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Notes by RBJ on

The Ways of Paradox

and other essays

by Willard Van Ormon Quine

PrefPreface
Group I"Semi-popular" Logic and the Foundations of Mathematics
Essay 1The Ways of Paradox (1961)
Essay 2On a Supposed Antinomy (1952)
Essay 3Foundations of Mathematics (1964)
Essay 4On the Application of Modern Logic (1960)
Group IIReminiscence of Carnap
Essay 5Homage to Rudolf Carnap (1970)
Group IIILogicophilosophical pieces aimed at linguists
Essay 6Logic as a Source of Syntactical Insights (1960)
Essay 7Vagaries of Definition (1972)
Essay 8Linguistics and Philosophy (1968)
Group IVlightly, of knowledge and necessary truth (radio talks)
Essay 9The Limits of Knowledge (1972)
Group VAnalyticity, modal logic, and propositional attitudes
Essay 10Necessary Truth (1963)
Essay 11Truth by Convention (1935)
Essay 12Carnap and Logical Truth (1954)
Essay 13Implicit Definition Sustained (1964)
Essay 14Mr. Strawson on Logical Theory (1953)
Group VIOntology
Essay 15Three Grades of Modal Involvement (1953)
Essay 16Reply to Professor Marcus (1962)
Essay 17Quantifiers and Propositional Attitudes (1955)
Essay 18A Logistical Approach to the Ontological Problem (1938)
Essay 19On Carnap's Views on Ontology
Essay 20Ontological Reduction and the World of Numbers (1964)
Essay 21On Mental Entities (1952)
Essay 22The Scope and Language of Science
Group VIIVariables
Essay 23Posits and Reality (1955)
Essay 24On Simple Theories of a Complex World (1960)
Essay 25On Multiplying Entities (1966-74)
Essay 26Ontological Remarks on the Propositional Calculus
Essay 27The Variable (1972)
Group VIIImore austerely logical
Essay 28Algebraic Logic and Predicate Functors
Essay 29Truth and Disquotation

Preface

Gives the breakdown into subject groups shown above.

Group 1 - "Semi-popular" Logic and the Foundations of Mathematics

Essay 1 - The Ways of Paradox (1961)

Explains the distinction between veridical (ones whose conclusion is true) and falsidical (ones whose conclusion is false) paradoxes (which can be explained away) and antinomies (which cannot be explained away, represent genuine demonstrable contradictions, and demand some change to the language or logic in which they are derived).

The paper begins in natural language but eventually proceeds to set theory and arithmetic. In the main the paradoxes or antinomies discussed, which include Zeno's (falsidical), Grelling's (falsidical), Berry's (antinomy), the liar (antinomy), Russell's (antinomy) and Cantor's (antinomy), are shown by Quine either to be veridical or falsidical paradoxes, or they are shown to be genuine antinomies, either in natural language or in some technical language (or both). In the latter case Quine indicates how the languages or their logic might be amended to eliminate the antinomy.

Quine presents no important difference in charater between the natural and more formal languages, not appearing to doubt that antinomies in natural languages can be repaired. The most clearly presented repair is that of the liar paradox and related semantic paradoxes by use of a heirarchy of languages at once, by means of suffixes on semantic attributes such as "true".

By contrast I would say that antinomies in natural languages cannot be fixed, that logical systems cannot be repaired peicemeal, and that the changes necessary to make a natural language into a coherent logical system are sufficiently radical, and must be adhered to with such rigidity that the result would no longer be a natural language.

Essay 2 - On a Supposed Antinomy (1952)

The supposed antinomy is about a prisoner sentenced to hang within a week, but to remain in ignorance of the date of his hanging until that day arrives. He deduces that his sentence cannot be carried out. Quine argues that this is a falsidical paradox.

Essay -

Group II - Reminiscence of Carnap

Group III - Logicophilosophical pieces aimed at linguists

Group IV - lightly, of knowledge and necessary truth (radio talks)

Group V - Analyticity, modal logic, and propositional attitudes

Essay 11 - Truth by Convention Notes

Group VI - Ontology

Essay 19 - On Carnap's Views on Ontology

Group VII - Variables

Group VIII - more austerely logical


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