads us (I guess if he had heard of it, he would put the Wason experiment in here), it could be that selection is systematically misleading us all of the way. In a sense, his argument is a version of that used by Descartes in the Meditations—we think we are on safe ground against skepticism when we turn to mathematics, but an evil demon could be misleading us systematically about even that. You, silly person, think that 2+2=4 and that Stephen Harper has your best interests at heart, but—who knows?—a malevolent god could be deceiving you….”
Re: A Deep Sense of Miserable Ignorance
Here a nice collection of Christian Siebeneicher on how arithmetics was teached long ago. If subconscious attidudes influence teaching, here an article on how to detect such attitudes.