Whether you know the shape of a pebble or the structure of a solar system, the axioms remain the same: that it exists and that you know it.
The eye of the understanding is like the eye of the sense; for as you may see great objects through small crannies or holes, so you may see great axioms of nature through small and contemptible instances.
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.
The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. ... It was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-Euclidean geometry and non-commutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalization of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
Ethical axioms are found and tested not very differently from the axioms of science. Truth is what stands the test of experience.
We must start with scientific fundamentals, and that means with the data of experiments and not with assumed axioms predicated only upon the misleading nature of that which only superficially seems to be obvious. It is the consensus of great scientists that science is the attempt to set in order the facts of experience.
There is an eternal antagonism of interest between the individual and the world at large. The individual will not so much care how much he may suffer in this world provided he can live in men's good thoughts long after he has left it. The world at large does not so much care how much suffering the individual may either endure or cause in this life, provided he will take himself clean away out of men's thoughts, whether for good or ill, when he has left it.
If there is no silence beyond and within the many words of doctrine, there is no religion, only a religious ideology. For religion goes beyond words and actions, and attains to the ultimate Truth only in silence and Love.
Science has its roots and origins outside its own rational realm of thinking. It is based on the conviction of every scientist and of society as a whole, that scientific truth is relevant and essential.
A real book is not one that we read, but one that reads us.
There are certain emotions which can find expression only in silence.)