Do philosophers raise their children differently? Is talking back to a teacher always a good thing so long as the child has good arguments?

Second question first: Of course not! If 'talking back' means picking arguments with a teacher, that's not very productive -- or very philosophically minded. That said, I think many philosophers would agree that too much of formal education emphasizes the memorization or assimilation of 'established' knowledge as the expense of the sort of curiosity and questioning found in philosophy. There's a worldwide movement to promote philosophy education for children. Here are some good resources on that front: http://depts.washington.edu/nwcenter/ http://p4c.com/ As to your first question: I don't have any empirical data to support this -- to my knowledge, how philosophers raise their children has never been studied. All the same , I would not at all be surprised to learn that many of the traits that one needs to be successful in philosophy -- a sense of puzzlement, attention to reasoning, comfort with uncertainty, respect for those with whom one disagrees -- are passed on by philosophers to their children. I...

How often do philosophers admit their own defeat in their own published academic articles?

Philosophy is a highly discursive discipline founded on argumentative give and take. Often when a philosopher's position is subject to criticism she believes she cannot answer, she modifies her position while trying to retain those elements of those position she believes are most central to it. In other words, the result of receiving criticism is rarely a philosopher 'admitting defeat.' Rather, her position evolves as she strives to absorb the criticisms as much as her extant positions allow. That said, there are some prominent examples of philosophers who clearly changed their minds over their lifetimes. Perhaps the clearest is Wittgenstein: The 'early Wittgenstein' inspired logical positivism, the 'later' ordinary language Wittgenstein was a critic of positivism. Russell seemed to change his mind a fair bit too. A recent example is John Rawls, who gives a very different foundation for his political liberalism in his early work than in his later work. Kant certainly changed his mind regarding whether...