Conclusion

There are many reasons why philosophers study philosophical paradoxes. Paradoxes force those who study and attempt to solve them to confront strong, conflicting intuitions; discover ways in which intuitions can be misleading; and analyze ways in which our ordinary concepts are problematic. In addition, paradoxes require the adventurous souls who seek to understand and solve them to go beyond a noncommittal awareness of philosophical problems to an evaluation of solutions that are—to varying degrees—successful. And most important, students of paradoxes learn that discovering a paradox—ironically—leads to advances in our knowledge, not the reverse. As scientist Niels Bohr wrote, “How wonderful that we have met with a paradox. Now we have some hope of making progress” (Moore 1966, 196). The contemporary solutions to the paradoxes we have met in this book show the wisdom of Bohr’s statement. Not only are the solutions to the paradoxes original and interesting, but the systematic theories here highlighted are interesting in their own right and have led to much progress in the way we think about a wide array of notions, whether in science, mathematics, politics, or philosophy. Where there is progress, there is paradox, and both fuel each other.