[PHI 3000] Preface Paradox and Cognitive Dissonance

The Preface Paradox arises because an author supposedly believes each proposition in her book but she also believes that she is fallible, and so her book surely contains some mistakes. She might express that latter belief by writing in the preface to her book something along the lines of "Despite my best efforts, I'm sure that this book, like all books, contains some mistakes."

Accordingly, these two beliefs (i.e., that each proposition in her book is true and that at least one is false) are apparently contradictory.

One response to the Preface Paradox is to deny the conjunction principle. (According to the conjunction principle, if one believes P1 and one believes P2, then one believes P1 and P2). So, the author believes P1 and she believes P2, and so on. But that doesn't mean that she believes P1 and P2, and ... Pn.

If we reject the conjunction principle, however, does it mean that epistemic agents cannot have flat-out contradictory beliefs?

Consider the following example:

The Daily Show with Jon Stewart
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Craig T. Nelson: I've been on food-stamps and welfare. Anybody helped me out? No!

Nelson seems to believe the following propositions:

1. I was on food-stamps and welfare.
2. No one helped me out.

If Nelson believes (1) and he believes (2), does it follow that he believes (1) and (2)?

Are (1) and (2) flat-out contradictory?