The teaching of axioms should come after conveying the theory in a looser version.
--
p. 740Ivor Grattan-Guinness
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There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgment and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.
Francis Bacon
In the popular mind, if Hoyle is remembered it is as the prime mover of the discredited Steady State theory of the universe. "Everybody knows" that the rival Big Bang theory won the battle of the cosmologies, but few (not even astronomers) appreciate that the mathematical formalism of the now-favoured version of Big Bang, called inflation, is identical to Hoyle's version of the Steady State model.
Fred Hoyle
In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster.
Ivor Grattan-Guinness
Ethical axioms are founded and tested not very differently from the axioms of science. Truth is what stands the test of experience.
Albert Einstein
Rules necessary for axioms. Not to demand in axioms any but things perfectly evident.
Blaise Pascal
Grattan-Guinness, Ivor
Graves, Robert
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