Laws of thought

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

The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. Defining such rules is a long-standing tradition in the history of philosophy and logic, which is possibly the reason the term is rarely used in the same sense by different authors.

The laws of thought are deemed as

• principles that guide and underlie everyone's thought processes

• the laws by which valid thought proceeds

• that justify valid inference

• to which all valid deduction is reducible

• rules that apply to all subject matter of thought

• etc. etc.

However, these classical ideas are often rejected in more recent developments of logic, especially in intuitionistic and fuzzy logic.

The three laws of thought

For a long time, it was held that the 3 basic laws of though are

• the law of identity (ID)

• the law of non-contradiction (NC)

• the law of excluded middle (EM)

Sometimes, these three expressions are taken as propositions of formal ontology having the widest possible subject matter, propositions that apply to entities as such:

• (ID) everything is (identical to itself)

• (NC) no thing having some quality has the negative of that quality

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

Common in older works is the use of these expressions for principles of metalogic about propositions:

• (ID) every proposition implies itself, p -> p

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

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