I know of nothing more terrible than the poor creatures who have learned too much. Instead of the sound powerful judgement which would probably have grown up if they had learned nothing, their thoughts creep timidly and hypnotically after words, principles and formulae, constantly by the same paths. What they have acquired is a spider's web of thoughts too weak to furnish sure supports, but complicated enough to provide confusion.

:...Vienna is the origin of so many schools of its own which were dominant in the 1920s. And one of the most fundamental and influential, in which we all were partially caught, was logical positivism. In fact, Mises' brother, Richard von Mises, became one of the leading figures. Now he and I all grew up in this Ernst Mach philosophy that ultimately everything must be rationally justified...

In the philosophy of Mach a world without matter is unthinkable. Matter in Mach's philosophy is not merely required as a test body to display properties of something already there ...it is an essential feature in causing those properties which it able to display, Inertia, for example, would not appear by the insertion of one test body in the world; in some way the presence of other matter is a necessary condition. It will be seen how welcome to such a philosophy is the theory that space and the inertial frame come into being with matter, and grow as it grows.

There was a loud echo of Hume in Mach's work, as both emphasized the tangibility of all knowledge-ultimately, all knowledge is based in the senses. Mach also emphasized the internal nature of all knowledge, in that it is experienced in the mind. Finally, he emphasized the importance of quantitative and mathematical methods and models to understand sensory experience.

To a contemporary reader, nonetheless, Mach's Analysis of Sensations (1886) disappoints. There is a loud echo of Hume in the work, for Mach, like Hume, emphasized the tangibility of all knowledge-ultimately, all knowledge is based in the senses.

Some Machians were sufficiently impressed by Einstein's interpretations of Brownian movement to accept atomism. Mach himself brushed such objections aside, and also emphatically rejected Einstein's relativity theory.

Mathematical and physiological researches have shown that the space of experience is simply an actual case of many conceivable cases, about whose peculiar properties experience alone can instruct us.

The aim of research is the discovery of the equations which subsist between the elements of phenomena.

The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,-an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.

The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not a logical process although such processes can be inserted as intermediary and auxiliary links. The principle effort that leads to the discovery of new knowledge is due to abstraction and imagination.

Nature consists of the elements given by the senses. Primitive man first takes out of them certain complexes of these elements that present themselves with a certain stability and are most important to him. The first and oldest words are names for "things". ... The sensations are no "symbols of things". On the contrary the "thing" is a mental symbol for a sensation-complex of relative stability. Not the things, the bodies, but colours, sounds, pressures, times (what we usually call sensations) are the true elements of the world.

Not bodies produce sensations, but element-complexes (sensation-complexes) constitute the bodies. When the physicist considers the bodies as the permanent reality, the `elements' as the transient appearance, he does not realise that all `bodies' are only mental symbols for element-complexes (sensation-complexes)

There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathematical methods would take a lifetime.

In reality, the law always contains less than the fact itself, because it does not reproduce the fact as a whole but only in that aspect of it which is important for us, the rest being intentionally or from necessity omitted.

Personally, people know themselves very poorly.

Scientists believe there is a hierarchy of facts and that among them may be made a judicious choice. They are right, since otherwise there would be no science... One need only open the eyes to see that the conquests of industry which have enriched so many practical men would never have seen the light, if these practical men alone had existed and if they had not been preceded by unselfish devotees who died poor, who never thought of utility, and yet had a guide far other than caprice.As Mach says, these devotees have spared their successors the trouble of thinking.