All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
Alfred North WhiteheadRead
Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.
Interpretation
Mathematics began when it transitioned from specific instances to general propositions.
Alfred North Whitehead emphasizes the pivotal moment in the history of mathematics when thinkers started to formulate general rules and theories that applied to abstract entities rather than only specific, tangible examples. This shift allowed mathematics to develop as a rigorous science, abstracting concepts to understand broader truths about the universe.
In practice
This quote can be used in a lecture on the philosophy of mathematics to highlight its evolution.
All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
The vitality of thought is in adventure. Idea's won't keep. Something must be done about them. When the idea is new, its custodians have fervour, live for it, and, if need be, die for it. Their inheritors receive the idea, perhaps now strong and successful, but without inheriting the fervour; so the idea settles down to a comfortable middle age, turns senile, and dies.
The guiding motto in the life of every natural philosopher should be, seek simplicity and distrust it.
As society is now constituted, a literal adherence to the moral precepts scattered throughout the Gospels would mean sudden death.
I consider Christianity to be one of the great disasters of the human race... It would be impossible to imagine anything more un - Christianlike than theology.
Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. "Necessity is the mother of invention" is a silly proverb. "Necessity is the mother of futile dodges" is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.
It {Darwin's theory of evolution] was a concept of such stunning simplicity, but it gave rise, naturally, to all of the infinite and baffling complexity of life. The awe it inspired in me made the awe that people talk about in respect of religious experience seem, frankly, silly beside it. I'd take the awe of understanding over the awe of ignorance any day.
We were staring at the origin of a piece of our own bodies inside this 375-million-year-old fish. We had a fish with a wrist.
To turn Karl [Popper]'s view on its head, it is precisely the abandonment of critical discourse that marks the transition of science. Once a field has made the transition, critical discourse recurs only at moments of crisis when the bases of the field are again in jeopardy. Only when they must choose between competing theories do scientists behave like philosophers.
Some 5 billion years from now, there will be a last perfect day on Earth... then the sun will begin to die, life will be extinguished, the oceans will boil and evaporate away.
Computer science is no more about computers than astronomy is about telescopes.
It is not just that science and technology are possible means of great human satisfaction, as well as a matrix of complex dominations. Cyborg imagery can suggest a way out of the maze of dualisms in which we have explained our bodies and our tools to ourselves.
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