An Investigation of the Laws of Thought: On which are Founded the Mathematical Theories of Logic and Probabilities

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Courier Corporation, 1958 - Philosophy - 424 pages
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Classic in symbolic logic, showing that classical logic can be treated algebraically. Timeless introduction.
 

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Contents

NATURE AND DESIGN OF THIS WORK
1
SIGNS AND THEIR LAWS
24
DERIVATION OF THE LAWS
39
DIVISION OF PROPOSITIONS
52
PRINCIPLES OF SYMBOLICAL REASONING
66
OF INTERPRETATION
80
OF ELIMINATION
99
OF REDUCTION
114
CLARKE AND SPINOZA
185
EXAMPLE OF ANALYSIS
219
OF THE ARISTOTELIAN LOGIC
226
OF THE THEORY OF PROBABILITIES
243
GENERAL METHOD IN PROBABILITIES
253
ELEMENTARY ILLUSTRATIONS
276
OF STATISTICAL CONDITIONS
295
PROBLEMS OF CAUSES
320

METHODS OF ABBREVIATION
130
CONDITIONS OF A PERFECT METHOD
150
OF SECONDARY PROPOSITIONS
159
METHODS IN SECONDARY PROPOSITIONS
177
PROBABILITY OF JUDGMENTS
376
CONSTITUTION OF THE INTELLECT
399
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About the author (1958)

Born in Lincolnshire, England, George Boole was a mathematician and logician at Queens College in Cork, Ireland, where he taught and developed his theory of logic. Well respected by his friends and associates, he had a reputation of being a kind of naive saint, who thought nothing of inviting a stranger to his home to continue a conversation that the two of them had begun on a train or in a shop. Boole's development of symbolic logic had three major emphases. First, Boole believed that mathematicians of his day unnecessarily restricted themselves to the study of quantities and did not pay enough attention to abstract symbols. Second, he concerned himself with the relation between logic and language. Third, he studied the proper representation of mental operations. Thus, Boole moved from quantity to symbols to language and finally to the rules of the thinking mind itself. In 1847 Boole expressed his ideas in a pamphlet titled The Mathematical Analysis of Logic. Boole is remembered for using familiar symbols of algebra and arithmetic to help represent ideas of logic. The system he used is now known as Boolean algebra. In creating his algebra of logic, Boole followed in the footsteps of the classical algebraists. Through careful analysis and resourcefulness, he developed a practical language for representing and solving a broad class of mathematical problems. Boole's contributions can be seen today in the design of the modern digital computer. Boole died in 1864.

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