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
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
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
“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
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
“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
“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
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
“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
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
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
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
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
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
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
