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No man is obliged to be what he might have been.
David Berlinski / Educator
Men
Has Beens
Might
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Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.
David Berlinski / Educator
Graffiti
Legacy
Logic
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However good an argument in philosophy may happen to be, it is generally not good enough.
David Berlinski / Educator
May
Not Good Enough
Philosophy
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In the end, every scheme and every science is justified by itself or it is not justified at all.
David Berlinski / Educator
Science
Ends
Justified
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The calculus is the story this [the Western] world first told itself as it became the modern world.
David Berlinski / Educator
Education
Firsts
Stories
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Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.
David Berlinski / Educator
Logic
Lying
Mathematics
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"Young men wish always to dream of what they have lost." "And old men?" "Of what they have not found."
David Berlinski / Educator
Dream
Men
Discovery
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Although every novel is derived directly from another novel, there is really only one novel, the Quixote.
David Berlinski / Educator
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Darwinism is not a sufficient condition for a phenomenon like Nazism but I think it's certainly a necessary one.
David Berlinski / Educator
Nazism
Phenomenon
Thinking
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Some philosophers see into themselves, and some into their times; still others forge an alliance with the future.
David Berlinski / Educator
Future
Time
Alliances
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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 / Educator
Certain
Community
Doe
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The motion of the mind is conveyed along a cloud of meaning.~ There is this paradox that we get to meaning only when we strip the meaning from symbols.
David Berlinski / Educator
Clouds
Mind
Paradox
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The desire to see and the desire to ratify what one has seen are desires at odds with one another, if only because they proceed from separate places in the imagination.
David Berlinski / Educator
Imagination
Odds
Sight
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No distinction in kind rather than degree between ourselves and the chimps? No distinction? Seriously, folks? Here is a simple operational test: the chimpanzees invariably are the one behind the bars of their cages.
David Berlinski / Educator
Bars
Degrees
Simple
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Validity is the touchstone of inference, and truth of judgment: the fact that vichyssoise is cold ratifies the judgment that vichyssoise is, indeed, cold, and the judgment that vichyssoise is cold expresses the fact that vichyssoise is cold.
David Berlinski / Educator
Cold
Facts
Judgement
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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.
David Berlinski / Educator
Education
Miracle
Moon
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There are gaps in the fossil graveyard, places where there should be intermediate forms, but where there is nothing whatsoever instead. No paleontologist..denies that this is so. It is simply a fact, Darwin's theory and the fossil record are in conflict.
David Berlinski / Educator
Facts
Fossils
Gaps
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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 asked timidly for dreams of wine and ease. Women asked for dreams of love, and men for dreams of women.
David Berlinski / Educator
Dream
Men
Wine
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For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This is a mistake-there is no other word. Where else can the restless human mind find means to tie the infinite in a finite bow?
David Berlinski / Educator
Men
Mean
Mistake
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At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.
David Berlinski / Educator
Science
Achievement
Way
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More than sixty years ago, mathematical logicians, by defining precisely the concept of an algorithm, gave content to the ancient human idea of an effective calculation. Their definitions led to the creation of the digital computer, an interesting example of thought bending matter to its ends.
David Berlinski / Educator
Ideas
Interesting
Years
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For all the great dreams profitlessly invested in the digital computer, it is nonetheless true that not since the framers of the American Constitution took seriously the idea that all men are created equal has an idea so transformed the material conditions of life, the expectations of the race.
David Berlinski / Educator
Dream
Life
Men
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Commentators who today talk of 'The Dark Ages' when faith instead of reason was said to ruthlessly rule, have for their animadversions only the excuse of perfect ignorance. Both Aquinas' intellectual gifts and his religious nature were of a kind that is no longer commonly seen in the Western world.
David Berlinski / Educator
Dark
Ignorance
Religious
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Darwin's theory of evolution is the last of the great nineteenth-century mystery religions. And as we speak it is now following Freudians and Marxism into the Nether regions, and I'm quite sure that Freud, Marx and Darwin are commiserating one with the other in the dark dungeon where discarded gods gather.
David Berlinski / Educator
Dark
Lasts
Theory Of Evolution
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Leibniz endeavored to provide an account of inference and judgment involving the mechanical play of symbols and very little else. The checklists that result are the first of humanity's intellectual artifacts. They express, they explain, and so they ratify a power of the mind. And, of course, they are artifacts in the process of becoming algorithms.
David Berlinski / Educator
Humanity
Intellectual
Play
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Just who has imposed on the suffering human race poison gas, barbed wire, high explosives, experiments in eugenics, the formula for zyklon b, heavy artillery, pseudo-scientific justifications for mass murder, cluster bombs, attack submarines, napalm, intercontinental missiles , military space platforms and nuclear weapons? If memory serves it was not the Vatican.
David Berlinski / Educator
Eugenics
Memories
Military
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At some time in the history of the universe, there were no human minds, and at some time later, there were. Within the blink of a cosmic eye, a universe in which all was chaos and void came to include hunches, beliefs, sentiments, raw sensations, pains, emotions, wishes, ideas, images, inferences, the feel of rubber, Schadenfreude, and the taste of banana ice cream.
David Berlinski / Educator
Eye
Ideas
Pain
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While science has nothing of value to say on the great and aching questions of life, death, love, and meaning, what the religious traditions of mankind have said forms a coherent body of thought... There is recompense for suffering. A principle beyond selfishness is at work in the cosmos. All will be well. 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 / Educator
Community
Religious
Suffering
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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 or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.
David Berlinski / Educator
Assuming
Enough
Steps
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Ultimately, Leibniz argued, there are only two absolutely simple concepts, God and Nothingness. From these, all other concepts may be constructed, the world, and everything within it, arising from some primordial argument between the deity and nothing whatsoever. And then, by some inscrutable incandescent insight, Leibniz came to see that what is crucial in what he had written is the alternation between God and Nothingness. And for this, the numbers 0 and 1 suffice.
David Berlinski / Educator
Numbers
Simple
Two
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Every computer divides itself into its hardware and its software, the machine host to its algorithm, the human being to his mind. It is hardly surprising that men and women have done what computers now do long before computers could do anything at all. The dissociation between mind and matter in men and machines is very striking; it suggests that almost any stable and reliable organization of material objects can execute an algorithm and so come to command some form of intelligence.
David Berlinski / Educator
Men
Long
Organization
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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, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.
David Berlinski / Educator
Eye
Hands
Intuition
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The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.
David Berlinski / Educator
Curves
Numbers
Rest Of Life
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If moral statements are about something, then the universe is not quite as science suggests it is, since physical theories, having said nothing about God, say nothing about right or wrong, good or bad. To admit this would force philosophers to confront the possibility that the physical sciences offer a grossly inadequate view of reality. And since philosophers very much wish to think of themselves as scientists, this would offer them an unattractive choice between changing their allegiances or accepting their irrelevance.
David Berlinski / Educator
Irrelevance
Reality
Thinking
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