A Quote by Gottfried Leibniz
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.
Related Quotes
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 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.
There are two principles on which all men of intellectual integrity and good will can agree, as a 'basic minimum,' as a precondition of any discussion, co-operation or movement toward an intellectual Renaissance. . . . They are not axioms, but until a man has proved them to himself and has accepted them, he is not fit for an intellectual discussion. These two principles are: a. that emotions are not tools of cognition; b. that no man has the right to initiate the use of physical force against others.
Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.
That human life must be some kind of mistake is sufficiently proved by the simple observation that man is a compound of needs which are hard to satisfy; that their satisfaction achieves nothing but a painless condition in which he is only given over to boredom . . .
For axioms in philosophy are not axioms until they are proved upon our pulses.
Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
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.
The perfectly natural thing to do with an unreadable book is to give it away; and the publication, for more than a quarter of a century, of volumes which fulfilled this one purpose and no other is a pleasant proof, if proof were needed, of the business principles which underlay the enlightened activity of publishers.
The mind being, as I have declared, furnished with a great number of the simple ideas conveyed in by the senses, as they are found in exterior things, or by reflection on its own operations, take notice, also, that a certain number of these simple ideas go constantly together... which, by inadvertency, we apt afterward to talk of and condier as one simple idea.
The human person, whose definition serves as the touchstone according to which good must be distinguished from evil, is considered as sacred, in what one might call the ritual sense of the word. It has something of that transcendental majesty which the churches of all times have given to their Gods.
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.
A definition is nothing else but an explication of the meaning of a word, by words whose meaning is already known. Hence it is evident that every word cannot be defined; for the definition must consist of words; and there could be no definition, if there were not words previously understood without definition.
I'm not comfortable with categories, and I distrust most definitions. The word 'definition' is based on the word 'finite,' which would seem to indicate that once we've defined something, we don't need to think about it anymore.
Intellectuals are judged not by their morals, but by the quality of their ideas, which are rarely reducible to simple verdicts of truth or falsity, if only because banalities are by definition accurate.
We depend on our words... Our task is to communicate experience and ideas to others. We must strive continually to extend the scope of our description, but in such a way that our messages do not thereby lose their objective or unambiguous character... We are suspended in language in such a way that we cannot say what is up and what is down. The word "reality" is also a word, a word which we must learn to use correctly.
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
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
Thomas Carlyle Quotes
Scottish
Philosopher
William James Quotes
American
Philosopher