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Methods of Logic
The Methods of Logic contaisn numerous texutal improvements. Chief among them are: a more complete justification of the deductive rules in section 28, completion of the Method. In the first eidtion these rules were indirectly justified; in the new edition the rules and restrictions are more intuitively and directly explained and justified. The discussion of theorems of Church and Godel has been rewritten and extended with a view to providing a fuller understanding of their nature. An added appendix proves Godel's theorem of the completeness of quantification theory and a related theorem of Lowenheim.
Although the book is a rigorous treatment of modern logic, its clarity of statement and quality of exposition make it indespensable to logical inquiry.
Although the book is a rigorous treatment of modern logic, its clarity of statement and quality of exposition make it indespensable to logical inquiry.
272 pages, Hardcover
Published January 1, 1961
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October 16, 2024
QUINE'S TEXT FOR A SEMESTER COURSE IN DEDUCTIVE LOGIC
Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University, and wrote many books.
He wrote in the Preface to the original (1950) edition, "This book undertakes both to convey a precise understanding of the formal concepts of modern logic and to develop convenient techniques of formal reasoning. Logic books exist which are strong in theory and rigorous and elegant in the manner of proofs, but the reader who would discover further proofs of his own has had painfully to develop his own method of discovery. In this book, though rigor has been preserved, the objective of inculcating technical facility has been allowed to prevail over that of elegance... This makes the book a new manual of logical method. But theory also comes in for a share... [this] book which develops modern logic from the ground up... About a sixth of the book is ... optional reading; the rest is intended as a text for a semester college course in deductive logic."
He wrote at the end of the Introduction, "it is indeed the case that the truths of mathematics treat ... of abstract nonlinguistic things, e.g., numbers and functions, whereas the truths of logic... have no such entities as specific subject matter. This is an important difference. Despite this difference, however, logic in its higher reaches is bound to bring us by natural stages into mathematics... which does have abstract entities of a special kind as subject matter.
"These entities are classes; and the logical theory of classes, or set theory, proves to be the basic discipline of pure mathematics... Before the end of the book we shall have ascended through four grades of logic in the narrower sense, and emerged into set theory; and here we shall see, as examples of the derivation of classical mathematics, how the concept of number and various related notions can be defined."
This second edition of Quine's book (which is now 75 years old, let us remember) would certainly not be used for many introductory classes today; but it is interesting and instructive to see how a "master" of modern logic approaches such a field.
Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University, and wrote many books.
He wrote in the Preface to the original (1950) edition, "This book undertakes both to convey a precise understanding of the formal concepts of modern logic and to develop convenient techniques of formal reasoning. Logic books exist which are strong in theory and rigorous and elegant in the manner of proofs, but the reader who would discover further proofs of his own has had painfully to develop his own method of discovery. In this book, though rigor has been preserved, the objective of inculcating technical facility has been allowed to prevail over that of elegance... This makes the book a new manual of logical method. But theory also comes in for a share... [this] book which develops modern logic from the ground up... About a sixth of the book is ... optional reading; the rest is intended as a text for a semester college course in deductive logic."
He wrote at the end of the Introduction, "it is indeed the case that the truths of mathematics treat ... of abstract nonlinguistic things, e.g., numbers and functions, whereas the truths of logic... have no such entities as specific subject matter. This is an important difference. Despite this difference, however, logic in its higher reaches is bound to bring us by natural stages into mathematics... which does have abstract entities of a special kind as subject matter.
"These entities are classes; and the logical theory of classes, or set theory, proves to be the basic discipline of pure mathematics... Before the end of the book we shall have ascended through four grades of logic in the narrower sense, and emerged into set theory; and here we shall see, as examples of the derivation of classical mathematics, how the concept of number and various related notions can be defined."
This second edition of Quine's book (which is now 75 years old, let us remember) would certainly not be used for many introductory classes today; but it is interesting and instructive to see how a "master" of modern logic approaches such a field.
Displaying 1 of 1 review