A Quote by Francis Bacon
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.
Related Quotes
It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active.
A science is something which is constructed from truth on workable axioms. There are 55 axioms in scientology which are very demonstrably true, and on these can be constructed a great deal.
Ethical axioms are found and tested not very differently from the axioms of science. Truth is what stands the test of experience.
When Keats says: 'Axioms in philosophy are not axioms until they are proved upon our pulses', what he means is that we don't necessarily believe what a poem is saying if it comes out and tells us in an absolutely head-on, in-your-face way; we only believe it to be true if we feel it to be true.
While the game of deadlocks and bottle-necks goes on, another more serious game is also being played. It is governed by two axioms. One is that there can be no peace without a general surrender of sovereignty: the other is that no country capable of defending its sovereignty ever surrenders it. If one keeps these axioms in mind one can generally see the relevant facts in international affairs through the smoke-screen with which the newspapers surround them.
For axioms in philosophy are not axioms until they are proved upon our pulses.
For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.
The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.
If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.
The principles of Jefferson are the definitions and axioms of free society.
I tell you the solemn truth, that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.
Those authors are to be read at schools that supply most axioms of prudence.
When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.
Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof.
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.
One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example.
Related Authors
Alan Watts Quotes
English
Philosopher
Albert Camus Quotes
French
Philosopher
Aristotle Quotes
Greek
Philosopher
Arthur Schopenhauer Quotes
German
Philosopher
Blaise Pascal Quotes
French
Philosopher
Confucius Quotes
Chinese
Philosopher
Friedrich Nietzsche Quotes
German
Philosopher
Jiddu Krishnamurti Quotes
Indian
Philosopher
Laozi Quotes
Chinese
Philosopher
Michel de Montaigne Quotes
French
Philosopher
Plato Quotes
Greek
Philosopher
Ralph Waldo Emerson Quotes
American
Philosopher
Seneca the Younger Quotes
Roman
Philosopher
Soren Kierkegaard Quotes
Danish
Philosopher
Thomas Carlyle Quotes
Scottish
Philosopher
William James Quotes
American
Philosopher