Axioms in philosophy are not axioms until they are proved upon our pulses: we read fine things but never feel them to the full until we have gone the same steps as the author.
--
Letter to John Hamilton Reynolds (May 3, 1818).John Keats
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
Rules necessary for axioms. Not to demand in axioms any but things perfectly evident.
Blaise Pascal
Rules for Axioms. I. Not to omit any necessary principle without asking whether it is admittied, however clear and evident it may be. II. Not to demand, in axioms, any but things that are perfectly evident in themselves.
Blaise Pascal
Ethical axioms are founded and tested not very differently from the axioms of science. Truth is what stands the test of experience.
Albert Einstein
I think the first thing that led me toward philosophy (though at that time the word 'philosophy' was still unknown to me) occurred at the age of eleven. My childhood was mainly solitary as my only brother was seven years older than I was. No doubt as a result of much solitude I became rather solemn, with a great deal of time for thinking but not much knowledge for my thoughtfulness to exercise itself upon. I had, though I was not yet aware of it, the pleasure in demonstrations which is typical of the mathematical mind. After I grew up I found others who felt as I did on this matter. My friend G. H. Hardy, who was professor of pure mathematics, enjoyed this pleasure in a very high degree. He told me once that if he could find a proof that I was going to die in five minutes he would of course be sorry to lose me, but this sorrow would be quite outweighed by pleasure in the proof. I entirely sympathized with him and was not at all offended. Before I began the study of geometry somebody had told me that it proved things and this caused me to feel delight when my brother said he would teach it to me. Geometry in those days was still 'Euclid.' My brother began at the beginning with the definitions. These I accepted readily enough. But he came next to the axioms. 'These,' he said, 'can't be proved, but they have to be assumed before the rest can be proved.' At these words my hopes crumbled. I had thought it would be wonderful to find something that one could prove, and then it turned out that this could only be done by means of assumptions of which there was no proof. I looked at my brother with a sort of indignation and said: 'But why should I admit these things if they can't be proved?' He replied, 'Well, if you won't, we can't go on.'
Bertrand Russell
Keats, John
Keble, John
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