Boolean algebra

1847 Boolean algebra

The book of science

Tom Sharp

George Boole computer science Boolean algebra

Boolean algebra

George Boole developed equations for Aristotle’s logic, the first algebraic logic. His successors dropped Boole’s uninterpretable terms and adopted inclusive or as the more basic to create modern Boolean algebras (Boole having favored the exclusive or). Given only two values, true and false, and three operations, and, or, and not, one is able to derive a complete system that we have animated with digital computers to become its own universe.

Tautology

The meanings of true and false and and, or, and not are arbitrary. The only important thing is that we can use them to make statements that are either true or false. A Boolean algebra can be defined as the set of statements that hold over the values true and false 1 and 0, or us and them. A statement having a truth value simply means that it has one of only two possible values, specifically, the value we hold as true or the value we hold as false.

Duality

True and false are dual to each other, as are and and or, which means they are interchangable. If the universe were composed of only right and wrong, then wrong would be as necessary as right.

Precision

When I try to be as precise in everyday life as I had to be when programming computers, other people get annoyed.

Arguments against torture, arguments against war

There never has been a war in which innocent people have not suffered. There never has been a confession under torture that a jury of peers would not doubt. When a policeman kills an innocent woman, law enforcement suffers. When a U.S. drone kills innocent people in Pakistan, national interests everywhere suffer. An act of torture debases both the victim and the torturer. The real reason for torture is not gaining information, but asserting the dominance of one group over another. If power itself is not evil, then its arrogance is. The benefits that war and torture claim are far smaller than their hidden costs. This is true of our own arrogance, and the arrogance of our enemies.

George Boole did not regard logic as a branch of mathematics, but as the laws of rational thought. His wife brought on his death by pouring buckets of water over him after he took to bed from a fever induced by walking through the rain to give a lecture wearing his wet clothes.

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