"Young men wish always to dream of what they have lost." by David Berlinski

"Young men wish always to dream of what they have lost."

David Berlinski

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Categorized in : Men Discovery Dream

Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

David Berlinski

logic mathematics lying

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

mistake men mean

No man is obliged to be what he might have been. by David Berlinski

No man is obliged to be what he might have been.

David Berlinski

has-beens might men

The calculus is the story this [the Western] world first told its... by David Berlinski

The calculus is the story this [the Western] world first told itself as it became the modern world.

David Berlinski

stories education firsts

In the end, every scheme and every science is justified by itself... by David Berlinski

In the end, every scheme and every science is justified by itself or it is not justified at all.

David Berlinski

justified ends science

Aristotelian logic is massive and marmoreal, but every monument a... by David Berlinski

Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.

David Berlinski

graffiti logic legacy

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

achievement science way

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

paradox mind clouds

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

intuition eye hands

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

miracle moon education

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

cold judgement facts

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

intellectual humanity play

However good an argument in philosophy may happen to be, it is ge... by David Berlinski

However good an argument in philosophy may happen to be, it is generally not good enough.

David Berlinski

not-good-enough may philosophy