A Quote by Blaise Pascal
A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the
art of persuading.
Quote Topics
Quote Author
Related Quotes
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
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.
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.
There is no scientific proof that only scientific proofs are good proofs; no way to prove by the scientific method that the scientific method is the only valid method.
In this science the illustrations and examples are not confined in their effect merely to the practice they afford in the analytical art, but [...] they also store the mind with independent geometrical and physical knowledge. Besides, it should be considered, that the only effectual method of impressing abstract formulae and rules upon the memory, and, indeed, of making them fully and clearly apprehended by the understanding, is by examples of their practical application.
The principles of Jefferson are the definitions and axioms of free society.
Art. Its definitions are legion, its meanings multitudinous, its importance often debated. But amid the many contradictory definitions of art, one has always stood the test of time, from the Upanishads in the East, to Michelangelo in the West: art is the perception and depiction of the sublime, the transcendent, the beautiful, the spiritual.
Design is the method of putting form and content together. Design, just as art, has multiple definitions; there is no single definition. Design can be art. Design can be aesthetics. Design is so simple, that's why it is so complicated.
Psychoanalysis cannot be considered a method of education if by education we mean the topiary art of clipping a tree into a beautiful artificial shape. But those who have a higher conception of education will prize most the method of cultivating a tree so that it fulfils to perfection its own natural conditions of growth.
In the times in which we live it is far too restricting to say that art can only be found in art galleries and not touch people's everyday lives. I want to use any means that are necessary to communicate with people what I feel about things. There are no rules. And if there are rules, then you may as well break them.
An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.
My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments: In order to which, I shall premise the following Definitions and Axioms.
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.
I'm just wondering if this is the most effective method to bring about change. So I'm more inclined to withhold some of my opinions, and not even be involved in any demonstrations of any sort and just really try to figure out a method that I feel is more potent.
I like rules. I like definitions, categories, and writing advice of all sorts. When I'm writing fiction, there are often a lot of things for me to try to get right at once, and rules help me to stay organized. But my favorite rule of all is that, ultimately, there are no rules.
For axioms in philosophy are not axioms until they are proved upon our pulses.
Related Authors
Alan Watts Quotes
English
Philosopher
Albert Camus Quotes
French
Philosopher
Aristotle Quotes
Greek
Philosopher
Arthur Schopenhauer Quotes
German
Philosopher
Confucius Quotes
Chinese
Philosopher
Francis Bacon Quotes
English
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