It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.

The operational approach demands that we make our reports and do our thinking in the freshest terms of which we are capable, in which we strip off the sophistications of millenia of culture and report as directly as we can on what happens.

The process that I want to call scientific is a process that involves the continual apprehension of meaning, the constant appraisal of significance accompanied by a running act of checking to be sure that I am doing what I want to do, and of judging correctness or incorrectness. This checking and judging and accepting, that together constitute understanding, are done by me and can be done for me by no one else. They are as private as my toothache, and without them science is dead.

... the scientist would maintain that knowledge in of itself is wholly good, and that there should be and are methods of dealing with misuses of knowledge by the ruffian or the bully other than by suppressing the knowledge.

In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations.

It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.

My point of view is that science is essentially private, whereas the almost universal counter point of view, explicitly stated in many of the articles in the Encyclopaedia, is that it must be public.