The paradoxes were inherent in the man, and in the conflicts between those beliefs and that honesty. His stern lectures on economic realities when he first became Education Secretary went down like a bucket of cold water with teacher unions and hostile conference audiences, but then he could turn down a voucher scheme which had intellectually attracted him because he was not finally convinced that it could work.
The force of argument and facts usually triumphed over ideology in the end. Thus he defended political education in schools at a time when it was regarded as subversive by many Cabinet colleagues, on the grounds that it was essential for young people to be taught to make up their own minds on the basis of the evidence. On several occasions, right-wing witch-hunts were dismissed by him after calling for the facts, considering what was offered, and then declaring the case "non-proven".
In some respects he was the mandarin's mandarin. Senior staff at the Department of Education and Science were stimulated by his heavyweight book-lists and seminars, but he could be friendly and informal and - not totally remote from the realities of life - could be encountered, after the break-up of his first marriage, wandering out of his local supermarket with a plastic carrier bag.
In spite of his legendary agonising, Sir Keith Joseph could not be called an indecisive Education Secretary. He took firm action where his predecessor, Shirley Williams, had procrastinated, to replace the divisive O-levels and CSE examinations with the General Certificate of Secondary Education.
In fact, he did go on agonising and caring about the GCSE long after he had left education, asking questions in the House of Lords, writing letters and quizzing educationists to discover whether criterion-referencing and differentiation of examination papers were really producing higher quality, as he had hoped.