Word: logical
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Dates: during 1990-1999
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...most succinctly, that children don't think like grownups. After thousands of interactions with young people often barely old enough to talk, Piaget began to suspect that behind their cute and seemingly illogical utterances were thought processes that had their own kind of order and their own special logic. Einstein called it a discovery "so simple that only a genius could have thought...
After World War I, Piaget became interested in psychoanalysis. He moved to Zurich, where he attended Carl Jung's lectures, and then to Paris to study logic and abnormal psychology. Working with Theodore Simon in Alfred Binet's child-psychology lab, he noticed that Parisian children of the same age made similar errors on true-false intelligence tests. Fascinated by their reasoning processes, he began to suspect that the key to human knowledge might be discovered by observing how the child's mind develops...
Kurt Godel was born in 1906 in Brunn, then part of the Austro-Hungarian Empire and now part of the Czech Republic, to a father who owned a textile factory and had a fondness for logic and reason and a mother who believed in starting her son's education early. By age 10, Godel was studying math, religion and several languages. By 25 he had produced what many consider the most important result of 20th century mathematics: his famous "incompleteness theorem." Godel's astonishing and disorienting discovery, published in 1931, proved that nearly a century of effort by the world...
...appreciate Godel's theorem, it is crucial to understand how mathematics was perceived at the time. After many centuries of being a typically sloppy human mishmash in which vague intuitions and precise logic coexisted on equal terms, mathematics at the end of the 19th century was finally being shaped up. So-called formal systems were devised (the prime example being Russell and Whitehead's Principia Mathematica) in which theorems, following strict rules of inference, sprout from axioms like limbs from a tree. This process of theorem sprouting had to start somewhere, and that is where the axioms came in: they...
...Alan Turing had done was answer, in the negative, a vexing question in the arcane realm of mathematical logic, few nonspecialists today would have any reason to remember him. But the method Turing used to show that certain propositions in a closed logical system cannot be proved within that system--a corollary to the proof that made Kurt Godel famous--had enormous consequences in the world at large. For what this eccentric young Cambridge don did was to dream up an imaginary machine--a fairly simple typewriter-like contraption capable somehow of scanning, or reading, instructions encoded on a tape...