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The Mathematical Analysis of Logic

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George Boole (1815-1864) is renowned as the first logician to apply algebraic methods to logic successfully. His Mathematical Analysis of Logic, first published in 1847, was the ground-breaking work that laid the foundations for what is known today as Boolean algebra and the propositional calculus. Written in response to the altercation between Sr. William Hamilton and Aug George Boole (1815-1864) is renowned as the first logician to apply algebraic methods to logic successfully. His Mathematical Analysis of Logic, first published in 1847, was the ground-breaking work that laid the foundations for what is known today as Boolean algebra and the propositional calculus. Written in response to the altercation between Sr. William Hamilton and Augustus de Morgan over the quantification of the predicate within syllogistic theory, its remarkable innovations led other logicians, among them William Stanley Jevons, John Venn, Charles Sanders Peirce, and Ernst Schroder, to refine and develop Boole's system. In turn, their efforts were incorporated by Alfred North Whitehead and Bertrand Russell into the monumental system of Principia Mathematica. In short, modern symbolic logic was founded in the pages of this book.


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George Boole (1815-1864) is renowned as the first logician to apply algebraic methods to logic successfully. His Mathematical Analysis of Logic, first published in 1847, was the ground-breaking work that laid the foundations for what is known today as Boolean algebra and the propositional calculus. Written in response to the altercation between Sr. William Hamilton and Aug George Boole (1815-1864) is renowned as the first logician to apply algebraic methods to logic successfully. His Mathematical Analysis of Logic, first published in 1847, was the ground-breaking work that laid the foundations for what is known today as Boolean algebra and the propositional calculus. Written in response to the altercation between Sr. William Hamilton and Augustus de Morgan over the quantification of the predicate within syllogistic theory, its remarkable innovations led other logicians, among them William Stanley Jevons, John Venn, Charles Sanders Peirce, and Ernst Schroder, to refine and develop Boole's system. In turn, their efforts were incorporated by Alfred North Whitehead and Bertrand Russell into the monumental system of Principia Mathematica. In short, modern symbolic logic was founded in the pages of this book.

30 review for The Mathematical Analysis of Logic

  1. 4 out of 5

    Roberto Rigolin F Lopes

    We are in 1847, Boole is standing in front of authorities to bravely defend that logic is a branch of mathematics. Listen to the great man shouting: "Logic is the mathematics of the human intellect!". We may have goosebumps reading his prediction that "with the advance of knowledge of all true sciences, an even-increasing harmony will be found to prevail among its separated branches". Even more striking, he states that 1 is the Universe (with capital “U”) and goes about laying the foundations fo We are in 1847, Boole is standing in front of authorities to bravely defend that logic is a branch of mathematics. Listen to the great man shouting: "Logic is the mathematics of the human intellect!". We may have goosebumps reading his prediction that "with the advance of knowledge of all true sciences, an even-increasing harmony will be found to prevail among its separated branches". Even more striking, he states that 1 is the Universe (with capital “U”) and goes about laying the foundations for propositional calculus. He was indeed creating a universe of zeros and ones. This is like the big bang of the digital universe!

  2. 4 out of 5

    Marts (Thinker)

    published first as a pamphlet in 1847, this is Boole's algebraic approach to Aristotelian logic... published first as a pamphlet in 1847, this is Boole's algebraic approach to Aristotelian logic...

  3. 5 out of 5

    Vladivostok

    “That which renders Logic possible, is the existence in our minds of general notions, -- our ability to conceive of abstractions, classes, and to designate their individual members by a common name. The theory of Logic is thus intimately connected with that of Language.” Statements of logic, regardless of their complexity, can be described by a system of mathematical formalisms and subsequently solved via Boolean algebra. Syllogisms, hypothetical propositions, elective equations, and every other “That which renders Logic possible, is the existence in our minds of general notions, -- our ability to conceive of abstractions, classes, and to designate their individual members by a common name. The theory of Logic is thus intimately connected with that of Language.” Statements of logic, regardless of their complexity, can be described by a system of mathematical formalisms and subsequently solved via Boolean algebra. Syllogisms, hypothetical propositions, elective equations, and every other form of Aristotelian arrangement are addressed. Boole’s writing makes it a more difficult read than it probably needs to be, but he makes up for it with some tremendous insights regarding the role of logic in philosophy. “I desire here to express my conviction, that with the advance of our knowledge of all true science, an ever-increasing harmony will be found to prevail among its separate branches. The view which leads to the rejection of one, ought, if consistent, to lead to the rejection of others. And indeed many of the authorities which have been quoted against the study of Mathematics, are even more explicit in their condemnation of Logic. ‘Natural science,’ says the Chian Aristo, ‘is above us, Logical science does not concern us.’ When such conclusions are founded (as they often are) upon a deep conviction of the preeminent value and importance of the study of Morals, we admit the premises, but must demur to the inference. For it has been well said by an ancient writer, that it is the ‘characteristic of the liberal sciences, not that they conduct us to Virtue, but that they prepare us for Virtue’; and Melancthon's sentiment, ‘abeunt studia in mores,’ has passed into a proverb. Moreover, there is a common ground upon which all sincere votaries of truth may meet, exchanging with each other the language of Flamsteed's appeal to Newton, ‘The works of the Eternal Providence will be better understood through your labors and mine.’” 3.45/5.0

  4. 4 out of 5

    Yuki

    3.8 stars I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new appli 3.8 stars I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage. A few years ago, when I first heard of Boolean algebra, I was immediately fascinated by it. Logic and algebra, though certainly related and can be successfully expresses by the language of each field, the global theory is nonexistent. However, in this book, Boole has made it unnecessarily long and a not - so - easy read, and I'd prefer books that are straight to the point. Also, one detail that I particularly dislike is the use of adverbs of certainty in a scientific paper. It is quite a pet peeve of mine. Despite the minor mistakes, to see the remarkably charming relationship of mathematics and logic expressed into printed words is such a pleasure, so, a rating near to 4 stars.

  5. 4 out of 5

    William Schram

    A historical scanning of a book on Logic. I have no complaints on the text, since I know it is a scanned reproduction of a previous work. It's pretty well explained, and it seems to be a bare bones introduction to Mathematical Logic. It shows the basis of the signs, and introduces a method to manipulate them. There isn't really much else to say, it doesn't have any workable problems, it only shows how to do the basic operations. This sort of thing didn't really surprise me, since it is pretty sh A historical scanning of a book on Logic. I have no complaints on the text, since I know it is a scanned reproduction of a previous work. It's pretty well explained, and it seems to be a bare bones introduction to Mathematical Logic. It shows the basis of the signs, and introduces a method to manipulate them. There isn't really much else to say, it doesn't have any workable problems, it only shows how to do the basic operations. This sort of thing didn't really surprise me, since it is pretty short.

  6. 5 out of 5

    Hakeem Ali

    Excellent explanation of the relationship between logic and mathematics I thought this book provided a brief but thorough explanation of the connection between the usage of logic within the thought process and its use in mathematical reasoning.

  7. 4 out of 5

    Dwight

    While I can't claim that my mind easily follows all of the math, I don't see why this isn't on the program at St. John's. I would really like to go through this with a few others and work through the tougher bits. While I can't claim that my mind easily follows all of the math, I don't see why this isn't on the program at St. John's. I would really like to go through this with a few others and work through the tougher bits.

  8. 5 out of 5

    Mark

  9. 4 out of 5

    Meremi

  10. 4 out of 5

    AwaisAlvi

  11. 5 out of 5

    Octipi

  12. 4 out of 5

    Rajeeva Jha

  13. 4 out of 5

    OTIS

  14. 5 out of 5

    Viktor

  15. 4 out of 5

    Douglas

  16. 5 out of 5

    Marcel Philippe

  17. 5 out of 5

    Robert

  18. 4 out of 5

    Vipin

  19. 5 out of 5

    Eashwari

  20. 5 out of 5

    Sheikh Tajamul

  21. 4 out of 5

    Asim Raza

  22. 4 out of 5

    Liz Molleur

  23. 5 out of 5

    Tom

  24. 4 out of 5

    Fabrizio Tabasso

  25. 4 out of 5

    Seraph_v3

  26. 5 out of 5

    Ferruccio Alessandria

  27. 5 out of 5

    Karin

  28. 4 out of 5

    Genevieve Morgan

  29. 4 out of 5

    Manuel

  30. 5 out of 5

    Amr Farid

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