{
  "argument": "Galileo's tied-stones argument, Dialogues Concerning Two New Sciences (1638), First Day; trans. Crew and de Salvio (1914), pp. 62-64",
  "premises": {
    "P1": "Of two bodies falling in the same medium, the heavier falls faster (the rule the dialogue gives Aristotle).",
    "P2": "When two bodies with different natural speeds are tied together, the pair moves at a speed between the two (granted by Simplicio, p. 63).",
    "P3": "By P1 the light stone is slower, so by P2 the pair falls slower than the heavy stone alone.",
    "P4": "The pair weighs more than the heavy stone, so by P1 it falls faster than the heavy stone alone."
  },
  "method_a": {
    "description": "every integer weight pair from 1 to 6 (heavy > light) with every speed triple from 1 to 12",
    "cases_checked": 25920,
    "cases_satisfying": {
      "P1 and P2": 0,
      "P1 only": 3300,
      "P2 only": 8760,
      "weak P1 (\"never slower\") and P2": 1170
    }
  },
  "method_b": {
    "description": "every weak ordering of the three speeds, with the weight order fixed (pair > heavy > light)",
    "orderings_checked": 13,
    "orderings_satisfying": {
      "P1 and P2": 0,
      "P1 only": 1,
      "P2 only": 5,
      "weak P1 (\"never slower\") and P2": 2
    }
  },
  "methods_agree": true,
  "result": "No case satisfies P1 and P2 together, so P3 and P4 cannot both hold: the premises are inconsistent. Each premise on its own is satisfiable.",
  "weaker_rule": {
    "rule": "a heavier body is never slower than a lighter one",
    "with_P2": "satisfiable, but in every satisfying case the heavy and light stones have the same speed",
    "heavy_and_light_equal_in_every_case": true
  },
  "dialogue_numbers_p63": {
    "speed_heavy": 8,
    "speed_light": 4,
    "P2_says_pair_below": 8,
    "P1_proportional_says_pair": 12,
    "both_possible": false
  }
}