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LESSON 3 · Paradoxes That Break Your Brain

Living with Vagueness

The Sorites paradox matters because real decisions hinge on vague boundaries every day:

  • Benefit cliffs cut off subsidies the moment income crosses a fixed line, so one extra dollar can cost thousands
  • Medical diagnoses draw lines through continuous spectrums of symptoms
  • Grading systems turn smooth performance curves into discrete letters
  • Courts must decide when speech becomes harassment or art becomes obscenity

Recognizing vagueness does not mean abandoning categories. It means holding them lightly and remembering that the map is never the territory.