The true meaning of a term is to be found by observing what a man does with it, not by what he says about it.

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.

To find the length of an object, we have to perform certain physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined.

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.

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

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

I can see no justification whatever for the attitude which refuses on purely a priori grounds to accept action at a distance ... Such an attitude bespeaks an unimaginativeness, a mental obtuseness and obstinacy.