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Selected Logic Papers
For more than two generations, W. V. Quine has contributed fundamentally to the substance, the pedagogy, and the philosophy of mathematical logic. Selected Logic Papers, long out of print and now reissued with eight additional essays, includes much of the author's important work on mathematical logic and the philosophy of mathematics from the past sixty years.
- GenresPhilosophyNonfiction
250 pages, Hardcover
First published June 12, 1966
31 people want to read
About the author
Willard Van Orman Quine
107 books230 followers"Willard Van Orman Quine (June 25, 1908 Akron, Ohio – December 25, 2000) (known to intimates as "Van"), was an American analytic philosopher and logician. From 1930 until his death 70 years later, Quine was affiliated in some way with Harvard University, first as a student, then as a professor of philosophy and a teacher of mathematics, and finally as an emeritus elder statesman who published or revised seven books in retirement. He filled the Edgar Pierce Chair of Philosophy at Harvard, 1956-78. Quine falls squarely into the analytic philosophy tradition while also being the main proponent of the view that philosophy is not conceptual analysis. His major writings include "Two Dogmas of Empiricism", which attacked the distinction between analytic and synthetic propositions and advocated a form of semantic holism, and Word and Object which further developed these positions and introduced the notorious indeterminacy of translation thesis." - http://en.wikipedia.org/wiki/Willard_...
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October 16, 2024
A SERIES OF RELATIVELY “EARLY” ESSAYS BY THE FAMED LOGICIAN
Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University.
He wrote in the Preface to this 1965 book, “This volume assembles twenty-three of my papers on mathematical logic, 1934-1960… All are technical. Still, apart from paper X, the collection is self-contained: points presupposed in one paper are covered in others. The papers were chosen with a view less to chronology than to present interest and utility. Ones whose substance has gone into my books were omitted.”
In the first paper, he says, “The principle of truth-functionality concerns only the constructing of statements from statements; whereas relationships such as implication or equivalence or rhyming are properly ascribed rather by attaching verbs to NAMES of statements. It is regrettable that Frege’s own scrupulous observance of this distinction between an expression and its name, between use and mention, was so little heeded by Whitehead, Russell, and their critics.” (Pg. 17)
He begins essay VII by explaining, “All notions of mathematical logic, as measured, e.g., by Principia Mathematica, can be constructed from a basis which embraces variables and just two further primitives: the familiar notions of inclusion and abstraction… A system of logic based on these primitives will be presented in this paper. The system involves the familiar theory of class types, which, for metamathematical convenience, will be recorded in the system by use of distinctive styles of variables…” (Pg. 100)
He comments on Frege’s proposed solution of “Russell’s paradox”: “It is not to Frege’s discredit that the explicitly speculative appendix now under discussion, written against time in a crisis, should turn out to possess less scientific value than biographical interest. Over the past half century the piece has perhaps had dozens of sympathetic readers who, after a certain amount of tinkering, have dismissed it as the wrong guess of a man in a hurry. One such reader was probably Frege himself, sometime in the ensuing twenty-two years of his life. Another, presumably, was Russell. We must remember that Russell’s initial favorable reaction… was a hurried conjecture indeed; five years later we have, in significant contrast, his theory of types. In any event, what Russell actually described in that quoted note was not Frege’s full suggestion, but only its broadest feature… This feature, though Russell later turned his back on it, is a good one…” (Pg. 153)
He begins essay XXIV with the explanation, “Gödel’s epoch-making theorem of 1931 is that there can be no complete proof procedure for elementary number theory. One constraint on what qualify as proof procedures is that they be specified by appeal only to sameness and difference of strings of signs, using first-order logic---hence without appeal to what the strings mean. PROSYNTAX is my word for that formal apparatus. The further constraint is that there be an EFFECTIVE or mechanical test of whether a purported proof of a formula is indeed a proof of it. Few of us would have been surprised to learn that there is no algorithm---no effective criterion, no outright test---for truth in elementary number theory. Such a test would make short work of unsolved problems such as Goldbach’s conjecture and Fermat’s Last Theorem; too good to be true. On the other hand Gödel’s theorem came as a shock, for we supposed that truth in mathematics CONSISTED in demonstrability.” (Pg. 236)
He acknowledges, “Granted that there are sets unspecifiable in our language, maybe they don’t matter to the validity of logical schemata. Maybe when a logical schema is satisfied by all the sets specifiable in OUR rich language, it is satisfied by all the other sets as well. How rich would our language have to be! The question can be answered in two words: not very. It has only to be rich enough for elementary number theory. I speak of expression, not proof… So I settle happily for the immanent definition of logical truth.” (Pg. 246-247)
He begins essay XXVI with the statement, “Modern logic---alias symbolic, alias mathematical---surpasses medieval logic somewhat as modern physics surpasses medieval conceptions of nature. Unlike physics, however, logic scarcely stirred from its medieval torpor until the nineteenth century. George Boole… is commonly singled out as the awakener, and this is what his name means to many of us today. Algebriasts and computer engineers know his name as the stem of an adjective, for Boolean algebra has figured in their work. It stems from Boole’s logic.” (Pg. 251)
The essays contained herein are indeed “technical”; but they will be of great interest to those concerning with the “technical” details of Quine and mathematical logic.
Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University.
He wrote in the Preface to this 1965 book, “This volume assembles twenty-three of my papers on mathematical logic, 1934-1960… All are technical. Still, apart from paper X, the collection is self-contained: points presupposed in one paper are covered in others. The papers were chosen with a view less to chronology than to present interest and utility. Ones whose substance has gone into my books were omitted.”
In the first paper, he says, “The principle of truth-functionality concerns only the constructing of statements from statements; whereas relationships such as implication or equivalence or rhyming are properly ascribed rather by attaching verbs to NAMES of statements. It is regrettable that Frege’s own scrupulous observance of this distinction between an expression and its name, between use and mention, was so little heeded by Whitehead, Russell, and their critics.” (Pg. 17)
He begins essay VII by explaining, “All notions of mathematical logic, as measured, e.g., by Principia Mathematica, can be constructed from a basis which embraces variables and just two further primitives: the familiar notions of inclusion and abstraction… A system of logic based on these primitives will be presented in this paper. The system involves the familiar theory of class types, which, for metamathematical convenience, will be recorded in the system by use of distinctive styles of variables…” (Pg. 100)
He comments on Frege’s proposed solution of “Russell’s paradox”: “It is not to Frege’s discredit that the explicitly speculative appendix now under discussion, written against time in a crisis, should turn out to possess less scientific value than biographical interest. Over the past half century the piece has perhaps had dozens of sympathetic readers who, after a certain amount of tinkering, have dismissed it as the wrong guess of a man in a hurry. One such reader was probably Frege himself, sometime in the ensuing twenty-two years of his life. Another, presumably, was Russell. We must remember that Russell’s initial favorable reaction… was a hurried conjecture indeed; five years later we have, in significant contrast, his theory of types. In any event, what Russell actually described in that quoted note was not Frege’s full suggestion, but only its broadest feature… This feature, though Russell later turned his back on it, is a good one…” (Pg. 153)
He begins essay XXIV with the explanation, “Gödel’s epoch-making theorem of 1931 is that there can be no complete proof procedure for elementary number theory. One constraint on what qualify as proof procedures is that they be specified by appeal only to sameness and difference of strings of signs, using first-order logic---hence without appeal to what the strings mean. PROSYNTAX is my word for that formal apparatus. The further constraint is that there be an EFFECTIVE or mechanical test of whether a purported proof of a formula is indeed a proof of it. Few of us would have been surprised to learn that there is no algorithm---no effective criterion, no outright test---for truth in elementary number theory. Such a test would make short work of unsolved problems such as Goldbach’s conjecture and Fermat’s Last Theorem; too good to be true. On the other hand Gödel’s theorem came as a shock, for we supposed that truth in mathematics CONSISTED in demonstrability.” (Pg. 236)
He acknowledges, “Granted that there are sets unspecifiable in our language, maybe they don’t matter to the validity of logical schemata. Maybe when a logical schema is satisfied by all the sets specifiable in OUR rich language, it is satisfied by all the other sets as well. How rich would our language have to be! The question can be answered in two words: not very. It has only to be rich enough for elementary number theory. I speak of expression, not proof… So I settle happily for the immanent definition of logical truth.” (Pg. 246-247)
He begins essay XXVI with the statement, “Modern logic---alias symbolic, alias mathematical---surpasses medieval logic somewhat as modern physics surpasses medieval conceptions of nature. Unlike physics, however, logic scarcely stirred from its medieval torpor until the nineteenth century. George Boole… is commonly singled out as the awakener, and this is what his name means to many of us today. Algebriasts and computer engineers know his name as the stem of an adjective, for Boolean algebra has figured in their work. It stems from Boole’s logic.” (Pg. 251)
The essays contained herein are indeed “technical”; but they will be of great interest to those concerning with the “technical” details of Quine and mathematical logic.
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