The tension between our knowledge and our ignorance is decisive for the growth of knowledge. It inspires the advance of knowledge, and it determines its ever-moving frontiers.
The word ‘problem’ is only another name for this tension or rather, a name denoting various concrete instances of it.
As I suggested above, a problem arises, grows, and becomes significant through our failures to solve it. Or to put it another way, the only way of getting to know a problem is to learn from our mistakes.
This applies to pre-scientific knowledge and to scientific knowledge.
My view of the method of science is, very simply, that it systematizes the pre-scientific method of learning from our mistakes. It does so by the device called critical discussion.
My whole view of scientific method may be summed up by saying that it consists of these three steps:
1. We stumble over some problem.
2. We try to solve it, for example by proposing some theory.
3. We learn from our mistakes, especially from those brought home to us by the critical discussion of our tentative solutions – a discussion which tends to lead to new problems.
Or in three words: problems – theories – criticism.
I believe that in these three words the whole procedure of rational science may be summed up. [100-1]