The Rules of Logic

2007/06/10 · by · in Idiocracy, Math

Taken from Scott Aaronson’s PHYS771 Quantum Computing Since Democritus


  • Propositional Tautologies: A or not A, not(A and not A), etc. are valid.
  • Modus Ponens: If A is valid and A implies B is valid then B is valid.
  • Equality Rules: x=x, x=y implies y=x, x=y and y=z implies x=z, and x=y implies f(x)=f(y) are all valid.
  • Change of Variables: Changing variable names leaves a statement valid.
  • Quantifier Elimination: If For all x, A(x) is valid, then A(y) is valid for any y.
  • Quantifier Addition: If A(y) is valid where y is an unrestricted variable, then For all x, A(x) is valid.
  • Quantifier Rules: If Not(For all x, A(x)) is valid, then There exists an x such that Not(A(x)) is valid. Etc.


Simple rules, I wonder why so much of the world seems to have such problems. I must be because the ways of logical fallacy are more numerous than those of correct deduction.