The Mathematical Analysis of Logic¶
Boole, G. (1854). The Mathematical Analysis of Logic. An Investigation of the Laws of Thought.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Commutativity
- rotations in 3D are non-commutative (rotating about two different axes produces different results depending on order); (3) commutativity supplies a standard reasoning pattern for reordering freedom and parallelization — if an operation is commutative, terms in a summation, factors in a product, or operations in a pipeline can be reordered for clarity, optimization, or parallelization without affecting results; commutativity also underpins abelian algebraic structures (abelian groups, commutative rings, fields), as Boole (1847/1854) prefigured in formalizing the commutativity of conjunction and disjunction in the algebra of logic
This sourceIntroduces the algebra of logic with the commutative law xy = yx for class-intersection (logical conjunction); directly supports the claim that Boole formalized the commutativity of conjunction and disjunction.
Supported in partVerified against the work's full text
Boole states that his elective (class-selection) symbols are commutative, with the order-indifference law; he does not frame this as underpinning abelian structures or treat disjunction separately.
“elective symbols are distributive, from the second that they are commutative”
- rotations in 3D are non-commutative (rotating about two different axes produces different results depending on order); (3) commutativity supplies a standard reasoning pattern for reordering freedom and parallelization — if an operation is commutative, terms in a summation, factors in a product, or operations in a pipeline can be reordered for clarity, optimization, or parallelization without affecting results; commutativity also underpins abelian algebraic structures (abelian groups, commutative rings, fields), as Boole (1847/1854) prefigured in formalizing the commutativity of conjunction and disjunction in the algebra of logic
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