List of laws in logic

• the law of identity (ID)

  • everything is (identical to itself)

  • B.Russell in PM, 1912: "Whatever is, is."

  • every proposition implies itself, p -> p

  • Law of identity

  • ID

  • axiom of classical logic

  • axiom of intuitionistic logic

• the law of non-contradiction (NC)

  • no proposition is both true and false, ¬(p ∧ ¬p)

  • contradictory statements cannot both at the same time be true

  • no thing having some quality has the negative of that quality

  • Law of non-contradiction

  • NC

  • axiom of classical logic

  • axiom of intuitionistic logic

• the law of excluded middle (EM)

  • every proposition is either true or false, p ∨ ¬p

  • a thing either has some quality or has the negative of that quality

  • Law of excluded middle

  • EM

  • axiom of classical logic

  • not an axiom of intuitionistic logic (also double negation elimination)

• Principle of Explosion ECQ

  Because the principle has been falsely attributed to philosopher John Duns Scotus (1265-1308), the principle is sometimes known as pseudo Scotus (PSP).

https://en.wikipedia.org/wiki/Laws_of_Form https://en.wikipedia.org/wiki/Laws_of_logic https://en.wikipedia.org/wiki/List_of_Hilbert_systems https://en.wikipedia.org/wiki/First-order_logic https://en.wikipedia.org/wiki/Propositional_calculus https://en.wikipedia.org/wiki/Rule_of_inference https://en.wikipedia.org/wiki/Conditional_proof https://en.wikipedia.org/wiki/Frege's_theorem