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.

# The Mathematical Analysis of Logic

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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4out of 5Roberto 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!

4out of 5Marts (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...

5out of 5Vladivostok–“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

4out of 5Yuki–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.

4out of 5William 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.

5out of 5Hakeem 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.

4out of 5Dwight–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.

5out of 5Mark–4out of 5Meremi–4out of 5AwaisAlvi–5out of 5Octipi–4out of 5Rajeeva Jha–4out of 5OTIS–5out of 5Viktor–4out of 5Douglas–5out of 5Marcel Philippe–5out of 5Robert–4out of 5Vipin–5out of 5Eashwari–5out of 5Sheikh Tajamul–4out of 5Asim Raza–4out of 5Liz Molleur–5out of 5Tom–4out of 5Fabrizio Tabasso–4out of 5Seraph_v3–5out of 5Ferruccio Alessandria–5out of 5Karin–4out of 5Genevieve Morgan–4out of 5Manuel–5out of 5Amr Farid–