Claim. Formal logic enumerates four laws of thought — identity, contradiction, excluded middle, and sufficient reason — from which all other laws are derived.
Elaboration. Sang Hun Lee summarizes the Aristotelian-Leibnizian inventory (1. The Laws of Thought):
Law of Identity — ‘A is A,’ as in ‘a flower is a flower.’ This implies that despite phenomenal change, the substance remains the same, and that concepts have stable meaning. It also covers concept-agreement statements like ‘a bird is an animal.’
Law of Contradiction — ‘A is not not-A.’ The identity principle stated negatively: ‘a flower is not a non-flower’ says the same thing as ‘a flower is a flower.’
Law of the Excluded Middle — ‘Everything is either A or not-A.’ No third or middle judgment is possible.
Law of Sufficient Reason — first advocated by Leibniz: every act of thinking comes into being for necessary reasons. Generalized, this becomes the law of cause and effect — everything that exists has a sufficient reason for its existence. ‘Reason’ here carries two senses: basis (opposite of conclusion) and cause (opposite of result). Thought always has a basis; existence always has a cause.
Lee notes that many other laws exist but all derive from these four. He quotes Kant’s famous verdict that since Aristotle, formal logic ‘has not required to retrace a single step’ and appears ‘a closed and completed body of doctrine.’ The endorsement is real but qualified: Lee will argue that formal logic is not incorrect but incomplete — it deals with form without content, purpose, or relation to other fields. The four laws will reappear in Section III as candidates to be subsumed under the more fundamental law of give-and-take action.
See also. logic-is-laws-and-forms-of-thinking, symbolic-logic-as-mathematical-formalization, marxist-dialectical-logic-and-its-aporia