Concept:Third conditional sentences express unreal past conditions and their imagined results.
Rule / Clue:The indirect speech retains “had been” and “would not have arisen” – the exact third conditional structure. Direct speech must keep this unchanged.
Explanation:The original sentence uses “had … been” (past perfect) and “would not have arisen” (perfect conditional). This matches the third conditional pattern: “If + past perfect, would have + past participle.”
Option C repeats the same inverted conditional (“Had the syllogism been valid”) and the same result clause (“would not have arisen”), so it is correct.
Option A changes to first conditional (present tense, “does not arise”) – wrong tense.
Option B changes the result to “would not arise” (simple conditional) – incomplete third conditional.
Option D uses “should not arise” and omits “the” – alters meaning and grammar.
Only option C preserves the original past unreal meaning exactly.
Answer:C. The philosopher said, "Had the syllogism been valid, the paradox would not have arisen."