Are laws of thoughts axioms or inference rules in logical systems?

153 Views Asked by At

https://en.wikipedia.org/wiki/Law_of_thought says

The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based.

https://en.wikipedia.org/wiki/Law_of_thought#The_three_traditional_laws lists three and represent them in formal logic:

Three traditional laws: identity, non-contradiction, excluded middle

  • The law of identity: For all a: a = a.

  • The law of non-contradiction: ¬(A∧¬A).

  • The law of excluded middle: A∨¬A.

Are laws of thoughts tautologies?

Are laws of thoughts axioms, theorems, or inference rules in logical systems? If not, what are they in logical systems?

Are tautologies axioms, theorems, or inference rules in logical systems? If not, what are they in logical systems?

Some of the laws of thoughts are used for defining the class of classical logics. https://en.wikipedia.org/wiki/Classical_logic#Characteristics. Does this link define the class of classical logics by having the laws of thoughts as their axioms, theorems, or as something else?

Each logical system in the class of classical logics shares characteristic properties:[3]

  • Law of excluded middle and double negation elimination

  • Law of noncontradiction, and the principle of explosion

  • Monotonicity of entailment and idempotency of entailment

  • Commutativity of conjunction

  • De Morgan duality: every logical operator is dual to another

Thanks.