OK, just updating to say that I did indeed pass my quals! I'll try to hammer out a proposal over the summer, and then it's on to the dissertation.
Meanwhile, in place of a real post, for now here are the questions I had on the first day...
Qualifying Exam Questions for Ben Burgis
Part I: Answer two of the questions below:
1. Compare and contrast Jon Barwise and John Etchemendy's approach to the liar paradox in terms of non-well-founded sets to the one offered by Saul Kripke in his theory of truth. Indicate the similarities and the main differences between these two approaches. Which difficulties do they face?
2. Explain how the dialetheist attempts to solve the liar paradox. What are the alleged benefits of the solution? Which problems must it overcome? Explain how the dialetheist attempts to solve the inconsistency found in naive set theory. Does this solution work? Why or why not?
3. Is truth a vague predicate? If so, does this help addressing the liar paradox? How?
....and here are the ones from the second day:
Qualfying Exam Questions for Ben Burgis
Part II: Answer two of the questions below:
1. The dialetheist suggest that we should change the underlying logic of our theories to a paraconsistent one. Can we make sense of the idea of changing a logic? In order to change a logic, don't we need a logic to assess such a change? Can this process get off the ground? If so, how?
2. Explain some of the main similarities between the liar paradox and the set-theoretic paradoxes. What are some of the main differences between them? What are the prospects of developing a unified solution to both paradoxes?
3. Set theory with an unrestricted comprehension schema is prima facie a plausible theory: it's simple, intuitive, and very powerful. All things considered, it's perhaps the best theory of sets we have. But the theory is also inconsistent. The indispensibility argument would then force us to conclude that we ought to believe in the existence of mathematical objects with inconsistent properties. Does this offer a reductio of the indispensibility argument? Why or why not? Does the fact that such a theory is inconsistent pose a problem for a realist interpretation of the theory? Why or why not? (To answer these questions, discuss in particular the approach to set theory developed by Penelope Maddy.)