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Philosophy of Logic
With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar―but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.
122 pages, Paperback
First published January 1, 1970
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About the author
Willard Van Orman Quine
105 books220 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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Displaying 1 - 12 of 12 reviews
October 16, 2024
AN EXCELLENT STATEMENT OF MODERN LOGICAL THEORY
Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University, and wrote many books such as 'Word and Object,' 'The Web of Belief,' 'From a Logical Point of View,' 'Ontological Relativity & Other Essays,' 'Pursuit of Truth,' 'Theories and Things,' 'Methods of Logic,' 'Quiddities: An Intermittently Philosophical Dictionary,' etc.
[NOTE: this review pertains to the 1970 first edition.]
He wrote in the Preface, “We shall be occupied in this book with the philosophy of logic … Precedent could be cited for applying the word collectively to two dissimilar studies: deductive and inductive logic. The philosophy of inductive logic, however, would be in no way distinguishable from philosophy’s main stem, the theory of knowledge. What arrogates a distinctive bit of philosophy to itself is deductive logic… I would say that logic is the systematic study of logical truths… I would say that at sentence if logically true if all sentences with its grammatical structure are true… Since I see logic thus as the resultant of two components, truth and grammar, I shall treat truth and grammar prominently. But I shall argue against the doctrine that logical truths are true because of grammar, or because of language.”
At the end of the first chapter, he states, “When we call a sentence eternal… we are calling it eternal relative only to a particular language at a particular time. Because of this awkward relativity there remains a theoretical advantage in assigning truth values to tokens, since in that quarter there is normally no question of choosing among languages and language stages; we are concerned simply with the language of the speaker or writer as of the time of speaking or writing. But in practice it can be convenient to talk simply of truth values of eternal sentences, tacitly understanding these as relativized to our present-day English language habits.” (Pg. 14)
He ends the fourth chapter: “a logical truth is a sentence that cannot be turned false by substituting the lexicon, even under supplementation of lexical resources… The definition is still not transcendent… The suggestion does nevertheless offer a welcome gain in generality, and, in addition, a notable connection between logic and grammar. What sentences of a language to count as logically true is determined, on this theory, when we have settled two things about the language: its grammar and its truth predicate. Logic is, in the jargon of mechanics, the resultant of two components: grammar and truth.” (Pg. 60)
In the last chapter, he says, “Mathematics and logic are supported by observation only in the indirect way that those aspects of natural science are supported by observation; namely, as participating in an organized whole which, way up at its empirical edges, squares with observation. I am concerned to urge the unempirical character of theoretical physics; it is rather their kinship that I am urging, and a doctrine of gradualism.” (Pg. 60)
This is an excellent logic text, and also gives insight into Quine’s own ideas about logical theory
Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University, and wrote many books such as 'Word and Object,' 'The Web of Belief,' 'From a Logical Point of View,' 'Ontological Relativity & Other Essays,' 'Pursuit of Truth,' 'Theories and Things,' 'Methods of Logic,' 'Quiddities: An Intermittently Philosophical Dictionary,' etc.
[NOTE: this review pertains to the 1970 first edition.]
He wrote in the Preface, “We shall be occupied in this book with the philosophy of logic … Precedent could be cited for applying the word collectively to two dissimilar studies: deductive and inductive logic. The philosophy of inductive logic, however, would be in no way distinguishable from philosophy’s main stem, the theory of knowledge. What arrogates a distinctive bit of philosophy to itself is deductive logic… I would say that logic is the systematic study of logical truths… I would say that at sentence if logically true if all sentences with its grammatical structure are true… Since I see logic thus as the resultant of two components, truth and grammar, I shall treat truth and grammar prominently. But I shall argue against the doctrine that logical truths are true because of grammar, or because of language.”
At the end of the first chapter, he states, “When we call a sentence eternal… we are calling it eternal relative only to a particular language at a particular time. Because of this awkward relativity there remains a theoretical advantage in assigning truth values to tokens, since in that quarter there is normally no question of choosing among languages and language stages; we are concerned simply with the language of the speaker or writer as of the time of speaking or writing. But in practice it can be convenient to talk simply of truth values of eternal sentences, tacitly understanding these as relativized to our present-day English language habits.” (Pg. 14)
He ends the fourth chapter: “a logical truth is a sentence that cannot be turned false by substituting the lexicon, even under supplementation of lexical resources… The definition is still not transcendent… The suggestion does nevertheless offer a welcome gain in generality, and, in addition, a notable connection between logic and grammar. What sentences of a language to count as logically true is determined, on this theory, when we have settled two things about the language: its grammar and its truth predicate. Logic is, in the jargon of mechanics, the resultant of two components: grammar and truth.” (Pg. 60)
In the last chapter, he says, “Mathematics and logic are supported by observation only in the indirect way that those aspects of natural science are supported by observation; namely, as participating in an organized whole which, way up at its empirical edges, squares with observation. I am concerned to urge the unempirical character of theoretical physics; it is rather their kinship that I am urging, and a doctrine of gradualism.” (Pg. 60)
This is an excellent logic text, and also gives insight into Quine’s own ideas about logical theory
July 24, 2024
Appropriately bitter medicine for the affliction of feeling intelligent.
Notes
But by what criterion may strings of phonemes be counted meaningful, short of whole sentences or perhaps longer units? Or, if the morpheme is to be called meaningful on the ground of its merely contributing to the meaning of a sentence, why cannot the sanle be said of each mere phoneme? The notion of meaning is in too bad shape to afford a definition of morpheme
Constructions
Predication - joining one-place predicate of intransitive verb with a variable: ‘x walks’ to form a sentence that is atomic (contains no subordinate sentence), open (true for some variables, false for others, of itself neither true nor false).
Predication of two-place predicate: x loves y - another atomic open sentence
Negation not: ~p
Conjunction and: p.q
Existential quantification on an open sentence and a variable: Ex(x walks) - there is something that walks
Alternation (p or q) superfluous in theory, can be replaced by ~(~p.~q)
Similarly conditional (if p, q) superfluous: ~(p.~q)
Biconditional (if and only if p, q) reduces to ‘if p, q. If q, p’ and thus ‘~(p.~q).~(q.~p)’ notated as p<->q
Universal quantification: \:/x Fx (open sentence Fx is satisfied by every object x)
Distinction between particle (parts of specific construction) and lexicon (words classed in categories): Japanese syllabary for particles but preserves Chinese characters for lexicon. So ~,.,E are all particles
In ~(x walks), why is x, walks lexical, but ~ a particle that is combined by construction? Indefiniteness and not infinitude is the reason predicates are lexical and not particles.
Logical grammar, like modern physics, is best served by treating time as a dimension coordinate with the spatial dimensions; treating date, in other words, as just another determinable on a par with position. A body is thus visualized eternally as a four-dimensional whole, extending up and down, north and south, east and west, hence and ago. A shrinking body is seen as tapered toward the hence; a growing body is tapered toward the ago
if a physical object happens to be fairly firm and coherent internally, but coheres only rather slightly and irregularly with its spatio-temporal surroundings, we are apt to call it a body. Other physical objects may be spoken of as processes, happenings, events.
In particular the logic of truth functions chases truth up through two constructions, negation and conjunction, determining the truth values of the compounds from those of the constituents. Implicitly all truth functions get this treatment, thanks to iteration.
Logical implication: The crucial restriction here is that no supporting supplementary assumption or information be invoked as to the truth of additional sentences. Logical implication rests wholly on how the truth functions, quantifiers, and variables stack up. It rests wholly on what we may call, in a word, the logical structure of the two sentences
Notes
But by what criterion may strings of phonemes be counted meaningful, short of whole sentences or perhaps longer units? Or, if the morpheme is to be called meaningful on the ground of its merely contributing to the meaning of a sentence, why cannot the sanle be said of each mere phoneme? The notion of meaning is in too bad shape to afford a definition of morpheme
Constructions
Predication - joining one-place predicate of intransitive verb with a variable: ‘x walks’ to form a sentence that is atomic (contains no subordinate sentence), open (true for some variables, false for others, of itself neither true nor false).
Predication of two-place predicate: x loves y - another atomic open sentence
Negation not: ~p
Conjunction and: p.q
Existential quantification on an open sentence and a variable: Ex(x walks) - there is something that walks
Alternation (p or q) superfluous in theory, can be replaced by ~(~p.~q)
Similarly conditional (if p, q) superfluous: ~(p.~q)
Biconditional (if and only if p, q) reduces to ‘if p, q. If q, p’ and thus ‘~(p.~q).~(q.~p)’ notated as p<->q
Universal quantification: \:/x Fx (open sentence Fx is satisfied by every object x)
Distinction between particle (parts of specific construction) and lexicon (words classed in categories): Japanese syllabary for particles but preserves Chinese characters for lexicon. So ~,.,E are all particles
In ~(x walks), why is x, walks lexical, but ~ a particle that is combined by construction? Indefiniteness and not infinitude is the reason predicates are lexical and not particles.
Logical grammar, like modern physics, is best served by treating time as a dimension coordinate with the spatial dimensions; treating date, in other words, as just another determinable on a par with position. A body is thus visualized eternally as a four-dimensional whole, extending up and down, north and south, east and west, hence and ago. A shrinking body is seen as tapered toward the hence; a growing body is tapered toward the ago
if a physical object happens to be fairly firm and coherent internally, but coheres only rather slightly and irregularly with its spatio-temporal surroundings, we are apt to call it a body. Other physical objects may be spoken of as processes, happenings, events.
In particular the logic of truth functions chases truth up through two constructions, negation and conjunction, determining the truth values of the compounds from those of the constituents. Implicitly all truth functions get this treatment, thanks to iteration.
Logical implication: The crucial restriction here is that no supporting supplementary assumption or information be invoked as to the truth of additional sentences. Logical implication rests wholly on how the truth functions, quantifiers, and variables stack up. It rests wholly on what we may call, in a word, the logical structure of the two sentences
June 7, 2024
Coming to this after having read Quine's more "philosophical" essays shows that Quine was first and foremost a logician; nearly every distinctive philosophical view he had arises from this or that issue in logic. He writes with exacting precision and economy, as if an extra word here or there would lose the war. But if you take the time to work through what he's saying, and are really, really into logic, it's worth the effort.
February 22, 2021
Quine is clearly incredibly intelligent, but that doesn't mean his readers will be. All 100 pages of this book were a battle trying to parse out long strings of logical symbols embedded completely unformatted in the middle of paragraphs.
Some interesting ideas in there, but so rough trying to get any value out of this not being a genius myself...
Some interesting ideas in there, but so rough trying to get any value out of this not being a genius myself...
January 26, 2023
Каждый раз поражаюсь силе мысли Куайна. Несмотря на то, что его взгляды часто рассматриваются как слишком ортодоксальные с современной точки зрения, почти вся современная философия логики отталкивается от его тезисов (соглашаясь с ними, или же модифицируя их).
Read
September 22, 2019I can't really blame Quine, but parts of this book are extremely difficult to understand, especially if you are not interested in the subject matter.
June 24, 2025
Modus Quinens
September 29, 2014
This is a very good introduction to logic. Quine deals with technical details, as well as the considerations that go into navigating these technicalities this way or that way. I picked at "The Logic Book" but was always confused over just why these connectives and those operations were considered to be THE elements of logic. Surely, you can "see" it, and rationalize it, but anything that claims the mantle of logic must be rigor itself; I don't want to hear some appeal to it's pleasing simplicity or striking character that decides it so.
Quine maps out the establishment of a logical language, showing various dead ends that might make the language trip over itself, as well as examples of various deviant logics that take different premises and move different directions. In doing so, he separates symbolic logic from the philosophy of logic, which is essential to understanding the whole package. Everything one might see in "The Logic Book" is the most neutral logical language that was produced by a intense, century long and highly technical debate.
Quine, though biased, does a very good job of showing how much is up the the air in this field, and the type of considerations that go into the construction of logical languages which otherwise seem monolithic and inscrutable.
Quine maps out the establishment of a logical language, showing various dead ends that might make the language trip over itself, as well as examples of various deviant logics that take different premises and move different directions. In doing so, he separates symbolic logic from the philosophy of logic, which is essential to understanding the whole package. Everything one might see in "The Logic Book" is the most neutral logical language that was produced by a intense, century long and highly technical debate.
Quine, though biased, does a very good job of showing how much is up the the air in this field, and the type of considerations that go into the construction of logical languages which otherwise seem monolithic and inscrutable.
December 16, 2018
For those passing through, this isn't an introduction to logic, that's for something like Jeffrey's Formal Logic: Its Scope and Limits. But you can still hold onto this, because once you understand the symbol manipulation, then philosophical issues, soundness and completeness of a system, interpretation, validity and logical truth all come into focus. This is Quine's own take on it. He'll bring up figures like Tarski and Godel to develop his ideas more so than to elaborate on theirs. The value of this is as a model example for approaching these questions, and his semantic ascent is interesting in itself.
February 27, 2008
Kind of dull, I didn't get the sense of vibrant engagement with the subject matter that Quine usually provides. Perhaps I've just been reading too much about logic these days.
July 11, 2019
Like a flash of light!
Displaying 1 - 12 of 12 reviews