Paradox Lost / Progress in Mathematics (PDF)

Paradox Lost covers ten of philosophy's most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included:

• The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false?
  
• The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap?
  
• The Puzzle of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars.
  
• Newcomb's Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000.
  
• The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week . . . but also that if this is so, then a surprise quiz can be given on any day.
  
• The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other.
  
• The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black.
  
• The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual's survival turns on the flip of a fair coin.
  

Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles.