Quotes About Axioms

You should never believe anything anyone said without first checking it. Suspect everybody, had been for many years, if not his whole life, one of his first axioms.

I was born into argument. Argument was my first nursemaid. Argument is my lifelong bedfellow. What's more, I believe in argument and I even love it. Argument is our most steadfast pathway toward truth, for it is the only proven arbalest against superstitious thinking, or lackadaisical axioms.

In particular the rules of logic tell us how to create, from the opening arrangement (the list of axioms), new arrangements (called "theorems").

Pure Reason, however, derives from axioms which can neither be proven nor disproven. These axioms appear in consciousness from a level of pre-logical apprehension in which we might as well be gesticulating and pointing — or waving sticks in the air like Zen Masters — instead of talking, because we are trying to indicate or invoke something that exists before words and categories.

Jan Huizinga, a Dutch sociologist, studied the game element in human behavior, and noted that we live by game rules which often have never risen to the level of conscious speech. In other words, we not only interpret data as we receive it, we also, quickly and unconsciously, fit the data to pre-existing axioms, or game-rules, of our culture (or our sub-culture).

Operationalism, created by Nobel physicist Percy W. Bridgman, attempts to deal with the common sense objections to Relativity and Quantum Mechanics, and owes a great deal to pragmatism and instrumentalism. Bridgman explicitly pointed out that common sense derives unknowingly from some tenets of ancient philosophy and speculation — particularly Platonic Idealism and Aristotelian essentialism — and that this philosophy assumes many axioms that now appear either untrue or unprovable.

If Nietzsche's existential relativism be accepted, then there will always be true things that do not fit any existing reality-tunnel, just as in mathematics Godel demonstrated that there will always be true theorems not deducible from any set of axioms. (See Chapter Two.)

To ask what it all means, what it's all for. To consider the axioms we are agreeing to live by. To acknowledge the reality of other people, and of the planet itself. To see other people's faces. To walk outdoors and look around.

Whether you know the shape of a pebble or the structure of a solar system, the anxioms remain the same: that it exists and that you know it.

We call these self-evident truths, such as the law of fair play, axioms. An axiom is a premise or starting point that is taken for granted before acquiring any additional knowledge. Axioms are self-evident beliefs that anchor the rest our beliefs.

Pure Reason left to herself relieth on axioms and essential premises which she can neither question nor resolve.

Mi padre comenzaba apoyándose en la fuerza de los dos axiomas siguientes: Primero: que, para un hombre, una onza de su propia inteligencia valía por una tonelada de la de cualquier otra persona; y Segundo (el cual, por cierto, era el fundamento del primer axioma—aunque viniera después): que la inteligencia de todo hombre debía necesariamente provenir de su propia alma—y jamás de la de ninguna otra persona.

There are no creeds in mathematics.

The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.

The progress of science, like an ancient desert trail, is strewn with the bleached skeletons of discarded theories, doctrines, and axioms which seemed to possess eternal life.

Ethical axioms are found and tested not very differently from the axioms of science. Truth is what stands the test of experience.

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.

It was in Rio that I realized the extent of the dilemma posed by the hallucinatory knowledge of indigenous people. On the one hand, its results are empirically confirmed and used by the pharmaceutical industry; on the other hand, its origin cannot be discussed scientifically because it contradicts the axioms of Western knowledge.

24. It cannot be that axioms established by argumentation should avail for the discovery of new works, for 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.

The principles of Jefferson are the definitions and axioms of free society.

Ethical axioms are found and tested not very differently from the axioms of science. Truth is what stands the test of experience.

The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.

Between every human consciousness and the rest of the world stands an invisible fence, a network of traditional thinking-and-feeling patterns, of secondhand notions that have turned into axioms, of ancient slogans revered as divine revelations.

Pongileoni se întrecu pe sine în Badineria final?. Axiomele euclidiene se înl?nÈ›uiau vesel cu formele de statistic? elementar?. Aritmetica f?cea un chef turbat, iar algebra s?rea dezordonat. Muzica se sfîrÈ™i într-o orgie de bun? dispoziÈ›ie matematic?.