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
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
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
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
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