The Mathematical Analysis of Logic: Being An Essay Towards a Calculus of Deductive Reasoning

by George Boole

( 20 ) OF EXPRESSION AND INTERPRETATION. A Proposition iB a sentence which either affirms or denies, as, All men are mortal, No creature is independent. A Proposition has necessarily two terms, as men, mortal; the former of which, or the one spoken of, h culled the subject; the latter, or tha! which is affirmed or denied of the subject, the predicate. These are connected together by the copula w, or m not, or by some other modification of the substantive verb. The substantive verb is the only verb recognised in Logic; all others are resolvable by means of the verb to be and a participle or adjective, e. g. " The Romans conquered"; the word conquered U both copula and predicate, being equivalent to "were (copula) victorious" (predicate). A Proposition must either be affirmative or negative, and must be also either universal or particular. Thus we reckon in ail, four kinds of pure categorical Propositions. 1st. Universal-affirmative, usually represented by A, Ex. All Xs

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Genres: Mathematics, Philosophy, Science, Logic, Nonfiction, Computer Science, Classics

90 pages, Kindle Edition

First published January 1, 1847

Reviews

[Roberto Rigolin F Lopes · Rating 4 out of 5]

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!

[Vladivostok · Rating 3 out of 5]

“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

[Yuki · Rating 3 out of 5]

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.

[William Schram · Rating 4 out of 5]

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.

[Jovany Agathe · Rating 4 out of 5]

By classifying thought and codifying it using algebraic language, Boole invented a new kind of mathematics. A century later, boolean algebra would provide an ideal foundation for designing the electronic structure of computers, and for manipulating information within computers.

[for-much-deliberation ... · Rating 5 out of 5]

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

[Shayaan · Rating 5 out of 5]

A Piece of History

Whenever I told anyone I was reading Boole be they friends and family or my peers from computer science, I got a response of confused faces with a curt "Why?"

I read the book as one talks about an occasional tour of their favourite museum. As a computer science student whose entire academic life is based on Boole's work, I read him to pay homage to the great man while also getting an insight into the mind of the giants on whose shoulder I stand and get his findings first-hand, not through the boring old course books of mine.

I certainly succeeded and found it a delightful read. Got introduced to Aristo of Chios, Boole's belief in logic laws as being the laws of thought and how the brain worked, and accomplishing another aim of mine, a better understanding of deductive analysis.

Next on the list is Hume's work on inductive analysis. Hope you find Boole as fun to read as I did.

(P.S. I did not understand more than a word of the elective functions chapter)

[Hakeem Ali · Rating 5 out of 5]

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.

[Dwight · Rating 4 out of 5]

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.