We know a great deal, but our ignorance is sobering and boundless. With each step forward, with each problem which we solve, we not only discover new and unsolved problems, but we also discover that where we believed that we were standing on firm and safe ground, all things are, in truth, insecure and in a state of flux.

The old scientific ideal of episteme - of absolutely certain, demonstrable knowledge - has proved to be an idol. The demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever.

We must plan for freedom, and not only for security, if for no other reason than only freedom can make security more secure.

Philosophers should consider the fact that the greatest happiness principle can easily be made an excuse for a benevolent dictatorship. We should replace it by a more modest and more realistic principle - the principle that the fight against avoidable misery should be a recognized aim of public policy, while the increase of happiness should be left, in the main, to private initiative.

The survival value of intelligence is that it allows us to extinct a bad idea, before the idea extincts us.

A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.

A system such as classical mechanics may be 'scientific' to any degree you like; but those who uphold it dogmatically - believing, perhaps, that it is their business to defend such a successful system against criticism as long as it is not conclusively disproved - are adopting the very reverse of that critical attitude which in my view is the proper one for the scientist.