An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his… — David Berlinski Copy Share Image
An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms,… — David Berlinski Copy Share Image
In the end, every scheme and every science is justified by itself or it is not justified at all. — David Berlinski Copy Share Image
For all the great dreams profitlessly invested in the digital computer, it is nonetheless true that not since the framers of the American Constitution… — David Berlinski Copy Share Image
The motion of the mind is conveyed along a cloud of meaning.~ There is this paradox that we get to meaning only when we… — David Berlinski Copy Share Image
“The argument that Hawking has offered may be conveyed by question-and-answer, as in the Catholic catechism. A Catechism of Quantum Cosmology Q: From… — David Berlinski Copy Share Image
If moral statements are about something, then the universe is not quite as science suggests it is, since physical theories, having said nothing about… — David Berlinski Copy Share Image
“Before you can ask 'Is Darwinian theory correct or not?', You have to ask the preliminary question 'Is it clear enough so that it… — David Berlinski Copy Share Image
“What Hitler did not believe and what Stalin did not believe and what Mao did not believe and what the SS did not believe… — David Berlinski Copy Share Image
Bystanders wandered in and out of the merchant's stall, passing the time, talking of dreams they might purchase. Workers and slaves stooped from labor… — David Berlinski Copy Share Image
“Whatever the degree to which Darwin may have “misled science into a dead end,” the biologist Shi V. Liu observed in commenting on Koonin’s… — David Berlinski Copy Share Image
No distinction in kind rather than degree between ourselves and the chimps? No distinction? Seriously, folks? Here is a simple operational test: the chimpanzees… — David Berlinski Copy Share Image
The desire to see and the desire to ratify what one has seen are desires at odds with one another, if only because they… — David Berlinski Copy Share Image
Every computer divides itself into its hardware and its software, the machine host to its algorithm, the human being to his mind. It is… — David Berlinski Copy Share Image
I do not know whether any of this is true. I am certain that the scientific community does not know that it is false. — David Berlinski Copy Share Image
For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This… — David Berlinski Copy Share Image
The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the… — David Berlinski Copy Share Image
![“Whatever the degree to which Darwin may have “misled science into a dead end,” the biologist Shi V. Liu observed in commenting on Koonin’s paper, “we may still appreciate the role of Darwin in helping scientists [win an] upper hand in fighting against the creationists.” quote by David Berlinski](https://sms4smile.com/quotes/img-quotes/0de/david-berlinski-16009_dead-end_whatever-the-degree-to-which-darwin-may_342124.jpg)
![“The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon.” quote by David Berlinski](https://sms4smile.com/quotes/img-quotes/340/david-berlinski-16009_calculus_the-definition-of-a-limit-is-essentially_1015218.jpg)