Aid Quotes - page 14
Although what is called ‘philosophical speculation' is undoubtedly on the decline, many of the practically minded have not yet freed themselves from a method of reasoning, which, in the last analysis, has its roots in theology and metaphysics. No science which pretends to be exact can accept an untested theory or doctrine; yet even in an exact science there is often an admixture of magic, theology, and philosophy. It is one of the tasks of our time to aid scientific reasoning to attain its goal without hindrance. Whoever undertakes this is concerned not so much with ‘philosophy,' properly speaking, as with ‘anti-philosophy.' For him there is but one science with subdivisions - a unified science of sciences. We have a science that deals with rocks, another that deals with plants, a third that deals with animals, but we need a science that unites them all.
Otto Neurath
We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.
...We ...choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows: "The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions, are only the fruit of an unconscious opportunism."
Henri Poincaré
Mathematics have a triple aim. They must furnish an instrument for the study of nature. But that is not all: they have a philosophic aim and, I dare maintain, an esthetic aim. They must aid the philosopher to fathom the notions of number, of space, of time. And above all, their adepts find therein delights analogous to those given by painting and music. They admire the delicate harmony of numbers and forms; they marvel when a new discovery opens to them an unexpected perspective; and has not the joy they thus feel the esthetic character, even though the senses take no part therein? Only a privileged few are called to enjoy it fully, it is true, but is not this the case for all the noblest arts?
This is why I do not hesitate to say that mathematics deserve to be cultivated for their own sake, and the theories inapplicable to physics as well as the others. Even if the physical aim and the esthetic aim were not united, we ought not to sacrifice either.
Henri Poincaré