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What follows from an inconsistent set of premises?

  • A.Only sentences that are themselves inconsistent
  • B.Every sentence whatever
  • C.Only sentences already among the premises
  • D.Nothing at all, since no conclusion is licensed

Answer: B

Since an inconsistent set has no models, every sentence is vacuously true in all of them, so everything is entailed. That is why detecting inconsistency matters so much: a system that has quietly become inconsistent will cheerfully derive anything asked of it. The other options understate the consequence. A property that makes a system useless rather than merely wrong is one worth checking for actively rather than hoping to notice. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

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