Concept
Boolean algebra
Overview
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.
Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854). According to Huntington, the term Boolean algebra was first suggested by Henry M. Sheffer in 1913, although Charles Sanders Peirce gave the title "A Boolian [sic] Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880. Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Strictly speaking, only the things which I have mentioned belong to the category of quantity: everything else that is called quantitative is a quantity in a secondary sense. It is because we have in mind some one of these quantities, properly so called, that we apply quantitative terms to other things. We speak of what is white as large, because the surface over which the white extends is large; we speak of an…
Aristotle, The Categories
States what Boolean algebra is; the author is tied to Boolean algebra in the knowledge graph.
The exercise of logical reason is always concerned with these absolutely general conditions. In its broadest sense, the discovery of mathematics is the discovery that the totality of these general abstract conditions, which are concurrently applicable to the relationships among the entities of any one concrete occasion, are themselves inter-connected in the manner of a pattern with a key to it. This pattern of…
Alfred North Whitehead, Science and the modern world
States what Boolean algebra is.
Indeed, is it by the will of God, for example, or is it not rather by the nature of numbers, that certain numbers allow more than others of various exact divisions? that some are more fitted than others for forming battalions, composing polygons and other regular figures? that the number six has the advantage of being the least of all the numbers that are called perfect? that in a plane six equal circles may touch a…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
States what Boolean algebra is; the author is tied to Boolean algebra in the knowledge graph.
Philosophers who discussed Boolean algebra
- Gottfried Wilhelm Leibniz
- Aristotle
- Willard Van Orman Quine
- George Boole
- Josiah Royce
- Charles Sanders Peirce
- Louis Couturat
- Grigore Moisil
Related ideas
- First-order logic
- Gottfried Wilhelm Leibniz
- Princeton University Press
- Springer Science+Business Media
- Integer
- Isomorphism
- Propositional variable
- Negation
- Truth value
- Intuitionistic logic
- Logical conjunction
- Logical connective
- Propositional logic
- Relevance logic
- Function (mathematics)
- Algebra
- Mathematics
- Group (mathematics)
- Mathematical logic
- Real number
- William Stanley Jevons
- Number
- Intersection (set theory)
- Power set
Place in the tradition
Part of British philosophy.