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An Investigation of the Laws of Thought
"A classic of pure mathematics and symbolic logic ... the publisher is to be thanked for making it available." — Scientific American
George Boole was on of the greatest mathematicians of the 19th century, and one of the most influential thinkers of all time. Not only did he make important contributions to differential equations and calculus of finite differences, he also was the discoverer of invariants, and the founder of modern symbolic logic. According to Bertrand Russell, "Pure mathematics was discovered by George Boole in his work published in 1854."
This work is the first extensive statement of the modern view that mathematics is a pure deductive science that can be applied to various situations. Boole first showed how classical logic could be treated with algebraic terminology and operations, and then proceeded to a general symbolic method of logical interference; he also attempted to devise a calculus of probabilities which could be applied to situations hitherto considered beyond investigation.
The enormous range of this work can be seen from chapter Nature and Design of This Work; Signs and Their Laws; Derivation of Laws; Division of Propositions; Principles of Symbolical Reasoning; Interpretation; Elimination; Reduction; Methods of Abbreviation; Conditions of a Perfect Method; Secondary Propositions; Methods in Secondary Propositions; Clarke and Spinoza; Analysis, Aristotelian Logic; Theory of Probabilities; General Method in Probabilities; Elementary Illustrations; Statistical Conditions; Problems on Causes; Probability of Judgments; Constitution of the Intellect. This last chapter, Constitution of the Intellect, is a very significant analysis of the psychology of discovery and scientific method.
George Boole was on of the greatest mathematicians of the 19th century, and one of the most influential thinkers of all time. Not only did he make important contributions to differential equations and calculus of finite differences, he also was the discoverer of invariants, and the founder of modern symbolic logic. According to Bertrand Russell, "Pure mathematics was discovered by George Boole in his work published in 1854."
This work is the first extensive statement of the modern view that mathematics is a pure deductive science that can be applied to various situations. Boole first showed how classical logic could be treated with algebraic terminology and operations, and then proceeded to a general symbolic method of logical interference; he also attempted to devise a calculus of probabilities which could be applied to situations hitherto considered beyond investigation.
The enormous range of this work can be seen from chapter Nature and Design of This Work; Signs and Their Laws; Derivation of Laws; Division of Propositions; Principles of Symbolical Reasoning; Interpretation; Elimination; Reduction; Methods of Abbreviation; Conditions of a Perfect Method; Secondary Propositions; Methods in Secondary Propositions; Clarke and Spinoza; Analysis, Aristotelian Logic; Theory of Probabilities; General Method in Probabilities; Elementary Illustrations; Statistical Conditions; Problems on Causes; Probability of Judgments; Constitution of the Intellect. This last chapter, Constitution of the Intellect, is a very significant analysis of the psychology of discovery and scientific method.
356 pages, Kindle Edition
First published January 1, 1854
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Displaying 1 - 12 of 12 reviews
March 31, 2013
Irreplaceable as the horse's mouth on Boolean algebra, and there's much more to the subject than most engineers, whether of digital electronics or software, realize, and so I have to recommend it for that reason.
However, I can only, in good conscience, give it three stars: Boole is clearly exasperated in his writing, and while his logic is impeccable, albeit expressed in a notation no one uses today (well, except Jaynes), when he ventures into probability, probably under the influence of Venn, he completely loses the plot. So from that perspective, we can see through the lens of history an early attempt at "refuting" Laplace. Unfortunately, this may be an example where brilliance in one category has a kind of halo effect, granting the author unwarranted authority in another category.
Computer scientists should read it anyway, either as a historical precursor to Jaynes, or after Jaynes to see what some of the ranting was about.
However, I can only, in good conscience, give it three stars: Boole is clearly exasperated in his writing, and while his logic is impeccable, albeit expressed in a notation no one uses today (well, except Jaynes), when he ventures into probability, probably under the influence of Venn, he completely loses the plot. So from that perspective, we can see through the lens of history an early attempt at "refuting" Laplace. Unfortunately, this may be an example where brilliance in one category has a kind of halo effect, granting the author unwarranted authority in another category.
Computer scientists should read it anyway, either as a historical precursor to Jaynes, or after Jaynes to see what some of the ranting was about.
November 2, 2020
[found in the following list]
Books with the best decision theoretic and philosophical foundation
by Michael Emmett Brady
The following books will provide an optimal understanding of how one should study and organize the data and observations that comprise the social sciences. These books provide a broad foundation in logical, epistemological, and philosophical techniques that are sound and valid. A reader who masters these books will quickly grasp the complex, dynamic, nonlinear aspects of social science systems as they evolve through time.
1. The General Theory of Employment, Interest, and Money - John Maynard Keynes
2. A Treatise on Probability - John Maynard Keynes
3. Risk, Uncertainty and Profit - Frank H. Knight
4. The Theory of Economic Development - Joseph A. Schumpter
5. The Wealth of Nations - Adam Smith
6. Risk, Ambiguity and Decision - Daniel Ellsberg
7. The (Mis)behavior of Markets - Beniot Mandelbrot and Richard L. Hudson
8. Probability, Econometrics and Truth - Hugo A. Keuzenkamp
9. The Unbround Prometheus: Technological Change and the Industrial Development in Western Europe from 1750 to the Present - Second Edition - David S. Landes
10. The Laws of Thought - George Boole
11. The Black Swan - Nassim Nicholas Taleb
12. Fooled by Randomness - Nassim Nicholas Taleb
13. J.M. Keynes Theory of Decision Making, Induction and Analogy - Michael Emmett Brady
Books with the best decision theoretic and philosophical foundation
by Michael Emmett Brady
The following books will provide an optimal understanding of how one should study and organize the data and observations that comprise the social sciences. These books provide a broad foundation in logical, epistemological, and philosophical techniques that are sound and valid. A reader who masters these books will quickly grasp the complex, dynamic, nonlinear aspects of social science systems as they evolve through time.
1. The General Theory of Employment, Interest, and Money - John Maynard Keynes
2. A Treatise on Probability - John Maynard Keynes
3. Risk, Uncertainty and Profit - Frank H. Knight
4. The Theory of Economic Development - Joseph A. Schumpter
5. The Wealth of Nations - Adam Smith
6. Risk, Ambiguity and Decision - Daniel Ellsberg
7. The (Mis)behavior of Markets - Beniot Mandelbrot and Richard L. Hudson
8. Probability, Econometrics and Truth - Hugo A. Keuzenkamp
9. The Unbround Prometheus: Technological Change and the Industrial Development in Western Europe from 1750 to the Present - Second Edition - David S. Landes
10. The Laws of Thought - George Boole
11. The Black Swan - Nassim Nicholas Taleb
12. Fooled by Randomness - Nassim Nicholas Taleb
13. J.M. Keynes Theory of Decision Making, Induction and Analogy - Michael Emmett Brady
December 23, 2024
Boole made a great leap forward from the standard logic of his time, exemplified by Whatley’s Elements of Logic and the Port Royal Logic (The Art of Reasoning, Arnaud & Nicole). These tended to see logic as a grammatico-rhetorical bastion built around a very small collection of rules for Correct Inference, passed down from Aristotle with very little alteration.
Boole’s algebra was messy, poorly motivated, and likely not fully understood even by the man himself. He wanted to use a binary domain to interpret equations, but also wanted to use a nearly full complement of algebraic techniques to manipulate them. This leads to many rules of thumb understood by him as deliverances of pure reason, or simply as the only possible conclusions. For example, he translated words like the English “or” as well as the + operator as XOR, and never OR: he argued with Jevons about which was the “correct” interpretation and eventually gave up, exasperated, claiming that OR was simply inconceivable. Notably, Jevons also did not see the choice as a matter of convention, but rather as a matter of discovery. At the same time, it’s not like Boole felt this way for no reason. It turns out that some of the algebraic manipulations he wanted to use required + to be interpreted as XOR rather than OR. However, the algebraic moves he made were not exactly inference rules, since he expected the intermediate formulae of a “proof” to be uninterpretable. It would be the task of his successors to transition from algebra to a truly logical calculus.
Seeing Boole exhibit his calculus in so much detail is an exciting look into a key transition point in the field of formal logic, and many of the developments that were to take place in the following decades are at least discussed here, with attempted but not ideal solutions.
Boole’s algebra was messy, poorly motivated, and likely not fully understood even by the man himself. He wanted to use a binary domain to interpret equations, but also wanted to use a nearly full complement of algebraic techniques to manipulate them. This leads to many rules of thumb understood by him as deliverances of pure reason, or simply as the only possible conclusions. For example, he translated words like the English “or” as well as the + operator as XOR, and never OR: he argued with Jevons about which was the “correct” interpretation and eventually gave up, exasperated, claiming that OR was simply inconceivable. Notably, Jevons also did not see the choice as a matter of convention, but rather as a matter of discovery. At the same time, it’s not like Boole felt this way for no reason. It turns out that some of the algebraic manipulations he wanted to use required + to be interpreted as XOR rather than OR. However, the algebraic moves he made were not exactly inference rules, since he expected the intermediate formulae of a “proof” to be uninterpretable. It would be the task of his successors to transition from algebra to a truly logical calculus.
Seeing Boole exhibit his calculus in so much detail is an exciting look into a key transition point in the field of formal logic, and many of the developments that were to take place in the following decades are at least discussed here, with attempted but not ideal solutions.
November 12, 2024
"An Investigation of the Laws of Thought"
By George Boole is a seminal work in the field of logic and mathematics, published in 1854.
This book lays the groundwork for what is now known as Boolean algebra, which is fundamental in computer science and digital circuit design.
Key Points:
Boolean Algebra: Boole introduces a form of algebra in which the values of the variables are true and false, typically represented as 1 and 0.
Logical Operators: He defines operations like AND, OR, and NOT, which are essential for digital logic and computer programming.
Mathematical Logic: The book explores the relationship between logic and mathematics, proposing that logical reasoning can be represented mathematically.
Influence on Modern Computing: Boole's work laid the foundation for the development of modern computing and digital circuits, making it possible to design complex computational systems.
Boole's pioneering ideas in this book have had a profound and lasting impact on various fields, including computer science, electrical engineering, and philosophy.
By Inti, Lake Titicaca Perú
By George Boole is a seminal work in the field of logic and mathematics, published in 1854.
This book lays the groundwork for what is now known as Boolean algebra, which is fundamental in computer science and digital circuit design.
Key Points:
Boolean Algebra: Boole introduces a form of algebra in which the values of the variables are true and false, typically represented as 1 and 0.
Logical Operators: He defines operations like AND, OR, and NOT, which are essential for digital logic and computer programming.
Mathematical Logic: The book explores the relationship between logic and mathematics, proposing that logical reasoning can be represented mathematically.
Influence on Modern Computing: Boole's work laid the foundation for the development of modern computing and digital circuits, making it possible to design complex computational systems.
Boole's pioneering ideas in this book have had a profound and lasting impact on various fields, including computer science, electrical engineering, and philosophy.
By Inti, Lake Titicaca Perú
December 2, 2025
George Boole establishes an algebraic language devoted to logic and probability in this book. An Investigation of the Laws of Thought is a perennial classic of the field and has opened many doors of reasoning. The book is heavier on prose than I expected, but I can understand it.
Although Boole invented the algebraic language of logic and developed it beyond Aristotle's syllogism, he did not go beyond that. It was his successors in the field who made Boolean Logic more rigorous.
Boole wrote 22 chapters covering topics such as the symbols he invented and the heuristics he established. I enjoyed the book. Thanks for reading my review, and see you next time.
Although Boole invented the algebraic language of logic and developed it beyond Aristotle's syllogism, he did not go beyond that. It was his successors in the field who made Boolean Logic more rigorous.
Boole wrote 22 chapters covering topics such as the symbols he invented and the heuristics he established. I enjoyed the book. Thanks for reading my review, and see you next time.
July 7, 2020
Don’t waste your money
This is a great and classic text.
But don’t waste your time on this ebook version/production of the text.
The digitisation was flawed and incompetent.
Many of the equations are garbled.
In a text about reducing human thought or at least logic to equations you can see where this would be a problem.
To all those enthusiastically awaiting to be digitally uploaded consider that rushed and possibly dishonest operators can’t even get a book right. There will be defects!
This is a great and classic text.
But don’t waste your time on this ebook version/production of the text.
The digitisation was flawed and incompetent.
Many of the equations are garbled.
In a text about reducing human thought or at least logic to equations you can see where this would be a problem.
To all those enthusiastically awaiting to be digitally uploaded consider that rushed and possibly dishonest operators can’t even get a book right. There will be defects!
August 6, 2017
Acceptable but could be better.
Although I was able to get an overall idea of Boole's ideas, the book was deficient in its structure. It had typos, misplaced sentences and paragraphs which got me lost sometimes.
Although I was able to get an overall idea of Boole's ideas, the book was deficient in its structure. It had typos, misplaced sentences and paragraphs which got me lost sometimes.
September 6, 2023
“If it was so, it might be, and if it were so, it would be, but since it isn’t, it ain’t."
May 27, 2015
This is clearly an excellent historical piece with an impact on modern society that is difficult to measure. It remains accessible and interesting. Of course it is often a bit overwrought as Boole is introducing a subject which now seems so much second nature. I really enjoy reading the source materials of major innovators like this and especially when their subject matter lends itself (or nearly) to layman readers.
The free kindle version I had did have textual defects due to scanning which often made the formulas hard to decipher. If I were to do this over I would either get a professionally produced kindle version or get a paper copy.
The free kindle version I had did have textual defects due to scanning which often made the formulas hard to decipher. If I were to do this over I would either get a professionally produced kindle version or get a paper copy.
February 9, 2015
The description of binary logic as a limit of probabilities where events either certainly happened or certainly didn't is clear. The algebra is muddy in places, with sometimes arbitrary meanings attached to terms. Boole is obviously very annoyed by Spinoza and spends a good long section on showing him to be wrong.
September 16, 2012
A must for anyone with an interest in epistemology or logic. I'm just glad I finally got through it!
July 16, 2015
it was great. I now have a metaphysics built upon logic and reason. :)
Displaying 1 - 12 of 12 reviews