The Logic of Algebra

The algebra of logic was founded by George Boole (1815-1864); it was developed and perfected by Ernst Schroder (1841-1902) The fundamental laws of this calculus were devised to express the principles of reasoning, the laws of thought But this calculus may be considered from the purely formal point of view, which is that of mathematics, as an algebra based upon certain principles arbitrarily laid down It belongs to the realm of philosophy to decide whether, and in what measure, this calculus corresponds to the actual operations of the mind, and is adapted to translate or even to replace argument; we cannot discuss this point here The formal value of this calculus and its interest for the mathematician are absolutely independent of the interpretation given it and of the application which can be made of it to logical problems In short, we shall discuss it not as logic but as algebra.
Contents

Preface
Bibliography
Introduction
The Two Interpretations of the Logical Calculus
Relation of Inclusion
Definition of Equality
Principle of Identity
Principle of the Syllogism
Multiplication and Addition
Principles of Simplification and Composition
The Laws of Tautology and of Absorption
Theorems on Multiplication and Addition
The First Formula for Transforming Inclusions into Equalities
The Distributive Law
Definition of 0 and 1
The Law of Duality
Definition of Negation
The Principles of Contradiction and of Excluded Middle
Law of Double Negation
Second Formulas for Transforming Inclusions into Equalities
The Law of Couturat
Postulate of Existence
The Development of 0 and of 1
Properties of the Constituents
Logical Functions
The Law of Development
The Formulas of De Morgan
Disjunctive Sums
Properties of Developed Functions
The Limits of a Function
Formula of Poretsky
Schroder's Theorem
The Resultant of Elimination
The Case of Indetermination
Sums and Products of Functions